Ismail Bensekrane

Pr Sergey Drakunov

Devadas Bhat

Tanushree Kane

Himani Garg

Piyush Jain

Sepal Daliwale

Vers une Stratégie de Planification Energétique pour la Conduite Autonome d'un Véhicule Routier Sur-actionnée THÈSE

Keywords: Energy Planning, Power consumption, Redundancy, Over-actuated, Autonomous driving Panification énergétique, Consommation d'énergie, Redondance, Sur-actionné, Conduite autonome

In this thesis, an energy planning for over-actuated unmanned road vehicles (URVs) with redundant steering configurations is proposed. In fact, indicators on the road profile geometry, the redundancy of actuation, the optimal velocity profile and the driving modes are identified for each segment of the URV's trajectory. Thus, a power consumption estimation model of an over-actuated autonomous driving vehicle is developed. Two methods for power consumption modeling are considered. The first method is based on an analytic model of power consumption, taking into account the degree of steerability, the degree of mobility and the degree of actuation redundancy. The second method used for power consumption modeling is based on data-learning qualitative method, namely: Adaptive Neuro Fuzzy Inference System (ANFIS). The latter has been considered in case of the presence of unknown dynamic parameters of the URV and uncertainties of interaction with the environment. Validation of the estimation of the power consumption has been applied on a real autonomous vehicle called RobuCar. Energy planning strategy has been built using two approaches, discrete and continuous. The discrete approach depends on the construction of an energy digraph with all feasible configurations taking into account kinematic and dynamic constraints based on a 3D grid map setup, according to the velocity, the arc-length,and the driving mode. In this weighted directed graph, the edges describe the consumed energy by the URV along a segment of a trajectory. An optimization algorithm is applied on the digraph to get a global optimal solution combining the driving mode, the power consumption and the velocity profile of the URV. The continuous approach is based on a multi-criteria optimization strategy using genetic algorithms (NSGA-II). Then a real road path is considered and modelled by using two smooth geometrical combinations: the first one uses lines, clothoids and arcs, and the second one uses lines and Pythagorean Hodograph (PH) curves. The energy planning strategy is then applied to the generated paths. Also, a directed graph is built to synthesis the optimal velocity profile that minimizes the overall energy consumption while accounting for all driving modes. Results are compared with those given by the dynamic programming method for global offline optimization.

iii This thesis is dedicated to my parents, Habib Bensekrane and Yamina Djaber, my wife, and my family for their love, endless support and encouragement. The CRIStAL research objectives affect the growth of fundamental, methodological, and technological research in the areas dealing with automatic control, computer engineering, and signal processing. The present work was designed under the guidance of Rochdi Merzouki, Professor at Polytech Lille -University of Lille. The research group MOCIS has vast experience with the combined design of systems, about modelling, structural analysis, control and diagnosis through the practice of unifying graphical tools. Fig. 1.1 explains the topological organization of this group. This integrated design can concentrate on the microscopic system, model representing an elementary robot as a physical system, or to the high-level macroscopic system, including other robots, environment, communication between robot to robot or robot to the environment. Such class of organizational architecture is planned with the idea of System of Systems (SoS). In this context, various research works have been realized over the last 10 years. In this work, we concentrate on energy planning for physical systems in transportation and robotics.

General Introduction

In the last decade, autonomous vehicles have been increasingly utilized in many sectors, including the industry and planetary research. These vehicles provide a reduction of emissions in big cities and allow to conduct autonomous operations in unfamiliar and confined spaces. These vehicles, due to their operational autonomy, facilitate the execution of repetitive or programmed tasks efficiently and safely. For the specifications of tasks repetition and environmental safety (human or material), the manufacturers are innovating the technology of unmanned road vehicles (URV)s, studied, redundant in actuation and ready to ensure the continuation of achievement of tasks in normal and imperfect situations. This redundancy of inputs has been already utilized for aircraft systems. Thus, in this thesis work, research on a class of over-actuated and over-instrumented URV has been designed. Notwithstanding the benefits of intelligent autonomous vehicles, energy dependence is one of the principal problems facing the manufacturers. This returned back the researchers to enhance the autonomous control and navigation of the URV in the function of the available driving energy efficiently. Many energy supply systems have been developed over time. Thermal engines are more efficient in energy autonomy, but emit a lot of CO 2 . Hybrid vehicles are a technology that succeeds thermal motorization and it is a blend of an electric motor and the engine using an alternator and a battery system for saving energy. Many manufacturers have utilized this technology that can be defined as an intermediate to a fully electric engine to reduce emissions of CO 2 in an urban environment ultimately.

Electric vehicles are the new age of motorized vehicles, where automotive man-ufacturers have actively invested because they are more sustainable and practice green energy. However, the warehouse of the electrical energy is done by the batteries, where their fabrication stays problematic in terms of respect of the environment.

One specification correlated to the battery design is that it needs a very long lifecycle, offering to make optimal management of the energy resources. Thus, the execution indicator of the batteries struggles about their optimal cycles for the charging and discharging. The best current battery technology is the lithium ion-based.

Power planning or energy management of electric vehicles is established to start analyzing from the last decade. Nowadays, energy autonomy of electric vehicles needs on-board power resources such as batteries. So, the operational execution of autonomous systems is based principally on the autonomy of the power supply. Many studies have been performed whose purpose is to increase the autonomy of onboard power systems so that it is sustainable in the time. These studies concentrate on the development of storage technologies; or of course, energy management and optimization while managing existing resources. Energetic systems that we address as part of this thesis define a class of mobile rolling and over-actuated vehicles, with redundancy in traction and steering actuation, which enables managing their mobility in various driving situations. In the literature, on-board energy optimization research has been conducted in terms of transportation kinematics, trajectory optimization, control/command optimization, and power management. For all these research activities, it is assumed that the power storage on-board is also optimal.

Optimal Energy Management (OEM) of autonomous systems combines between multiple methods of optimization implemented to the path planning, the trajectory planning, the tasks allocation, and the routing. The objective of the OEM is to find the optimal velocity profile and control/command that consumes the minimum of energy on an identified road profile. The OEM needs a set of information affecting the power consumption of vehicles, where its distribution requires the modeling of:

• Charging capability of the batteries,

• Kinematics and dynamics of the URVs,

• 3-D path or curvature profile,

• Velocity profile

The OEM is generally applied for the online driving of autonomous vehicles. therefore, it is essential to have a baseline of energy consumption along the traveled path. Thus, energy planning is a methodology allowing identifying an optimal distribution of the energy, those autonomous vehicles can use as a reference, to manage its driving modes and energy consumption automatically. This is the main contribution to this Ph.D. thesis.

Chapter 1. General Introduction

Thesis objective

The objective of this thesis is to propose an offline methodology for optimal distribution of energy in the case of autonomous and over-actuated vehicles, in the presence of normal or faulty situations. This is called energy planning, which defines an offline optimal allocation of the power before the vehicle travel, allowing then, the online management of the energy, in terms of optimal control distribution. Our objective from this thesis work is to extend the existing technique of effort-based "Control Allocation -CA" to the dual of flow and effortbased "Power Allocation -PA". The aim is to master the energy management in different driving modes. The energy planning will allow estimating the mobility and manoeuvrability required by the over-actuated URV to achieve its mission for a given trajectory and the driving in the normal and degraded situations.

Problem Statement

Let us consider the second order dynamic equation of an URV expressed in vehicle coordinated can be given as follows:

M (q)q + H( q, q) q + G(q) = τ (1.1) where, q is the generalized position vector which represents position or angle, q is a generalized velocity vector which represents linear or angular velocity of the URV, M (q) is the inertia matrix, H( q, q) is a matrix of centrifugal and Coriolis effects, G(q) is the gravitational matrix, and τ is the generalized vector of the external efforts.

Thus, the power consumption of the URV can be estimated as follows:

P = qT τ (1.2)
From equations 1.1 and 1.2, the power consumption can be written as follows: P = qT [ M (q)q + H( q, q) q + G(q)] = qT M (q)q + qT H( q, q) q + qT G(q) (1.

3)

The problem of energy planning can be stated as an optimization problem and given by its discrete form as follows:

min V i,k ,M i,m J = n i=1 Pi,k (t i , V i,k , A i,k , C i , M i,m ) × (∆t i ) (1.4)
1.5. Contribution 9 subject-to

t i < t max V min ≤ V i,k ≤ V max A min ≤ A i,k ≤ A max (1.4a)
Where, V i,k , A i,k represent respectively the k th velocity and the acceleration profiles, defined for the i th road segment. M i,m is the m th driving modes for the i th road segment and Pi,k is the k th consumed power by the URV for the i th road segment. The parameters t i and C i represent respectively the traveling time and the curvature of the i th road segment. m depends of the number of independent steering system and actuated wheels.

Upper and lower limits restrict the velocity and acceleration profiles of the centre of gravity.J denotes the evaluation function of energy consumption of the URV along n road segment.

In this thesis work, it is considered a generic class of URVs which are redundant in actuation (over-actuated URV), with independent traction wheels and independent steering systems. Such URV is a vehicle-like robot with 3 Degree of Freedom (DoF) and can have different steering configurations of driving modes, characterized by a degree of steerability δs and a degree of redundancy δ R , which are dependent, as shown in Fig. 1.2, where:

• The dual configuration (δs = 2) has two steering actuation for the front and rear wheels.

• The single configuration (δs = 1) has only one steering actuation for the front wheels.

• The skid configuration (δs = 0) has no steering actuation, where the vehicle orientation is obtained from the difference of the velocity, obtained from the traction wheels.

The active wheels (actuated) are filled with black , and the white colour represents the passive wheels (non actuated). The description of all the configurations of the URV is given in Table 1.1.

Contribution

In this thesis work, we proposed a methodology to support for energy planning.

The proposed methodology will allow the URVs to identify an optimal 10 Chapter 1. General Introduction Table 1.1: Parameters describing URV driving configurations for m = 6.

2, 2, 1 T S R N N     2 S   2, 1, 0 T S R N N     1 S   2, 0, 1 T S R N N      0 S   4, 2, 3 T S R N N     2 S   4, 1, 2 T S R N N     1 S   4, 0, 1 T S R N N     0 S  

Traction actuators Steering actuators Skid4

(δ s = 0, δ R = 1) 4 0 Single4 (δ s = 1, δ R = 2) 4 1 Dual4 (δ s = 2, δ R = 3) 4 2 Skid2 (δ s = 0, δ R = -1) 2 0 Single2 (δ s = 1, δ R = 0) 2 1 Dual2 (δ s = 2, δ R = 1)
2 2 couple of power allocation and driving modes along a defined trajectory. This energy planning is assumed to be executed offline before the URV starts operating. This methodology aim is to ensure the power availability to the URV before it begins realizing its mission (routing, path planning, task allocation, trajectory planning). This planning energy should respect the dynamic constraints (vehicle load, interaction with the ground): the kinematic constraints (driving modes of the vehicle) and the road geometry (curvature profile).

• The Power consumption estimation of an over-actuated URV is developed using two approaches:

-A qualitative approach based on the data-learning method.

-A quantitative approach based on the generalization of Newton-Euler formulation to multiple driving modes.

• Energy planning for over-actuated URVs is proposed using discrete and continuous methods. It determines the optimal velocity profile and the corresponding driving mode for every segment of the trajectory, considering into account the road curvature and the kinematic parameters of the URV.

• Simulations and Experimental results are applied on a real URV called Robucar, in presence with decentralized driving modes (m = 6).

Disseminated Results

The obtained results are disseminated through the following publications: Journals

Manuscript organization

The document is organized in the following six chapters:

• The second chapter presents a literature review in the area of power consumption modelling and the energy management of manned and unmanned vehicles. This chapter allows making a scientific positioning of the energy planning methodology, proposed in this work, relative to different approaches used in energy management methodology.

• The third chapter presents the power consumption modeling of an overactuated URV. The power consumption is estimated with quantitative and qualitative approaches. In the quantitative, the power consumption is formulated according to geometrical criteria, kinematics and dynamic parameters, and the different driving modes. In the qualitative approach, a learning data based method is discussed. The inputs of this model are the curvature of the road path, the velocity profile, and the acceleration of the URV. The qualitative based-approach is considered for taking into account the quantitative modeling uncertainties.

• The fourth chapter summarizes deals with the discrete based approach for energy planning. This approach is developed based on a discrete model and curvature filtering of the road path. An energy digraph is then constructed based on the path segmentation. The latter is utilized with different methods for graph search as dynamic programming, Dijkstra and A * . These algorithms provide a global optimal solution of a couple of the velocity profile and the driving mode in each segment of the filtered road path. Finally, the comparison of the performances of power consumption of a real URV, according to the travel time is discussed.

• In the fifth chapter, a continuous energy planning is proposed for an overactuated URV based on a multi-criteria optimization methodology utilizing the genetic algorithm (NSGA-II). The aim is to approximate the road path profile by a succession of continuous curves. A real road path of University of Lille campus is considered and modelled by utilizing two smooth geometrical combinations: the first one is lines, clothoids, and arcs, and the second one is lines and Pythagorean Hodograph (PH) curves. The energy planning methodology is then applied to the generated paths. In the proposed methodology, a target point is selected from the Pareto front in order to set-up the best velocity profile for each driving mode. Also, a directed graph is built to synthesis the optimal velocity profile, that minimizes the overall energy consumption while accounting for the driving modes.

• Finally, the sixth chapter summarizes the conclusions of the main contributions and the perspective of this work for the online case and its generalization to various autonomous systems.

Introduction

This chapter discusses with the literature review on power management for Unmanned Road Vehicles (URVs). These denote the targeted autonomous systems, analysed in this work. This state of the art is essential for the positioning of the scientific contributions produced in this PhD thesis work. First, the kinematic properties of the URVs are presented. This includes the definitions of: degree of freedom, degree of mobility, degree of steerability and degree of manoeuvrability, holonomy and omni-directional motions. These properties are helpful for autonomous road vehicle design. Knowing that the power consumption of the URVs is estimated based on the kinematics of the vehicle and the dynamic of the interaction with the Chapter 2. Power Management of Autonomous Road Vehicles ground. More the vehicle has an actuation, more it consumes power. Therefore, having multiple actuators allow to make a tolerant control and maintain the autonomous navigation of the URV. Thus, the energy planning for URVs is an optimization problem, where the objective is to identify the best driving configuration with appropriate kinematics, offering less power consumption.

Kinematic Properties of Unmanned Road Vehicles (URVs)

URVs are rapidly expanding in the automotive industry. Various research works are developed in this area to overcome the problems of modelling and control of URVs. Most of the URVs are generally redundant in actuation and sensors. This has an advantage to facilitate the monitoring and avoid the blocking situations in case of presence of faults. Over-actuated URVs can have many driving configurations according to their kinematic properties. Five properties of vehicle like-robots are defined, according to their kinematics, namely: the degree of mobility, the degree of steerability, the degree of manoeuvrability, the holonomy and the omnidirectionality [Campion 1996], [START_REF] Siegwart | [END_REF]]. The mobility of the URVs is not directly dependent on the number of wheels but on the types of wheels: conventional or omnidirectional, steerable or fixed. The frame of a URV can be equipped with these four types of wheels, each giving rise to a set of generalized coordinates.

The classification of the different kinds of wheels is detailed below [Campion 1996]:

• Fixed Standard Wheel: Such wheel is also named conventional or nonsteerable wheels. Its orientation angle is not varying and so, it has no steering rotation axis (Fig. 2.1):

Q: is a fixed point in the chassis and is defined with the polar coordinate (l, α) in the frame P, i, j as follows: l = ---→ P Q , α = ( i, --→ P Q) S is the center of the wheel. β is the angle between --→ P Q and the normal oriented to the plane of the wheel. d is the norm of -→ QS projection on the horizontal plan. h is the norm of -→ QS projection on a vertical axis. φ is the rotation angle of the wheel.

• Steered Standard Wheel: Steerable wheel means that its orientation angle is modifying and its steering rotation axis is defined by two points: the centre of the wheel and the ground contact. In this type of wheel, the steering system is actuated (Fig. 2.2).

• Castor Wheel: Castor wheel is also steerable, but its steering rotation axis does not cross through the ground contact point. Furthermore, the steering system is not driven by an actuator, where the motion is free (Fig. 2.3).

P i j Q h i S     l Fixed Orientation Figure 2.1: Configuration of Fixed Standard Wheel P i j Q h i S     l Commanded Orientation
• Swedish Wheel: Swedish wheel is composed of one established standard wheel and a set of small rollers connected to its circumference. The axis of the small rollers are not parallel to those of the established standard wheel, and their orientation angles are typically about 45 degrees or 90 degrees. This type of wheel do not steer rotation axis, but it can move omni-directionally (Fig. 2.4). γ is the angle between the plane of the omni-directional wheel and the perpendicular to the direction of free evolution.

Degree of freedom

The degrees of freedom (DoF) of the URV can be represented as the whole of the independent parameters needed to define its pose in the considered workspace. The most common workspace is a plane in which the URV can go with two translation motions (longitudinal and lateral) along two principal axes; and one rotation motion (yaw) about the axis perpendicular to the plane. Therefore, total DoF is:

DoF = 3 (2.1)

Degree of mobility

The degree of mobility (DoM) of the URV is a sum of the number of DoF that it can achieve through rotation of the wheels without steering [START_REF] Siegwart | [END_REF]]. It can be defined by:

DoM = 3 -rank [C] (2.2) P i j Q h i S     i   2   l Fixed Orientation Figure 2.4: Configuration of Swedish Wheel
The range of DoM is compromised between 0 3 , where C is the constraint matrix, described as follows:

C = C f C s (2.3)
C f is a constant matrix of orthogonal motions to the effective direction for all fixed wheels, and C s is a variable matrix of orthogonal motion to the effective direction for all steerable wheels. C s varies with time as a function of steering angles of the wheels, noted β(t) .

C s = cos(α + β) sin(α + β) l sin β (2.4)

Degree of steerability

The degree of steerability (DoS) of the URV is a measure of the number of independently controllable steering systems. It can be defined by:

DoS = rank [C s ] (2.5)
The range of DoS varies in between 0 2 .

Degree of manoeuverability

The degree of manoeuvrability (DoMS) of the URV is a measure of the overall DoF that the URV can achieve through rotation of the wheels around their centers. It can be defined by: DoM S = DoM + DoS (2.6)

Chapter 2. Power Management of Autonomous Road Vehicles

The range of DoMS is defined in between 0 3

Holonomy Constraint

A URV is holonomous if all the kinematic constraints of the URV body are holonomic. A holonomic kinematic constraint can be expressed as an explicit function of position and time. The URV is holonomous if and only if:

DoM = DoF (2.7)

Omni-directional Property

An omni-directional URV can have mobility in all the directions of the DoF. Therefore, an omni-directional URV has a DoM equals to three: Robucar with dual configuration Robutainer

DoM = DoF = 3 (

Power Consumption and Energy Management of URVs

The URV is undergoing a necessary shift in expansion and dimension. It has broad participation in the industry and the daily lives of humans. Their involvement is to make life easier, to save time, and to make repetitive tasks in complex conditions. Most of these URVs are powered with electric sources like batteries. Nowadays, the energy management of the autonomy of the URVs has become a real challenge, in order to optimize the overall energy consumption.

Modelling the energy consumption of the URVs [START_REF] Liu | [END_REF]] allows analyzing the influence of operating modes of the vehicle on its energy consumption, and provides the best strategy of energy management [Xu 2016].

To optimize the energy consumption of the URVs, some contributions have adopted different methods, based on the optimization of the trajectory [Verstraten 2016], [Lu 2000], the optimization of the control [MartÃn 2008], [START_REF] Haidegger | [END_REF]], or the optimization of the vehicle design [START_REF] Vrkalovic | [END_REF]].

Chapter 2. Power Management of Autonomous Road Vehicles

Energy Consumption of URVs:

URVs Power consumption can be the source of three main components [START_REF] Kim | [END_REF]]: propulsion, steering and embedded technologies (2.5). In this Figure, rectangle boxes symbolize components of the URV, while the ellipses indicate the component energy consumption. Energy is drawn from the battery pack at the starting stage of the chain. The battery's left energy is called "Residual Battery Energy" [Xiao 2014].

Power consumption from the propulsion

The overall battery energy of the URV is used to drive the actuators, while the rest of the energy is used to power the embedded electronics [START_REF] Vantsevich | [END_REF]]. The "Power Electronics Loss" consists mainly of heat loss and the fan power cooling. The actuators also consume the energy at the bearings due to resistance losses in windings, core losses and mechanical losses [START_REF] Aarniovuori | [END_REF]]. Almost the electrical power is transformed into mechanical power, where the internal resistance in the gears, the bearings, etc..., are considered as internal friction. This mechanicalbased power loss depends on the type of drive train, the lubrication, etc. The external friction also called external efforts, consume the important part of the battery energy. These efforts represent the multi-domain dynamics of the interaction between the wheel and the ground [START_REF] Merzouki | [END_REF]] Depending on the type of the wheel tire, a part of the energy is not preserved due to the damping effect in the tires. The aerodynamic loss is proportional to the square velocity [Hucho 1993], so when the vehicle velocity is high, it can constitute a significant fraction of energy consumption.

Power consumption for the steering

Steering system [START_REF] Hassan | [END_REF]] represents another source of multi-domain energy consumption for a URV. The energy chain configuration for the steering system is almost the same as the propulsion configuration (2.5). This consumption is hard to quantify as it depends on multiple factors such as ground (terrain) type, traverse path, steering modes, etc.

When the vehicle's turning velocity is slow, the Ackerman-based kinematic steering is considered [Harrer 2017]. Significant lateral acceleration is needed when the vehicle turns fast, and therefore the wheels operate at high angles of slip. The loads on the inner wheels will also be significantly lower than the outer wheels. Tire-based wheel performance curves show that less slip angle is needed to reach the peak of lateral force by increasing the wheel load. Under these conditions, a kinematic steering vehicle's inner front wheel would be at a higher slip angle than the maximum lateral force required. Consequently, a vehicle's inner wheel in a high-velocity turn must operate at a lower steering angle than kinematic steering. Reducing the internal wheel steering angle minimizes the difference between the inner and outer wheel steering angles. Parallel or reverse steering is standard for race vehicles. Parallel and reverse Ackerman's steering are illustrated in Fig. 2.6 in [Jazar 2017]. Therefore, the inner wheel of a vehicle in a high speed turn must operate at a lower steer angle than kinematic steering. Reducing the steer angle of the inner wheel reduces the difference between steer angles of the inner and outer wheels.

For race cars, it is common to use parallel or reverse steering. Ackerman, parallel, and reverse Ackerman steering are illustrated in Figure 7.15.

The correct steer angle is a function of the instant wheel load, road condition, speed, and tire characteristics. Furthermore, the vehicle must also be able to turn at a low speed under an Ackerman steering condition. Hence, there is no ideal steering mechanism unless we control the steer angle of each steerable wheel independently using a smart system.

Example 267 F Speed dependent steering system.

There is a speed adjustment idea that says it is better to have a harder steering system at high speeds. This idea can be applied in power steering systems to make them speed dependent, such that the steering be heavily assisted at low speeds and lightly assisted at high speeds. The idea is supported by this fact that the drivers might need large steering for parking, and small steering when traveling at high speeds.

Example 268 F Ackerman condition history.

Correct steering geometry was a major problem in the early days of carriages, horse-drawn vehicles, and cars. Four-or six-wheel cars and carriages always left rubber marks behind. This is why there were so many three-wheeled cars and carriages in the past. The problem was making a mechanism to give the inner wheel a smaller turning radius than the outside wheel when the vehicle was driven in a circle.

The required geometric condition for a front-wheel-steering four-wheelcarriage was introduced in 1816 by George Langensperger in Munich, Germany. Langensperger's mechanism is illustrated in Figure 7.16.

Rudolf Ackerman met Langensperger and saw his invention. Ackerman The correct steering angle depends on instantaneous characteristics: wheel load, road condition, wheel velocity, and wheel tire. In addition, under an Ackerman's steering condition, the vehicle must also be able to turn at low velocity. Therefore, there is no ideal steering mechanism unless the use of a smart system to independently control the steering angle of each steerable wheel.

Power consumption for vehicle-like robotics functions

Robotics functions consume a large percentage of all the energy extracted from the battery. Unlike most distance-dependent propulsion and steering energy, robotics consumption is calculated by mission time. URV must consume energy during traverse to perform the assigned tasks, such as sensing environment, data collection, photography, or rescuing survivors in unknown situations. Some URVs must communicate with the base. The onboard computer, GPS(Global Positioning System), Inertial Unit, etc..., is also continually consuming energy. The URV may have other robotic consumption, such as the lighting in caves, mines, and sewers, to operate. As they vary significantly from URV to URV, it is impossible to generalize all types of consumption in one model. There are three main groups of sensor systems which consume more power: camera, radar, and lidar-based systems, as shown in Fig. 2 After taking into account other factors such as robotics power, rover mass, terrain resistance coefficient, Fig. 5 shows that rover velocity and driving duty cycle, which together determine average rover velocity, have the most significant influence on energy required to finish 2km traverse. Robotics power is also important. The mass and terrain resistance coefficient, which play a role in mobility energy, influence the required energy least.

Wheeled Mobile Robots Energetic Model

The big picture of energy utilization from battery for wheeled mobile robots is illustrated in Fig. 6. In Fig. 6, rectangle boxes represent system components inside mobile robot, while ellipses show the related energy consumption.

At the beginning stage of the chain, energy is drawn from battery pack. Although the capacity of a certain battery pack should be a constant value in the specification, it is unreasonable to assume that all energy stored can be extracted. For reasons of packaging, cell enclosures, and not completely draining the battery, only a fraction of the energy is drawn. The left energy in the battery is termed as "Residual Battery Energy".

Propulsion

A fraction of available battery energy is used by power train, where energy is output in mechanical form. The energy is firstly regulated by power electronics, who consumes energy itself. This is defined as "Power Electronics Loss". This part of loss is mainly made up of heat loss and cooling fan power. The effective energy is further fed into 9 We are taking into account other factors such as URV power, URV mass, terrain resistance coefficient Fig. 2.9 in [Xiao 2014] shows that URV velocity and driving duty cycle, have the most significant impact on the energy required to finish a defined trajectory.

In Fig. 2.10 in [Hou 2019], the URV can use the energy model to calculate and predict the energy consumption, which provides a guide for facilitating energy-efficient strategy. The URV's energy consumption is first modelled by taking into account three main factors: the sensor system, the control system, and the motion system. The authors in this work developed a global formula for the three systems. The experimental results showed that energy consumption for the motion is the most important in the four omni-directional wheeled URV with 94.7%. The control consumption power and the sensor consumption power represent 4%, and 1.25% respectively.

In the literature, the power consumption is studied for different kinematic configurations. For instance, [Shamah 1999] presents an experimental power consumption comparison of skid steering and explicit steering for a URV Fig.

2.11.

The moon rover Fig. 2.11 is a URV, where each wheel is independently driven to apply any desired angular velocity. We can distinguish an explicit steering and skid steering Fig. 2.12. Furthermore, the steerable wheels of such vehicles can turn more than 90 deg to the left and right. Such a vehicle is highly maneuverable at a low velocity. Fig. 2.12 illustrates the advantages of such a steerable vehicle and its possible turnings. The arrows by the rear Figure 14a shows the change in the percentage of electrical power of the three parts of the robot from the startup to 1 m/s of robot movement. Figure 14b shows the electrical power percentage of the robot's three parts during the smooth-running state of the robot. The proportion of the motion system to the total power far exceeds that of the sensor system and control system.

Energies 2018, 10, x FOR PEER REVIEW 13 of 15

Figure 14a shows the change in the percentage of electrical power of the three parts of the robot from the startup to 1 m/s of robot movement. Figure 14b shows the electrical power percentage of the robot's three parts during the smooth-running state of the robot. The proportion of the motion system to the total power far exceeds that of the sensor system and control system.

Conclusions and Future Work

The energy modeling method for mobile robots presented in this paper can be used to calculate and predict energy consumption, providing a guide to facilitate energy-efficient strategies as well as avoiding action obstacles due to lack of energy. The operation of robots can be divided into three states: standby, startup, and running. Compared with the other modeling methods, this model does not consider the path of the robot. The electrical power calculation method is related to the speed of the robot and the characteristics of the robot itself. By dividing the energy consumption of the robot into three parts, the model can be simplified. Therefore, very complicated parameters in the process of motion are not needed, and the calculation of electrical power becomes very simple. It is convenient for us to put this model into our program so that the robot has the ability of self-perception. Through our model, we established the relationship and connection among the three parts, which can make the model of the robot more complete.

Experiments showed that the power model created in this paper is feasible and effective. However, the experiments were carried out on horizontal roads only. The operation of robot involves stopping, accelerating, slowing down, turning, movement uphill and downhill, and so on, all of which is not entirely covered by the proposed energy model. Thus, further research should aim to complete the energy model according to all robot actions, using a better and more comprehensive experimental field. Moreover, the battery energy model is very important and should be included in a complete energy model for mobile robots.

Conclusions and Future Work

The energy modeling method for mobile robots presented in this paper can be used to calculate and predict energy consumption, providing a guide to facilitate energy-efficient strategies as well as avoiding action obstacles due to lack of energy. The operation of robots can be divided into three states: standby, startup, and running. Compared with the other modeling methods, this model does not consider the path of the robot. The electrical power calculation method is related to the speed of the robot and the characteristics of the robot itself. By dividing the energy consumption of the robot into three parts, the model can be simplified. Therefore, very complicated parameters in the process of motion are not needed, and the calculation of electrical power becomes very simple. It is convenient for us to put this model into our program so that the robot has the ability of self-perception. Through our model, we established the relationship and connection among the three parts, which can make the model of the robot more complete.

Experiments showed that the power model created in this paper is feasible and effective. However, the experiments were carried out on horizontal roads only. The operation of robot involves stopping, accelerating, slowing down, turning, movement uphill and downhill, and so on, all of which is not entirely covered by the proposed energy model. Thus, further research should aim to complete the energy model according to all robot actions, using a better and more comprehensive experimental field. Moreover, the battery energy model is very important and should be included in a complete energy model for mobile robots. wheels, illustrate the magnitude of the angular velocity of the wheel, and the arrows on the front wheels illustrate the direction of their motion.

For some special-purpose vehicles, such as moon rovers and other URVs, we may attach each actuated wheel to an independently controlled motor to apply any desired angular velocity. Furthermore, the steerable wheels of such vehicles are able to turn more than 90 deg to the left and the right. Such a vehicle is highly manoeuvrable at a low velocity. Having such a vehicle allows to have many driving configurations based on its steering. Front steering, Rear steering, dual steering, and point turning are the different driving modes. In any of the above scenarios, the steer angle of the front or rear wheels should be determined using a proper equation.

Refer to Fig. 2.13a and Fig. 2.13b, a comparison between the power consumption for explicit and skid steering for Nomad URV is given with respect to the radius of the trajectory ( [Shamah 1999] ). The experiments show that the power consumption of the Nomad URV decreases with the increase of the radius of the trajectory, while the skid steering consumes more than the explicit steering.

Most of the works given in the literature studied the case of modeling the power consumption of one single driving mode. For example, [START_REF] Yu | [END_REF]] studied the case of a skid-steered wheeled vehicle is Fig. 2.16b. The authors elaborate a power consumption model for different types of contact surfaces for general 2-D motion and linear 3-D motion. However, the authors in

Results

Power and torque for skid and explicit turning degenerate to equal values at infinite radius (or straight driving). As the turn radius decreases from straight driving to a point turn, greater power and torque are required because a greater sideslip angle is encountered. For all turns skid steering requires greater power and torque than for explicit turning. This is because sideslip angles are greater in all cases. In the limiting case of a point turn, the power for skid steering is approximately double that for an explicit point turn. The primary contribution of this research is the experimental quantification of the power and torque requirements over turn radii from a radius equal to zero to an infinite radius. In order to provide non-dimensional values, the power of steady state steering is divided by the power to drive up a vertical wall, known as dead lift power.

[14]

[15]

In order to provide a useful non-dimensional power value, only the power necessary to provide thrust on the terrain is used. No load power is removed since it varies significantly between different vehicles. As soon as the robot is started, the power consumed by various components is recorded by activating or controlling the components one by one. Programs for deriving the power models from a series of operations (Fig. 4, right) and calculating the energy consumption of each component (by determining the duration for which each component was active) were written in MATLAB and tested with the robot's datasets created during the experiments. Initially the computer is turned on and hence P comp is calculated. Then, the controllers are activated and the power P con is noted. Each other component's power consumption is calculated by subtracting from the previous power value after the activation of the respective components.

( ) = 725kg ( )0.15 m s ----     9.8 m s 2 ----     1065.8Watts = (b) gravity
Since all sensors data were needed during teleoperation to ensure safety of the robot and surroundings, all the sensing elements were active at maximum freq experiments. Motors are the only dynam the static power component is the sum and computer power. P static = P sen + P and P dynamic = P motion . The computer 0.5 W power. Therefore, the sensing a obtained by subtracting 0.5 W from the As the Khepera mobile robot is sma the power model for locomotion is ass in the experiments) to be linear with r speed (of both motors) and the only c constant payload on a flat surface. Howe this assumption does not hold true an energy model (Equation 7or 9) should acceleration effects are negligible when c of velocity on power consumed by the m equation 9 can further be reduced adding mass m p as: In addition, the authors in [Morales 2009], proposed a static power model for skid-steer tracked URVs, moving at walking velocity on hard plane terrains Fig. 2.15a.

P i motion = C υ • υ i + C mp •
In [Morales 2010], the authors proposed a simplified model of power consumption for skid-steered robotic vehicles on the hard horizontal ground at walking velocities based on a kinematic approach. This static model provides an estimation of the power consumption of the actuator as a function of the velocities of the left and right wheels Fig. 2.16a. Furthermore, [Tokekar 2011] presented a problem of computing a velocity profile for a vehicle-like robot, so as to minimize the energy consumed while traveling along a given path on a flat surface Fig. 2.16c. [START_REF] Guo | [END_REF]] presented a simplified model to computer torque and power consumption of tracked URV, driving on soft terrain (i.e. sand) Fig. 2.15b. The authors in [START_REF] Maclaurin | Comparing the steering performances of skid-and Ackermann-steered vehicles[END_REF]] analyzed the steering performance of an 18tons and 6×6 skid-steered URV and compare it with the performance of an equivalent Ackerman steered vehicle Fig. 2.17c. The Skid configuration of the vehicle presented in [START_REF] Maclaurin | Comparing the steering performances of skid-and Ackermann-steered vehicles[END_REF]] is shown in Fig. track is V max y = 0.86 m/s. The track train consists of a sprocket and an idler wheel, with two rollers in between (see Fig. 5). These are mounted on a rigid suspension system, i.e., without springs or shock absorbers. Track belt tension is adjusted by a spring that shifts the idler in the longitudinal direction of the track. Gearheads between each motor and its sprocket provide a mechanical efficiency of about 93%.

Two different rubber belt sets have been employed. They only differ on their width, which is 0.16 m and 0.11 m for the wide and narrow tracks, respectively (see Fig. 6). In both cases, the Apart from the resolvers, the robot includes an inertial measurement unit with gyroscopes. It is also equipped with a GPS receiver that accepts local-area differential corrections. This differential GPS (DGPS) provides positioning errors around 0.02 m with good sky visibility.

The computation system is based on a Pentium IV industrial computer and a cFieldPoint, which is a programmable logic controller. The computer acts as the user interface, whereas the cFieldPoint interfaces with the motor drivers and sensors through several input-output modules.

The cFieldPoint executes a real-time LabVIEW program for autonomous navigation, which consists of several concurrent processes. The main process implements a finite-state machine that initializes the robot and changes the operation mode (standby, manual operation, and autonomous navigation). The other processes interact with the sensors and the drivers to gather information and to update motion references.

B. Power System of Auriga-β

The power needed by the vehicle is provided by an onboard 3.8-kW petrol-fed 220 V ac generator. The maximum power consumption for the different components of the mobile robot is shown in Table I. Note that in this kind of vehicles, the locomotion system can be responsible for most of the power consumption (up to 80% for Auriga-β).

Motors are fed by two independent ac drivers that do not allow regenerated electric power to be transferred from one driver to the other, nor to the onboard ac generator. Instead, regenerated power exceeding the internal capacitor bank of each driver is

A. Internal power consumption modeling

For a simplified DC motor and drivetrain working in steady state, the torque generated should overcome resistances in both motor and transmission, including damping resistances and rotational coulomb frictions. The steady state torque balance for powertrain can be expressed as follows (23) where i is current of the motor, K t is motor constant and G r is the overall drive train ratio, b eff is the effective damping resistance coefficient of the powertrain observed at the sprocket, ω s is the rotational speed of the sprocket, τ c is the Coulomb torque observed at the sprocket, T is net output output torque. The power consumption can be expressed as:

(24)
Therefore, a quadratic polynomial can describe internal power consumption for the electric powertrain. For soft terrains the net torque T overcomes both frictional resistance and soil compaction resistance. For solid and hard terrain (e.g., asphalt), net torque output T is only to overcome frictional resistance. Since this study is for skid steering power consumption analysis on soft terrain, specific description of track-terrain interaction resistance is not discussed here. The steady state torque balance equation can be rewritten into steady state power balance equation as the following:

(25)
where , and r is the sprocket wheel radius. The motor power stages employed in this vehicle are regenerative, which means that most electric power can be transferred back to the batteries a motor acts as a generator (i.e., motor power consumption is negative [11]).

Hall Effect current sensors have been installed to measure the instantaneous power consumption of each motor P l M , P r M . With this configuration, measurements are not affected by the consumption of other vehicle components unrelated to the traction system. Thus, the total mechanical power of the traction system PM can be calculated as:

PM = P l M + P r M . ( 6
)
Data acquisition and high level motion control are performed by a compact onboard computer using a LabVIEW program. This computer interfaces with the embedded motor controller and the current sensors through two serial links. Manual operation is possible through a wireless joystick.

A. Experimental Power Model

The experimental model has been estimated on two terrain types: marble flooring and concrete, and with the water tank full and empty.

The first step in the power model identification procedure is estimating the local x-coordinate of the tread ICRs. Applying (5) with data from turning on spot experiments has given the same Ĉx = 0.47 m for the four terrain-load combinations.

The pressure under each wheel has been measured with four scales for the full and empty water tank cases (see Fig. 4). In both cases, the center of gravity is almost coincident with the origin of the local frame of the vehicle (see Table I). This fact supports the assumption of symmetric tread ICRs [13]. The summation in ( 2) is a constant value if constant tread ICR positions are assumed. For Quadriga, this constant is 466 Nm and 264 Nm for the full and empty tank cases, respectively.

With data acquired from a manually guided spiral-like path, parameters K and μ can be easily identified by using the Simplex optimization method [14]. The cost function to be minimized is based on the error between ( 4) and ( 6):

J(K, μ) = ∀t | PM (t; K, μ) -PM (t)|. ( 7
)
Figure 5 presents measurements from the experiment on marble flooring with the full tank. Note that in the interval from 7 s to 17 s, the left and right side wheels move forward but with different speeds. This provokes that the right side wheels are dragged by the faster left side [11]. Therefore, the right motor is acting as a generator as shown by its negative P r M values. This does not happen when wheel speeds are similar or have opposite signs. Let µ sa denote the coefficient of friction for the wheels when the current and angular velocity of the motor have the same sign, such that the motor applies a propulsive force. Let µ op denote the coefficient of friction for a wheel when the two have the opposite sign, resulting in the motor applying a braking force. The values of the parameters K, µ sa , and µ op are terraindependent and are difficult to determine by direct measurement. As a result, the values of K, µ sa , and µ op are computed by solving the nonlinear optimization problem r Res are the values of the difference between the steady-state simulation and experimental torques. The commanded turning radius R is defined as the turning radius resulting from applying the wheel speeds ω l and ω r to the kinematic model ( 2) assuming no slip. The set of experimental indexes i given by {1, 2, . . . , 31} map to the set of commanded turning radii R given by The other terrain-dependent parame rolling resistance µ roll , is computed by c velocity to a vehicle going straight on rolling resistance is obtained from the av the wheel. The coefficient of rolling resis resistance divided by the weight of vehic Since they are terrain-dependent, the (µ sa and µ op ), shear modulus (K), and resistance (µ roll ) must be determined fo aforementioned optimization procedure model changes with the terrain being tra All of the key parameters for the mo system are listed in Table II. These param of the PID controller, which are the c skid-steered vehicle of Fig. 7.

The experiments described in Sect quire the vehicle to traverse particular (b) Pioneer robot [START_REF] Yu | [END_REF] or is given by,

E ω(t)
(2) the motor, K E and K T T F and T L are internal e internal damping force moments of inertia. ot and angular velocity re proportional to each nd 2 to yield the energy

2 (t) + c 3 v(t) (t)a(t) dt.
binations of the motor the linear velocity and rom ω(t) and the radius al velocity values are the the terms corresponding ewrite the energy model

c 3 v(t) + c 4 dt. (3)
n the motor parameters

The solutions for Problems 1, 2 and 3 are presented in Sections IV, V and VI respectively. We begin by describing the calibration procedure to determine the model parameters.

III. CALIBRATION

In this section, we describe a simple procedure to find the energy model (Equation 3) of the robot for a given flat surface. We use a custom-built robot (see Figure 1) for experiments. The robot is driven using two DC motors whose output shafts are connected together. It has car-like steering controlled by an independent servo motor. Separate batteries are used to drive the DC motors and power the rest of the electronics on the robot.

A. Experimental Setup

Our method utilizes a simple current and voltage measurement circuit (Figure 1) connected between the output of the motor driver circuit and the motor. This circuit measures the where

v~v v 1{kt ~vnc 1{kt ð21Þ
Thus

Psn~2 X Fx vnc 1{kt ð22Þ
where SFx is the sum of the longitudinal tyre forces on each side of the vehicle.

If the required yaw rate is 0.75 rad/s, i.e. a complete turn in 8.4 s, then the required output power from the steer motor is 206 kW. Allowing for a steering system drive efficiency of 0.85, then the input power to the steering system increases to 242 kW. This is a high proportion of the engine power, later assumed to be 250 kW. A compromise often needs to be set between the steering power and the rate of turn.

If the vehicle has individual wheel drive, with electric motors for example, then the steering power requirement can be reduced by running the centre wheels at a slower speed than the corner wheels, i.e. at a speed that gives maximum traction for minimum slip. Setting up a Solver search routine for minimum steering power, with the ratio of centre to corner wheel speed as a further variable, then the required steering power is reduced from 206 to 148 kW with the centre wheels running at a slip of 0.16 and the corner wheels at a slip of 0.58, a ratio of 1:3.65.

Variation in the slewing moment with the radius of turn

Figure 7 shows how the slewing moment varies with radius of turn at low latacs. At small radii of turn the slip angles are large and the tyre lateral forces are below their peak. As the radii increase, slip angles decrease and tyre lateral forces and slewing moments increase to a peak of 117.7 kNm at 7.5 m radius. Here the mean of the slip angles on the front and rear wheels is 12u and this corresponds to the peak of the lateral force-slip angle relationship. As the radius of turn further increases, then slip angles and lateral forces decrease; the slewing moment steadily falls and by 100 m radius it is 16.9 kNm. Also shown is the slewing moment for a tracked vehicle with six wheels per side and of the same weight, wheelbase and track as the wheeled vehicle. The flexibility of the track pad is allowed for using the method shown in reference [9]. The slewing moments of the tracked vehicle are seen to be significantly less than those for the wheeled vehicle partly because of the lower stiffness of the track pad compared with that of the tyre and also because of the greater number of wheels of the tracked vehicle. 1. The middle wheels steer at half the angle of the front wheels. 2. The wheels on each axle remain parallel when steering. 3. The total longitudinal forces of the outer wheels equal those of the inner wheels, i.e. the vehicle has a free centre differential.

Model results

The effect of pneumatic trail

The model was initially set up without any allowance for pneumatic trail. Running on a 15 m turn showed that the slip angles of the tyres remain largely in the linear range of the characteristic. Reference [15] shows a Gough diagram for the tyre and this indicates that the pneumatic trail is approximately 40 mm for most conditions. A further model was In [START_REF] Brembeck | [END_REF]], optimal control strategy for a highly manoeuvrable URV (ROboMObil) is applied, Fig. 2.18.

Most of power consumption models are developed for a single configuration mode, and in the literature, no generic model or formula is elaborated for power consumption estimation for different driving modes. Such, in chapter 3, a generic formula is proposed for power consumption modeling in the function of the degree of steerability, degree of actuation redundancy, and the kinematic and dynamic parameters of an over-actuated URV. Hereafter, we propose in the following chapters a new energy planning methodology for optimal autonomous driving, where the power consumption estimation plays an important role for planning the power distribution on the trajectory traversed by the URVs. (Fig. 1) is an electro-mobility concept gent central control of four Wheel ate the drivetrain, brakes, steering and n electric drives. The full X-by-Wire intelligent and input independent MObil. In this way it is possible to a side-stick either within the car or station. Furthermore, various levels of le, from partial to fully autonomous 360 degrees perception system. With oming increasingly critical in all forms is paper focuses on the energy optimal ertrain actuators to follow a given level planner or an interpreted driver approach utilizes the over-actuated tely to achieve minimal control effort ergy efficiency via real-time capable er is organized as follows: In chapter f the transfer from robotics to vehicles n III the modeling of the controlled ry 31, 2012. earch assistant and PhD student at the DLR s Center (RMC), Oberpfaffenhofen, Germany. k@dlr.de). Peter Ritzer is BSc. and is currently Technical University of Munich plant and the derivation of the control allocation (CA) algorithm are stated. Section IV discusses an extension to nonlinear dynamic inversion. The different implementation and simulation results are given in chapter V. Finally the approaches and further development steps are sketched in section VI.

II. ROMO CONTROL -STARTING POINT, PERFORMANCE & ENHANCEMENTS

In [2] we presented a control strategy from the point of view of an easy to handle Human Machine Interface. The concept is to provide a user-friendly interface to address the third degree of freedom (DOF) and to distribute the user input to the overall ten actuators of the ROboMObil. This geometric approach does not take any further considerations of the actuator dynamics, the losses in the power train or the wheel slip into account. Although we have experienced good results with the geometric approach, we decided to develop a new control approach with focus on minimal power consumption.

The idea is to drive the ROboMObil with the lowest possible power demand and losses so that the range is maximized while sufficient dynamics is retained. The proposed algorithm is part of a complex energy management (EM) strategy, which is organized as an inverse pyramid (similar as proposed in [START_REF] Chen | Audio-visual speech processing[END_REF]) with three different management levels.

Optimal autonomous driving of URVs

Many fields for autonomous driving of URVs are studied in the literature [START_REF] Coutinho | [END_REF]], such as optimal path planning, optimal task assignment, trajectory optimization, and routing. In this thesis work, we proposed an offline energy planning that comes before the assignment of the previously mentioned techniques of autonomous navigation as shown in Fig. 2.19.

URV path planning problem

The Path Planning (PP) problem consists of finding a feasible pathway to a URV that visits the sequence of way-points (objectives) in 2D space, without taking into consideration the dynamics of the URV. PP is a geometrical problem, according to [START_REF] Gasparetto | [END_REF], where it is defined as a geometric path, irrespective of any specific time law. However, Trajectory Optimization (TO) consists of assigning a time law to a controlled geometric way. More sophisticated variants of the PP problem such as motion constraints require substantial simplifications and assumptions to be solved heuristically [Kunchev 2006], [Betts 1998] and [Betts 2010]. The field of TO has, however, not considered routing decisions, i.e. given a set of ordered way-points, it is possible to find a feasible trajectory for a generic URV D: Let A be an object (URV) moving in a workspace S (e.g., in an euclidean space S = R n , n=2 or 3). A set of obstacles B 1 , . . . , B m is assumed to be distributed over S . The problem of PP consists in, given initial and final configurations (position and orientation) for A , then finding a path in S that avoids collisions with the objects B 1 , . . . , B m ([Latombe 2012]). It has been shown that the problem of PP is N P-hard if the velocity of the object A is unbounded and no rotation is considered [START_REF] Reif | [END_REF]]. For [START_REF] Gasparetto | [END_REF]], a PP problem consists of find-

Optimal Autonomous Driving of URVs

Optimal path planning

Optimal task assignment

Energy management

Routing

Trajectory optimization The output of discrete methods is often polygonal paths, i.e. paths with no limitation of curvature. Continuous methods represent S , through the use of a continuous function using a potential field method [START_REF] Barraquand | [END_REF]].

Shortest path[Lavalle2001] Heuristics[Kunchev2006] Potentiel field [Lattombe2012] Cell Decomposition[Brooks1985] . . . Stochastic methods[Khamis2015] Deterministic Methods[Khamis2015] Metaheuristics[Horst2000] . . . SQP [Zhang2001] DDP[Lyshenvski1998] Rule based[Ao2007] GA[Niu2007] DirectMethod[Gao2005] . . . Geometric methods [Adewumi2000] Shortest path algorithms[Misra2005] Heuristics[goodridge2005] . . .

Energy planning Techniques of autonomous driving

Most of PP methods use one of three types, called roadmap, cell decomposition and potential fields of space configuration. Roadmap model links particular targets in the graph, while cell decomposition methods decompose the workspace into grids, and possible areas model the workspace with mathematical fields. From the three most common ways, cell decomposition methods are the most used for PP. These methods can be either topological or metric. All methods listed below should be discrete with the exception of the Potential Field method, that can be continuously implemented in state space as well.

• Cell decomposition methods are methods for outdoor robotics and the most studied. The planning space is divided by these methods into discrete, non-overlapping regions that are subsets of the c-space and whose union exactly forms part of space S . The result is a graph that is adjacent to each other cell. The connectivity graph is called the methods to go from one cell to adjacent cells. In cell decomposition, it can be distinguished approximate decomposition using regular grids [START_REF] Brooks | [END_REF] and [Zhu 1990], exact decomposition [START_REF] Sleumer | [END_REF]], [Schwartz 1983], [START_REF] Avnaim | [END_REF]] and adaptive decomposition using quad-tree and framed quad-tree [START_REF][END_REF]], [Samet 1988], and [START_REF] Hiroshi Noborio | A quadtree-based path-planning algorithm for a mobile robot[END_REF]].

• Roadmap Methods Roadmap Methods are the second most significant type of representation. Roadmaps are graphs that show how to go from one node to another node. Roadmap planning methods identify a set of one-dimensional curve connections between the URV's free space. Once the roadmap has been created, the planner will use it as a set of normalized paths to find the optimal solution. As examples, visibility graph [Nilsson 1984] and [Choset 1996], Probabilistic Roadmap (PRM) [START_REF] Kavraki | [END_REF]]. and Exploring Random Trees RRT [Cheng 2001], [START_REF] Frazzoli | Robust hybrid control for autonomous vehicle motion planning[END_REF]], [Kuffner Jr 2000], and [START_REF] Lavalle | [END_REF]].

• Potential Fields

The third primary form of representation used in path planning is Potential Fields. The potential field methods are quite different from the planning methods and have been widely used in the past. A mathematical description is used in the whole area of robotic travel. This method treats the URV motion likes an electron in an electrical field, as a point under the influence of fields generated by the world's objectives and obstacles. Obstacles create repulsive forces, and free-obstacles generate attractive forces [Khatib 1985] and [Latombe 2012].

Once a method of representing the environment has been established, it is then necessary to search for the best path through that representation. Graph search algorithms are used with the cell decomposition or roadmap methods of path planning, and also with the potential field methods. These search algorithms come from a wide variety of applications including general problem solving, artificial intelligence, computer networking, and mechanical manipulation. After an environment representative process is established, the best path through that representation must be searched. Graph search algorithms are used in path planning methods with cell decomposition methods, roadmaps methods, and also with potential field methods. Many graph search algorithms have been studied in the literature such as Dynamic Programming (DP), Dijkstra, A * , ... etc.

Trajectory optimization problem of URVs

General formulation of optimal control problem

An optimal control problem is posed formally as follows. Determine the state (equivalently, the trajectory or path), x(t) ∈ R n , the control u(t) ∈ R m , the vector of static parameters p ∈ R q , the initial time, t 0 ∈ R and the terminal Indirect Methods

Direct Methods

System of Nonlinear Equations

Differential Equations and Integration of Functions Nonlinear Optimization time, t f ∈ R (where t ∈ [t 0 , t f ] is the independent variable) that optimizes the performance index

J = Φ [x(t 0 ), t 0 , x(t f ), t f ; p] + t f t 0 L [x(t), u(t), t; p] dt (2.14)
subject to the dynamic constraints (i.e., differential equation constraints),

ẋ(t) = f [x(t), u(t), t; p] (2.15) the path constraints C min ≤ C [x(t), u(t), t; p] ≤ C max (2.16)
and the boundary conditions

φ min ≤ φ [x(t 0 ), t 0 , x(t f ), t f ; p] ≤ φ max (2.17)
The state, control, and static parameter can each be written in component form as

x(t) =    x 1 (t) . . . x n (t)    ; u(t) =    u 1 (t) . . . u m (t)    ; p =    p 1 . . . p q    (2.18) 2.4.2.

Numerical methods used in optimal control

The following three fundamental components are at the heart of a reliable method to resolve optimal control problems: (1) ways to solve the differential equations and integrating functions;

(2) a method to determine the system of nonlinear algebraic equal treatment; and (3) a process to resolve a nonlinear optimization problem. For all statistical purposes under optimal control, techniques for solving differential equations and integrating functions are rechoired. An indirect method is used to conjugate the numerical solution of differential equations with the numerical solution of nonlinear equations, while a direct way combines the numerical solution of differential equations with nonlinear optimization. A scheme showing the components of the optimum control methods used for each class is presented in Fig. 2.21.

The trajectory optimization problem

A trajectory is usually associated with a set of Equations of Motions (EOMs), which describes the spatial-temporal change relationship of a system. The problem of TO is closely related to the issue of Optimal Control (OC) [Betts 2010]. Trajectory Optimization Problems (TOPs) include specific cases of Optimal Control (OC) problems, which determine a system trajectory (e.g., URVs) while minimizing performance and satisfying boundary conditions, path limitations and system dynamics.

Usually, system dynamics are modelled by a set of EOMs that can be nonlinear and discontinuous. six degrees of freedom (6DOF) EOMs are composed by translational equations (containing forces, position, velocity, acceleration, etc.) and rotational equations (containing moments, angular velocities, angular acceleration, etc.). Under simplifying assumptions, 6DOF EOMs can be decoupled into three degrees of freedom (3DOF) EOMs.

For example, in the case of 3DOF, the state vector may represent the URV position, velocity, path angle, and yaw angle. Solving a Trajectory Optimization Problem (TOP) for a URV consists of generating the control vector inputs for the URV to deliver an optimal set of maneuvers. Dynamic and kinematic constraints are considered in TOP, and the optimal solution is produced as time-indexed states and controls such as positions, velocities, and accelerations. The TOP can be more complex and difficult if the considered boundary conditions depend on unknown variables or if the URV dynamics and kinematics vary over time.

In this case, TOPs can be divided into two or more phases so that changes of URV, operational or physical characteristics can be properly modelled. A phase in which the dynamic system remains unchanged can be defined as a segment of a trajectory. Phases can be described through their own constraints, differential equation of the system, operational constraints, and time.

For example, Euler methods are the most common single-step methods, while Adams-Bashforth and Adams-Moulton multi-step methods [Dahlquist 2003] are the most commonly used multi-step methods. The ability to resolve nonlinear optimization or nonlinear programming problems is a key ingredient in solving trajectory optimization problems , [START_REF] Sherali | [END_REF]], [Bertsekas 2006] and [START_REF] Boyd | [END_REF]] (NLPs). In addition, [START_REF] William | Numerical initial value problems in ordinary differential equations[END_REF] showed that the implicit methods are more stable than explicit methods. Runge-Kutta is used by [START_REF] Butcher | [END_REF]] as an explicit method. The divided methods of collocation [Betts 2010] fall into three general categories: Gauss methods, Radau methods, and Lobatto methods. TO problem can be solved by using two main methods class Direct methods and indirect methods [Rao 2014].

3.1. Direct and indirect methods for trajectory optimization problems Two main classes of numerical methods, direct and indirect methods, became very common in solving TOPs. The direct methods depend on discretization into a problem of finite-dimensional optimization of an infinitedimensional OC. This approach is frequently known as "discretize, then optimize", [START_REF] Sherali | [END_REF]], [Bertsekas 2006], [Betts 2001], [START_REF] Boyd | [END_REF]], and [START_REF] Gill | [END_REF]]. For instance, the controls are discretized on a fixed grid using an arbitrary parametrization scheme in a direct single shooting method. The next phase of this technique is to solve the problem of non-linear programming to identify an optimal parameter vector. The indirect techniques are to determine the optimal criteria needed for an OC problem and then use a discretization method to solve the resulting equations. Indirect methods usually use "optimize, then discretize" strategy, [Athans 2013], [START_REF] Bliss | [END_REF]], [START_REF] Bryson | [END_REF]], [Fleming 2012], [START_REF] Hildebrand | [END_REF]], [Hull 2013], [START_REF] Leitmann | The calculus of variations and optimal control: an introduction[END_REF]], [Vintner 2000]. For instance, the resulting optimality conditions in an indirect single shooting method consist of a boundary value problem that can be solved by a means of simple single shooting algorithm [Betts 2010]. In order to solve TOPs, several advanced algorithms were created.

URV routing problem

The Vehicle Routing Problem (VRP) in operational research and combinatorial optimization is a very well-known problem. In the VRP, it is necessary to assign routes to a set of vehicles that have to serve a set of customers to minimize the total cost of the operation. Its classic variant is called the Capacitated Vehicle Routing Problem (CVRP), in which each URV is allocated a load capability. The CVRP can be described generally as follows. A set of vertices V = {0, • • • , } and a set of arcs A are provided to connect these vertices. Each vertex reflects a client with costdi, i ∈ V \ {0}. A value of c ij is allocated to each arc (i, j) ∈ A, which represents the travel cost between two customers. Let C = {1, • • • , m} be a collection of Q capacity homogeneous URVs. Here we specify the depot vertex I = 0 (launching site). The CVRP consists of finding a minimum cost set of m routes starting and ending at the depot so that all customers are visited exactly once, the demands of all customers are met and the vehicles' capacity is respected. It is known that the CVRP is N P-hard. More explanation and details about the VRP and its variants, such as [Cao 2017], [Caceres-Cruz 2015], [START_REF] Kumar | [END_REF]], [START_REF] Zirour | Vehicle routing problem: models and solutions[END_REF]], [START_REF] Ousingsawat | Multiple vehicle team tasking for cooperative estimation[END_REF]], and [Adewumi 2018].

MRTA Schemes

URV task assignment problem

The problem of URV task assignment (URVTAP) is to find an optimal allocation of URVs to a set of tasks. The URVs frequently have distinguishable features and characteristics, and the jobs depend on the application's nature. This issue has been shown to be N P-hard [START_REF] Alidaee | [END_REF]]. Every day new complicated assignment issues arise due to the rapid growth of URV technology and many algorithms have been designed to defeat the unique challenges. One can notice that the science community has gained attention in this field of research. More literature review can be contained in [Khamis 2015] on algorithms for Multi-Robot Task Assignment (MRTA) issues.

As illustrated in Fig. 2.22, eexisting task allocation schemes can be categorized according to several dimensions [Dasgupta 2011]:

• Single task (ST) versus multi-task (MT), related to the parallel task performing capabilities of robots,

• Single robot (SR) versus multi-robot (MR), related to the number of robots required to perform a task, and

• Instantaneous assignment (IA) versus time extended assignment (TA), related to the planning performed by robots to allocate tasks.

Single task (ST) signifies that each robot can perform as most of one job at the moment, while MT implies that some robots can perform various functions at the same moment. Very similarly, SR indicates that to achieve this, each task needs precisely one robot, while MR implies that numerous robots may be needed for specific tasks. In IA approaches, the accessible data about robots, jobs, and environment allows only instant distribution of tasks to robots (i.e. tasks independence is a strong assumption). Sometimes these methods are used to prevent the need for algorithms with high computational scheduling. In the other side, there are continuous task allocation or time extended assignment, where more information can be collected. TA is more challenging from a planning viewpoint because robots have to worry about the dependencies between tasks [START_REF] Khamis | [END_REF]].

There are two popular approaches to the problem of task allocation from the planning viewpoint: decompose-then-allocate and allocate-thendecompose. In the first method, the complex task is decomposed into simplified sub-tasks and then these sub-tasks are distributed to the team members based on their ability and accessibility to finish the sub-tasks as needed, [START_REF] Aylett | [END_REF]] and [START_REF] Botelho | [END_REF]]. The cost of the final plan cannot be fully regarded in this sort of methods, because the task is decomposed without identifying to whom tasks need to be assigned. Another disadvantage of this form is that modifications in the constructed strategy are inflexible. So, even if it is found expensive, the plan designed by the central agent cannot be rectified. On the other hand, the complicated tasks are assigned to mobile sensors in the allocate-then-decompose strategy [START_REF] Botelho | [END_REF]], and then each mobile sensor decomposes the assigned tasks locally. The major disadvantage of this strategy is that all functions are allocated to only one mobile sensor and therefore the preferred task decomposition is solely dependent on that mobile sensor's plan, which improves the chance of achieving a sub-optimal solution. Allocating tasks to more than one mobile sensor to consider distinct methods for the desired job may be more useful. While the techniques of decomposingthen-allocating and allocating-then-decomposing may be able to find possible plans, then both approaches have disadvantages.

Optimization-Based Approaches are the branch of applied mathematics that focuses on solving a particular problem to find the optimum solution to this issue from a set of available solutions. This set of possible solutions are limited by a set of constraints, and the optimum solution is selected This criteria defines the objective function of the problem describing the system goal quantitatively [START_REF] Horst | [END_REF]]. There are a large variety of available optimization approaches, and the use of these approaches depends on the nature and complexity of the problem to be optimized. Besides, optimization-based approach algorithms have more exceptional ability to explore new search domains in the search space because the randomness of the algorithm variables also allows for increased efficiency when dealing with noisy input information [START_REF] Spall | [END_REF]], [START_REF] Diwekar | Introduction to applied optimization[END_REF]], and [START_REF] Lenagh | [END_REF]]. Fig. 2.23 presents a general classification of optimization methods, [Khamis 2015]. Deterministic methods follow a strict procedure. The path and the values of variables of the functions are repeatable. The methods used are numerical and classical methods, such as quadratic programming, graphical methods, penalty methods, gradient and hessian based methods, derivative-free approaches, q sequential quadratic programming, etc. In these methods, the same path will be followed every time. They also involve graphics techniques like blind/uninformed searches and informed search procedures. Stochastic techniques always have some randomness. These techniques can be classified into trajectory-based and population-based algorithms. A trajectory-based metaheuristic algorithm such as simulated annealing uses a single agent or solution which moves through the design space or search space in a piecewise style. A better move or solution is always accepted, while a not-so-good step can be taken with a certain probability. The steps or moves trace a trajectory in the search space, with a non-zero probability so that this trajectory can reach the global optimum. On the other hand, populationbased algorithms such as genetic algorithms, ant colony optimization, and particle swarm optimization use multiple agents to search for an optimal or near-optimal solution. Stochastic methods are always random. These methods can be categorized into algorithms based on trajectory and population. A metaheuristic trajectory algorithm such as simulated annealing utilizes one agent or solution that moves in a piece-wise manner through the design area or searches space. It is always acceptable to move better, while a less good move with a certain probability can be chosen. The steps or motions trace a search space trajectory, with a non-zero probability to make this trajectory achieve the global optimum. Population-based algorithms, for instance, such as genetic algorithms, optimization of the ant colony and optimization of particle swarm use multiple agents to find an optimal or nearly optimal solution.

Chapter 2. Power Management of Autonomous Road Vehicles 2.4.4.1 URV energy management Energy Management (EM) for URVs is a special case in optimal control. The energy management approach uses different techniques. Dynamic programming, for example, is often used to reach the world's best. As described in Fig. 2.24, a clustering review of co-words is also done in particular energy management approaches to further explore distinct types of energy management approaches such Genetic Algorithms (GA), Pontryagin's Minimum Principle (PMP), Model Predictive Control, NN and Edge Cloud Management Controller (ECMS). The two most commonly utilized energy management strategies are DP and Fuzzy Logic Control. The other energy management strategies include rule-based control, Particle Swarm Optimization (PSO), robust control, stochastic optimal control, Evolutionary Algorithm (EA), Support Vector Machine(SVM), convex optimization, Bees Algorithm(BA), direct method, machine learning, simulated annealing (SA), Quadratic Programming(QP), simplex method, shooting method, extremum seeking(ES), Game Theory (GT), Parallel Chaos Optimization Algorithm(PCOA), Dividing RECT angles algorithm(DIRECT), varying-domain optimization and soon.

Two major classes can be classified for the energy management strategy [Zhang 2015].Rule-based energy management strategy, and optimizationbased energy management strategy. Rule-based energy management strategy can be considered as a deterministic rule-based and a fuzzy rules-based energy management strategy, while optimization energy management strategies can be classified into a global energy management optimization strategy and realtime energy management optimization strategy based on operating driving conditions.

There are three primary solution techniques in consideration of the optimization problem of HEVs. The first approach optimizes the strategy parameters of a rules-based energy management strategy and therefore, the energy management problem becomes the parameter optimization problem, also known as the static optimization problem. The second approach formulates energy management as dynamic, nonlinear, and constrained optimization problem, Dynamic optimization algorithms can solve this problem. The third one simplifies the URVs optimal control problems with model approximations such as a mathematical programming, like sequential quadratic programming problem [Zhang 2001], quadratic programming problem [START_REF] Kessels | Electronic horizon: Energy management using telematics information[END_REF]], mixed integer linear programming problem [Salman 2005], [Wu 2014a], and convex programming problem [Elbert 2014]. Since Lyshevski et al. [Lyshevski 1998] first apply Deterministic Dynamic Programming (DDP) to optimal energy management of series HEVs in 1998, DDP has been widely used to optimization control for various types of HEVs, covering parallel HEV [Lin 2003], power-split HEV [START_REF][END_REF]], and PHEV [START_REF] Gong | [END_REF]]. DDP is generally aimed to obtain, or evaluate the high performance of HEVs, easy, imple-implemented using state machine logic. Although it has been success-fully used in commercial HEVs, like Toyota Prius, due to fixed rules, it lacks the flexibility to different driving cycles and the ability to deal mentable, and best-performing rules in a rule-based energy management strategy [START_REF] Ao | Exploring the fuel economy potential of ISG hybrid electric vehicles through dynamic programming[END_REF]].Although some feasible rule extraction methods have been proposed [START_REF] Bianchi | [END_REF]], [Yu 2009], the rule extraction process is generally timeconsuming; moreover, extracted rules are only suitable for a specific driving cycle. To overcome the above drawbacks of DDP, [Lin 2004] first propose SDP energy management strategy.

SP-SDP can benefit from an SDP-based energy management strategy with better SOC control and fewer parameters to adjust without a discount factor. After that, [START_REF] Opila | [END_REF]], [Opila 2013], developed an energy management strategy based on SP-SDP, with a series-parallel HEV that takes account of fuel saving and drivability; while Moura et al. designed a battery health-conscious energy management strategy by applying SP-SDP. Various extended algorithms based on DP are implemented to decrease computational load and dependence on future driving cycles of DP. Fast Dynamic Programming (FDP) [START_REF] Bin | [END_REF]], Neuro-Dynamic Programming (NDP) [START_REF] Boyali | [END_REF]], Iterative Dynamic Programming (IDP) [Wang 2012], boundary-line DP [START_REF] Sundström | [END_REF]], two-scale DP [START_REF] Gong | [END_REF]], multi-rate DP [START_REF] Johri | [END_REF]], and hybrid optimal energy management strategy combining DP and classical control theory [START_REF] Ngo | [END_REF]] are proposed to improve computational efficiency.

Also, an online learning energy management strategy composed of SDP and Temporal Difference (TD) method is used to improve the robustness to varying driving cycles and lower computational cost simultaneously [START_REF] Li | [END_REF]].

To overcome the above disadvantages, the second approach is based on the future driving condition from the driving cycle [START_REF] Kim | [END_REF]], [START_REF] Boehme | [END_REF]] or driving cycle recognition [START_REF] Jeong | [END_REF]]. For driving cycle prediction, the driving information is collected from a global position system (GPS). The optimal value of initial costate is approximated on the basis of effective SOC drop rate and effective mean required power in [START_REF] Kim | [END_REF]] while it is estimated based on cruise time and available regenerative energy in [START_REF] Razavian | [END_REF]]. Different from the methods proposed by [START_REF] Kim | [END_REF]] and [START_REF] Razavian | [END_REF]], Boehme et al. [START_REF] Boehme | [END_REF]] and Kim et al. [START_REF] Kim | [END_REF]] determine initial costate by solving an obvious optimal control problem with an indirect variation of extremals such as dampened Newton-method and a shooting method with multiple initial conditions based on Newton-Raphson method. Except for the estimation of initial costate, the discrepancy between the computation load of PMP and computational power of the vehicle controller also limits the application of PMP on a real-time control system. Generally, the look-up table is an excellent solution to the limits of storage capacity and computational power for the vehicle controller, which has been used to implement PMP online [START_REF] Boehme | [END_REF]]. However, the size of the table will grow exponentially with the number of dimensions. Therefore, approximate PMP (A-PMP) is introduced by Hou et al. [START_REF] Hou | [END_REF]]. Due to difficulty in dealing with inequality constraints, control variable parameterization methods are not suitable for solving optimal control problems of HEVs. So, only direct collocation methods are employed to solve optimal control problems of HEVs [START_REF] Pérez | [END_REF]]. Other optimization methods that were used in energy management optimization control for HEVs include GT [START_REF] Dextreit | Game theory controller for hybrid electric vehicles[END_REF]], stochastic optimal control [Kolmanovsky 2008] and nonlinear optimal regulation feedback control [Sampathnarayanan 2014].

For example, the Sequential Quadratic Programming (SQP) algorithm has been applied in the optimization of energy management strategy parameters for a parallel HEV [Oh 2007].

Derivative-free methods that applied to energy management methodology optimization of HEVs mainly include simplex method [START_REF] Tseng | [END_REF]], modified simplex method [Zhang 2001], complex method [START_REF] Shuaiyu | [END_REF]], DIRECT [START_REF] Gao | [END_REF]] and stochastic search methods (also called meta-heuristic search methods) [START_REF] Montazeri-Gh | [END_REF]]- [Wu 2014b]]. Due to global optimality and robustness, stochastic search methods are more suitable for optimal control problems of HEVs and thus attract more attention. These stochastic search methods include GA [START_REF] Montazeri-Gh | [END_REF], SA [Wang 2007], PSO [START_REF] Wu | [END_REF]], EA [START_REF] Zhang | [END_REF]], BA [Long 2012], and PCOA [Wu 2014a]. Each algorithm has its advantages and disadvantages, Adaptive SA(ASA) [Wang 2014], Adaptive Differential Evolution Algorithm (ADEA) [Wu 2011], genetic-algorithm swarm hybrid algorithm [START_REF] Niu | [END_REF]], Real-valued GA (RGA) [START_REF] Xiong | [END_REF]], space exploration and unimodal region elimination (SEUMRE) [START_REF] Younis | [END_REF]] also have been proposed to improve convergence velocity and robustness.

In order to overcome the above limits, a varying-domain the method is presented to give a flexible priority among multi-objectives [Zhang 2014], improved non-dominated sorting genetic algorithm (NSGA-II) is utilized to solve multi-objective problems directly [Fang 2011]. However, like dynamic optimization methods, all above static optimization methods are sensitive to the driving cycle. Hence, driving cycle recognition is also necessary for improving the adaptability of this kind of method [Liang 2009].

URV energy planning

Most of the URVs used for robotics and civil applications present a low autonomy. Therefore, it is essential for URV routing algorithms to accurately model battery life. According to [START_REF] Abousleiman | Electric vehicle modelling and energy-efficient routing using particle swarm optimisation[END_REF]] and [Thibault 2018], this can be achieved by integrating the URVs dynamics with routing. As mentioned by the authors, for powered URVs, a proper modelling of the actual fuel consumption must include, for instance, the current weight, the distance, the velocity and climb/descent rate. URV energy planning can be defined as the operation to execute before the realization of the everyday tasks in autonomous driving, as trajectory planning, path planning, routing, and task allocation. In our work, we proposed two main methodologies for energy planning, Discrete methodology, and continuous methods. The Discrete methodology is based on the application of graph search methods on a digraph where the energy represents the cost of travelling from one node to another. The nodes in the digraph represent the segments of the path obtained after geometrical filtering. Graph search methods like dynamic programming [START_REF] Bensekrane | [END_REF]], Dijkstra, and A * are applied to obtain the optimal energy consumption of the vehicle. The continuous methodology is another approach of energy planning. This methodology consists of the use of mono-objective algorithms which can be solved with fmincon solver, Interior Point OPTimizer (IPOPT) solver or YALMIP solver, etc ..., or with multi-objective algorithms which can be solved with Genetic Algorithms (GA).

Conclusion

This chapter presents the global positioning of our work in terms of power consumption estimation and energy planning strategies. The rest of the thesis manuscript is organized as follows. In Chapter 3 a power estimation consumption is studied for different configuration driving modes with a quantitative and qualitative approach. Chapter 4 present a discrete methodology of energy planning. Whereas in Chapter 5 a continuous energy planning methodology is developed. Finally, in Chapter 6 a continuous energy planning methodology is developed.

Chapter 3

Power Consumption Modeling for

Over-actuated URVs

Introduction

URVs consume a substantial amount of energy while executing their tasks and missions. As the primary source of energy for autonomous electric URVs, the energy efficiency of these robots should be taken into consideration. The energy consumption model is the solution to investigate and develop the energy efficiency of URVs. In chapter 2, a comprehensive literature review of power consumption modelling is studied for URVs. Generally, most of the robots used have a differentiated driving configuration of velocity or skid driving. Power consumption has been considered for conventional vehicles, but no generic modelling has been highlighted to model the case of an over-actuated URV. This chapter focuses on the energy consumption modeling of URVs with two main methods. An analytic model with a global formulation of the power consumption taking into account the different parameters of kinematic properties. The second method consists of the use of Artificial Intelligence (AI) based on Neuro-Fuzzy Logic. A comparison of the power consumption of the autonomous URV RobuCAR for its different driving configurations is studied.

Quantitative approach of power consumption modeling estimation

In the present work, we propose a model of power consumption calculation expressed in function of the degree of steerability, the degree of redundancy and the path curvature. The aim is to formulate the power consumption according to geometric (path curvature) and kinematic (degree of steerability and degree of redundancy) parameters of the UV and its surrounding environment (forces and torques) in expressions of ground interaction. In this work, we examine only wheeled unmanned road vehicle.

The schematic top view of the considered URV is shown in Fig. 3.1, where all the dimensions and the forces operating on the system are described. The body-fixed frame is attached to the CoG of the URV, where X and Y axes represent longitudinal and lateral directions, respectively. The yaw motion of the URV is about an axis perpendicular to the X -Y plane. Referring to Fig. 3.1, F x i and F y i represent the traction and cornering forces acting on the i th wheel, respectively, where the subscript i represents the wheel number (i =1, 2, 3, and 4, for the front left, front right, rear left, and rear right wheel, respectively). The steering angle of the i th wheel is denoted by α i , and the dimensions of the chassis are represented by l s , l r , and l f . The yaw angle of the vehicle is denoted by β. The forces acting on CoG are represented by F x and F y in the longitudinal and lateral directions, respectively. The yaw moment of CoG is represented by M z . The effects of the suspensions are neglected on the overall dynamics because the URV is moving with low velocity and on a plane area.

1 x F 1 y F 2 x F 2 y F 4 x F 4 y F 3 x F 3 y F z M  1  f l r l s l s l 2  3  4  CoG Y X v
The overall power consumption can be decomposed into three elements of power estimation including inertia power Pi , rolling resistance power Pr , and 3.2. Quantitative approach of power consumption modeling estimation 47 gravitational power Pg . For general formulation of power consumption, we add the static power Ps caused by various electrical components.

P = Pi + Pr + Pg + Ps (3.1)
where,

Pi = qT M (q)q (3.2) Pr = qT H( q, q) (3.3) Pg = qT G(q) (3.4)
The power caused by the rolling resistance has a relation with the curvature of the trajectory C, the degree of steerability δs, and the degree of redundancy δ R .

Pr = qT H( q, q) = v β F t M Z T = (F t + M Z β v )v (3.5) C = β v (3.6)
The linear and angular velocities of the URV are denoted by v and β, respectively. From equations (3.5) and (3.6):

Pr = (F t + M Z C)v (3.7)
where, F t is total traction force, which is given by:

F t = (F 2 x + F 2 y ) (3.8)
The Ackerman steering angles [Jazar 2017] are given by:

tan α 1 = l f 1 C -ls 2 (3.9) tan α 2 = l f 1 C + ls 2 (3.10) tan α 3 = l r 1 C -ls 2 (3.11) tan α 4 = l r 1 C + ls 2 (3.12) cot α f = cot α 1 + cot α 2 2 (3.13) cot α r = cot α 3 + cot α 4 2 (3.14)
where, α f and α r denote the equivalent angles for front and rear steering respectively. Power consumption for a URV can be estimated in terms of longitudinal F x and lateral F y forces, and yaw moment M z about the axis perpendicular to the plane of motion. F x , F y , and M z can be given by [START_REF] Wang | [END_REF]]:

F x = 4 i=1 F x i cos α i - 4 i=1 F y i sin α i (3.15) F y = 4 i=1 F x i sin α i + 4 i=1 F y i cos α i (3.16) M z = 4 i=1 (-1) i l s (F x i cos α i -F y i sin α i )+ 2 i=1 l f (F x i sin α i + F y i cos α i )- 4 i=3 l r (F x i sin α i + F y i cos α i ) (3.17)
In the above equations (3.15) to (3.17), F x , F y , and M z are calculated for a single configuration only, while δ S and δ R are not included in the model. Therefore, we propose a model for calculating F x , F y , and M z in terms of δ S and δ R , so that these forces can be calculated for different configurations. The forces and moment can be given by [START_REF] Bensekrane | [END_REF]]:

F x = δ R -δ S +3 i=1 F x i cos α i - δ R -δ S +1 i=1 δ S 2 (3 -δ S ) F y i sin α i - δ R -δ S +3 i=δ R -δ S +2 δ S 2 (δ S -1) F y i sin α i (3.18) F y = δ R -δ S +3 i=1 F y i cos α i + δ R -δ S +1 i=1 δ S 2 (3 -δ S ) F x i sin α i + δ R -δ S +3 i=δ R -δ S +2 δ S 2 (δ S -1) F x i sin α i (3.19)
3.2. Quantitative approach of power consumption modeling estimation 49

M z = δ R -δ S +3 i=1 (-1) i l s F x i cos α i + δ R -δ S +1 i=1 l f F y i cos α i - δ R -δ S +3 i=δ R -δ S +2 l r F y i cos α i + δ R -δ S +1 i=1 (-1) i+1 l s δ S 2 (3 -δ S ) F y i sin α i + δ R -δ S +3 i=δ R -δ S +2 (-1) i+1 l s δ S 2 (δ S -1) F y i sin α i + δ R -δ S +1 i=1 l f δ S 2 (3 -δ S ) F x i sin α i - δ R -δ S +3 i=δ R -δ S +2 l r δ S 2 (δ S -1) F x i sin α i (3.20)
Refer to equations (3.5) to (3.17) and (3.18) to (3.20), the power consumption estimation for the URV is developed, which includes δ R , δ S , and C. Therefore, the power consumption for a URV can be estimated for the different configurations (single, dual, and skid) and for the different degree of actuation redundancy for a given trajectory of varying curvature. The wheel and ground contact forces F x i and F y i can be estimated using the magic formula given by Pacejka [START_REF] Pacejka | Hans Pacejka. Tire and vehicle dynamics[END_REF]]. Hence, the proposed model for the power consumption estimation can be exploited for power planning of a URV for a specific task with different configurations.

The formulation given in [START_REF] Bensekrane | [END_REF]] for the analytic model is considered for fully actuated URV. How this new formulation compared to the one given in [START_REF] Bensekrane | [END_REF]], and how it is derived for F x , F y , and M z which can also handle the case of not-actuated wheels.

F x = δ R -δ S +1 i=1 F x i cos α i + δ R -δ S +3 i=δ R -δ S +2 1 2 (1 -δ S + δ R )F x i cos α i - δ R -δ S +1 i=1 δ S 2 (3 -δ S ) F y i sin α i - δ R -δ S +3 i=δ R -δ S +2 δ S 4 (δ S -1)(1 -δ S + δ R ) F y i sin α i (3.21) F y = δ R -δ S +3 i=1 F y i cos α i + δ R -δ S +3 i=δ R -δ S +2 1 2 (1 -δ S + δ R )F y i cos α i + δ R -δ S +1 i=1 δ S 2 (3 -δ S ) F x i sin α i + δ R -δ S +3 i=δ R -δ S +2 δ S 4 (δ S -1)(1 -δ S + δ R ) F y i sin α i (3.22) M z = δ R -δ S +1 i=1 (-1) i l s F x i cos α i + δ R -δ S +3 i=δ R -δ S +2 1 2 (1 -δ S + δ R )(-1) i l s F x i cos α i + δ R -δ S +1 i=1 l f F y i cos α i - δ R -δ S +3 i=δ R -δ S +2 1 2 (1 -δ S + δ R )l r F y i cos α i + δ R -δ S +1 i=1 (-1) i+1 l s δ S 4 (δ S -1)(1 -δ S + δ R ) F y i sin α i + δ R -δ S +3 i=δ R -δ S +2 (-1) i+1 l s δ S 2 (δ S -1) F y i sin α i + δ R -δ S +1 i=1 l f δ S 2 (3 -δ S ) F x i sin α i - δ R -δ S +3 i=δ R -δ S +2 l r δ S 4 (δ S -1)(1 -δ S + δ R ) F x i sin α i (3.23)
Due to the presence of unknown dynamic parameters of the URV and uncertainties about its interaction with the environment, it is difficult to estimate with accuracy the efforts due to the interaction wheel-ground. Thus, an artificial intelligence technique based on a data-learning qualitative method for power consumption estimation is proposed, namely: Adaptive Neuro-Fuzzy Inference System (ANFIS).

3.3. Qualitative approach of power consumption modeling estimation51

Qualitative approach of power consumption modeling estimation

In this section, we present a qualitative data-learning approach, based on Adaptive Neuro Fuzzy Inference System (ANFIS) for power consumption estimation, where both of the velocity profile and the driving modes are considered. The estimation is compared with the experimental measurements taken from a real URV, i.e. RobuCAR. This choice is motivated mainly by the topology of the sampled input-output data pairs. However, the power consumed by the URV abruptly can change from one range of the input parameter values to another. This is due to the conditions of driving the URV and uncertainties on vehicle dynamics and interfered environment. Thus, the aim of this work is to classify the sampled input-output data pairs in clusters and proceed in local regression, thereafter. The fuzzy logic layers perform clustering while the neural network layers handle local regressions. The principle is to build an ANFIS model which emulates the different URV's driving modes. However, if we consider the six driving modes described above, the URV's dynamic behavior can change from one mode to another. to improve the regression performance, six separate ANFIS models are considered, one for each driving mode. In the following subsections, the ANFIS architecture and the data-learning algorithm are presented.

ANFIS architecture

The considered ANFIS is structured as in Fig. 3.2, where the model inputs are the curvature of the road C, the velocity V and the acceleration A of the URV, while the power P which is consumed by the URV is considered as an output of the ANFIS model. For that, the Takagi and Sugeno's type rules are considered [Jang 1993] as follows:

Rule1: If C is C 1 and V is V 1 and A is A 1 , then P is p 1 C + q 1 V + r 1 A + s 1 .
Where, p 1 , q 1 , r 1 , and s 1 are constants, while, V 1 , A 1 , and C 1 , are the fuzzy sets in the antecedents parts of the rule, and

P = f (C, V, A) is a crisp function in the consequent part.
The output of each ANFIS layer is evaluated as follows: Layer 1: Each i th node in this layer is given by:

O 1 i = µ A i (x) (3.24)
where, x is the input to i th node, A i is the linguistic variable associated with this node function, and µ A i is the membership function of A i . The generalized bell-shaped membership function is chosen for µ A i (x) :

µ A i (x) = 1 1 + (x -c i /a i ) 2 b i (3.25)
where, {a i , b i , c i } is the premise parameter set.

Layer 2: Each node in this layer calculates the firing strength w i of a rule. The output of each node is the product of all the incoming signals to it:

O 2 i = w i = µ C i (C) × µ V i (V ) × µ A i (A), i = 1, 2, ..., n. (3.26)
Layer 3: The output of each node represents the normalized firing strength, which is given by:

O 3 i = w i = w i w 1 + w 2 + • • • + w n (3.27)
Layer 4: Every i th node in this layer is an adaptive node, associated to a function given by:

O 4 i = w i f i = w i (p i C + q i V + r i A + s i ) (3.28)
where, w i is the output of Layer 3 and {p i , q i , r i , s i } is the consequent parameter set.

Layer 5: This layer comprises one node, and computes the overall output as the summation of all incoming signals, i.e,

O 5 i = i w i f i = i w i f i i w i (3.29) 3.
3. Qualitative approach of power consumption modeling estimation53

Data-Learning algorithm

By observing the ANFIS structure, it can be observed that the values of the premise parameters and the output of the system can be expressed as a linear combination of the consequent parameters (p 1 , q 1 , r 1 , s 1 , . . . , p n , q n , r n , s n ) as follows:

P = w 1 w 1 + w 2 + • • • + w n f 1 + w 2 w 1 + w 2 + • • • + w n f 2 + • • • + w n w 1 + w 2 + • • • + w n f n = w 1 f 1 + w 2 f 2 + • • • + w n f n = (w 1 C) p 1 + (w 1 V ) q 1 + (w 1 A) r 1 + (w 1 ) s 1 + (w 2 C) p 2 + (w 2 V ) q 2 + (w 2 A) r 2 + (w 2 ) s 1 + • • • + (w n C) p n + (w n V ) q n + (w n A) r n + (w n ) s n (3.30)
In the learning process, the following parameters are recognized by using the least squares calculated in the forward pass. In the backward pass, the premise parameters are updated by the mean of the gradient descent algorithm using the error signals [Jang 1993].

Estimation of Power Consumption

The database for ANFIS model learning is built by SCANeR TM studio. Different training paths containing data of the curvature points in the vehicle's trajectory are considered. In SCANeR TM studio environment, the velocity profile is varied in the range [START_REF] Burghardt | Monitoring the parameters of the robot-operated quality control process[END_REF]16] km/h with a step size of 1 km/h for each driving mode; then, velocity profile, acceleration, path curvature, and the consumed power are recorded. We obtained the databases described in Table 3.1. Each database is divided into three subsets: training, validation and test sets. The training set is used during the learning phase, and the test set is only used to evaluate the performance of ANFIS models. For a good generalization and to avoid the over-fitting situation, the validation set is used during the training phase and the early-stopping method is applied for training. The early-stopping method requires that after a period of training (an epoch) using the training set, the weight matrices of ANFIS are fixed, and the ANFIS operates in the forward mode utilizing the validation set. The process is reiterated until the mean square error from learning (ML) on the validation set reaches its minimum value. Fig. 3.3 describes the flowchart for the estimation of power consumption. For a given trajectory, the inputs of the training model are driving modes, road profile (curvature of the trajectory), velocity and acceleration profiles.

Road profile

For the road geometry, we used a Geographical Information System (GIS) to represent the road by polylines [START_REF] Jakkula | [END_REF]], describing the central axis of its surface. Each point of this polyline is defined by the 3D geographic coordinates (longitude, latitude, and altitude). This discrete representation is not always appropriate for realistic simulation or path planning. A continuous representation, often parametric, is necessary to estimate all the parameters required for the calculation (contact angle of yaw, radius, etc.) in each point of the curve. To simplify this representation, the road path is decomposed into horizontal and vertical curves representing respectively the roads mapped onto the plane (Fig. 3.4). In this work, the cubic spline interpolation approach for polylines is used to describe the real trajectory [Ahlberg 1967].

The GIS data for real road is often affected by errors of acquisition systems, which explains the fluctuations presented in the estimated curvature of the 2D trajectory for the University of Lille campus as shown in Fig. 3.5.

For ANFIS parameters initialization, three membership functions are considered for each linguistic variable, and the grid partitioning method is used to initialize the fuzzy rules, the premise, and the consequent parameters. The ANFIS models converge approximately after 2000 epochs. In Table 3.1, different ML are obtained on the corresponding test sets.

Experimental results and Model validation

To estimate the URV's power consumption with all possible driving modes and velocity profile along a defined trajectory, it is useful to use a professional realtime simulation software of vehicle dynamics [Okt ] called SCANeR TM studio, that can emulate the numerous experimental scenarios that we should realize with the real URV Fig. 3.6. With SCANeR TM studio, it is possible to simulate both: the vehicle dynamics, the terrain, and the environment. For that, we need first to validate the vehicle dynamics of the URV from the simulator. To A comparison between experimental and simulated angular velocities for each wheel, the longitudinal acceleration of CoG, steering angles for each wheel, the lateral acceleration of CoG, of the RobuCAR URV are given respectively in Fig. 3.8, Fig. 3.9, Fig. 3.10 and Fig. 3.11 respectively. Fig. 3.12 compares between experimental and simulated (a) battery voltage, (b) battery current, and (c) power consumption of the RobuCAR URV. The difference in the battery voltage and power consumption amplitudes between the real measures and simulated data can be explained in part by the presence of uncertainties related to the driving wheel-road efforts, where they are difficult to reproduce accurately as in the experiments. Therefore, the estimated power consumption using the simulator SCANeR TM studio conforms macroscopically to the profile of the power of the real RobuCAR. Due to the use of a numerical filter, the amplitude of the power consumption differs from the simulated and the real power consumption.

In Fig. 3.13(a) and (b), a superposition between the power-time consumption, calculated from ANFIS, from Analytic model, and the experiments are shown for the Skid4 and Skid2 cases, while in Fig. 3.14(a) and (b), show the comparison between the power consumption, calculated from ANFIS, from Analytic model, and the experiments in case of Single4 and Single2. Finally, in Fig. 3.15(a) and (b), comparison between the power consumption from ANFIS, from Analytic model, and the experiments in case Dual4 and Dual2 steering configurations is shown. From the results of power consumption estimation, it can be observed that ANFIS and analytic models follow the experimental power consumption, and it can be seen that the Skid2/4 consume more power than other modes, but the power consumption can be less with Single2, Single4, Dual2, or Dual4 mode at different points of trajectory as shown in Fig. 3.14-Fig. 3.15. It can be noticed also that the ANFIS model show better accuracy than the analytic models. The values of mean errors for each mode are given in Table 3.1. ML 3.03e -2 2.27e -3 2.56e -3 2.01e -2 8.21e -4 1.06e In Table 3.1, MS is mean square error from simulation, where the unit of ML and MS is Watt. DS is a set of data samples for the learning process in ANFIS, the duration time for a skid2 sample with 1 km/h is 7.82e3 seconds and the traveling length is 2177.1 m. Similarly, the time duration for other driving modes depends on the given velocity.

Conclusion

The estimation of power consumption for an over-actuated URV is important for power planning, due to its different configurations and significant power consumption in the curvature of the trajectory. In this chapter, two approaches are proposed to estimate the power consumption estimation for different configurations of a URV in terms of the degree of steerability, the degree of actuator redundancy, and the curvature of the trajectory. The proposed models are validated through experiments of a URV called RobuCAR. Therefore, the proposed models can be used for power planning of a URV to perform a specific task for its different configurations. For future work, it is interesting to extend the proposed work for power estimation in the presence of faults in actuators.

Introduction

In the last decade, autonomous vehicles have been increasingly used in many sectors such as industry and planetary exploration. These vehicles contribute to reducing CO 2 emission inside big cities and enable to perform autonomous operations in unknown and confined spaces [Kumar 2014]. The performances of these systems to achieve successful missions depend strongly on the deployment of efficient algorithms for path planning [Chen 2018], velocity planning [START_REF] Goto | [END_REF]], autonomous control [Barthelmes 2017], energy management [START_REF][END_REF]]. Despite the numerous advantages of using Unmanned Road Vehicles, their autonomous navigation is substantially dependent on the performances of the batteries. Thus, the management of the battery's power is a recent research topic, dealing with the issue of sustainable URV. The estimation of the power consumption needs an accurate behavioral model to evaluate the overall energy, necessary to drive the vehicle autonomously. In this chapter, a discrete energy planning for over-actuated unmanned road vehicles (URVs) with redundant steering configuration is proposed. After that, an optimization algorithm is applied on the digraph to get a global optimal solution combining driving mode, power consumption and velocity profile of the URV. Results are compared with those given by the dynamic programming method for global offline optimization. Finally, the obtained simulations and experimental results, applied to RobuCar URV, highlight the effectiveness of the proposed energy planning.

Main contributions

the main contributions of this work can be summarized as follows:

• Energy digraph is developed with all feasible configurations taking into account kinematic and dynamic constraints based on a 3D grid map, in the function of velocity, arc-length and driving mode.

• Discrete Energy planning for over-actuated URVs is developed with a variable step in time or in the distance. It calculates the optimal velocity profile and the corresponding driving mode for each segment of the trajectory, taking into account the road curvature and the kinematic parameters of the URV.

• Simulations and Experimental results have been applied on a real overactuated URV called Robucar, in presence of six decentralized driving modes.

Problem formulation

The problem of energy planning can be stated as an optimization problem as follows:

min V i,k ,M i,m J = n i=1 Pi,k (t i , V i,k , A i,k , C i , M i,m ) × (∆t i ) (4.1) subject -to t i < t max V min ≤ V i,k ≤ V max A min ≤ A i,k ≤ A max (4.1a)
Where, V i,k , A i,k represent respectively the k th velocity and the acceleration profiles, defined for the i th road segment. M i,m is the m th driving modes for the i th road segment and Pi,k is the k th consumed power by the URV for the i th road segment. The parameters t i and C i represent respectively the traveling time and the curvature of the i th road segment respectively. m depends on the number of the independent steering system and actuated wheels. t max is the maximum time imposed to finish the travel, while lower and upper limits of V i,k and A i,k are A min to A max and V min to V max , respectively. The longitudinal velocity is bounded by the lateral acceleration A y for the stability of URV, which can be given as follows.

A y = V i,k 2 C i (4.
2)

The condition for the non-rollover of URV:

mA y h < mg d 2 (4.3)
where, m, g, d, and h are mass, acceleration due to gravity, wheel base, and height of CG from ground, respectively. Hence, V i,k is given by:

V i,k < mgd 2C i h (4.4)
This optimal control problem will be solved by an optimal search on a power digraph as explained in the following section.

Descrete Energy Planning for Autonomous Navigation of the URV

The proposed methodology for energy planning is briefly described in Fig. 4.1.

The approach is categorised into two main phases. In the first phase of preprocessing, power consumption estimation is developed based on data of the terrain, the vehicle, and the assigned task. The second phase concerns the optimization process of the power concerning the velocity profile and the driving modes.

Modeling assumptions: i) RobuCAR URV moves in a known situation and the dynamic limitations including other road users are not taken into consideration, ii) the URV moves on a planar surface and the road elevations are not considered i.e, the roll and pitch effects are neglected, iii) frequent switching of driving modes from one mode to another mode is possible, and iv) the URV moves with a low velocity under 16 km/h which is the most extreme speed of RobuCAR; thus,effects of aerodynamics are ignored. These assumptions can be justified because of the known condition and low speed of URV, which decrease unnecessary complexity in the model and computational expense.

Pre-Processing Phase: Power Consumption Estimation

In this subsection, we present a qualitative data-learning approach, based on Adaptive Neuro Fuzzy Inference System (ANFIS) for power consumption estimation, where both of the velocity profile and the driving modes are considered. The estimation is compared with the experimental measurements taken from a real URV, i.e. RobuCAR. This choice is motivated mainly by the topology of the sampled input-output data pairs. However, the power consumed by the URV abruptly may vary from one range of the input parameter values to another. This is because of the conditions of driving the URV and difficulties on vehicle dynamics and interfered environment. Thus, this work aims to categorize the sampled input-output data pairs in clusters and proceed in local regression, after that. The fuzzy logic layers perform clustering while the neural network layers handle local regressions. The principle is to build an ANFIS model which emulates the different URV's driving modes. However, if we consider the six driving modes described above, the URV's dynamic behaviour can change from one mode to another. Therefore, six separate ANFIS models are considered, one for each driving mode, to improve the regression performance. In the following subsections, the ANFIS architecture and the data-learning algorithm are presented.

Optimization Phase: Energy planning

The proposed energy planning methodology is elaborately shown in Fig. 4.2. Graph theory is used to evaluate the optimal path for satisfying the driving mode and the energy minimization concerning the velocity profile and roadpath curvature. A graph is a discrete form of the intricate problem described by the relation (4.1).

Descrete Energy Planning for Autonomous Navigation of the URV 69

First, a directed graph is created to promote the optimization process (Fig. 4.5). The assigned mission path is divided into a finite set segments based on the curvature information by taking into consideration three types of road segments, namely: line, clothoid and arc.

The digraph is a weighted directed graph, where the edges have directions associated with them [START_REF] West | Introduction to graph theory[END_REF]]. A directed graph is an ordered pair G = (V e, Ed), where V e is a set of vertices representing endpoints of each segment, and Ed is a set of edges representing the connection between vertices as a function of velocity, driving mode, and arc-length. The weight on each edge represents the energy consumed by the URV to travel on the corresponding segment for each driving mode.

Each vertex is denoted with a specific number say, jkl ; where j, k, and l represent j th row of the velocity vector, k th row of the driving mode vector, and l th row of the segment vector. In addition, a starting and an ending vertex are added on the top and the bottom of the digraph. The starting vertex is connected to the first set of vertices with zero weights on edges. Similarly, the ending vertex is connected to the last set of vertices with zero weights on edges.

In fact, for the i th segment, the curvature of the trajectory can take three forms [START_REF] Olver | [END_REF]]:

C i =    0 Straight line constant Arc as + b Clothoid (4.5)
where, s represents the arc-length; while a and b are constant parameters of the Clothoid in Cs plan.

For the subsequent development, a road profile of the "cité scientifique" campus of the University of Lille is taken into consideration. The calculated and filtered curvatures of this road geometry are represented in Fig. 4.3 (C -s plane). In Fig. 4.4, the estimated and filtered trajectories of this 2D-road are discretized into 138 segments. The difference between real and filtered curvature is due to the change of interpolation of the real curvature from cubic spline to linear interpolation in filtered curvature. Due to this interpolation change, the corresponding actual and filtered trajectory are represented in Fig. 4.4.

Further, a 3D grid is developed according to three axes: velocity, segment arc-length, and driving mode (Fig. 4.5). In this grid, all feasible points for each driving mode are identified based on kinematic constraints of the URV. Indeed, in each segment, a unique drive pattern is applied, as shown in Fig. 4.6. Besides, it is considered that each section (line, clothoid, arc) has the constraint of driving mode, which is detailed in Table 4.1. After that, the required energy to travel each segment of the road is calculated. This allows us to set up the weights on the edges of the digraph.

Driving mode

Line Energy planning is calculated from the constructed digraph by starting at one vertex and exploring adjacent vertices until the destination vertex is reached to find the optimal path. The research is conducted employing two methods, namely Dijkstra and A * algorithms and associated with the dynamic programming (DP) method as a reference. The output of the complete process is the optimal driving mode and the optimal velocity profile for each segment of the trajectory. Based on the built graph, the energy optimization problem (4.1) is formulated in a discrete form as follows:

c = 0 Clothoid c = var Arc c = cst Skid4 (δ s = 0, δ R = 1) X X X Single4 (δ s = 1, δ R = 2) X X Dual4 (δ s = 2, δ R = 3) X X Skid2 (δ s = 0, δ R = -1) X X X Single2 (δ s = 1, δ R = 0) X X Dual2 (δ s = 2, δ R = 1) X X
sm min v max v v  s  Top view ij M1 ij Mk ij Mk ij M2 ij M2 ij M2 ij M1 ij M1 Figure 4.5: Energy digraph in 3D grid. V V V t t t i t 1 i t  i v 1 i v  v 0 a  0 a  0 a  () a () b () c i t 1 i t  i v 1 i v  i t 1 i t 
E k (t i , V i , C i , M i,k ) = t k+1 t k P k ∆t i (4.6)
Where, P k represents instantaneous power consumption calculated from the ANFIS model for the k th configuration of the URV, and ∆t i is the travel time for i t h segment. In the following, we resume the principle of the global offline optimization methods used for energy planning.

Dynamic Programming

To resolve the nonlinear problem of energy planning, an algorithm, often used to get a globally optimal, based on dynamic programming [START_REF] Bertsekas | [END_REF]] is taken into consideration. Here dynamic programming is applied on the weighted digraph. Then a 3D constructed grid consists of 3 axes: i) arc-length which is represented with a set of samples of distance d = {d 0 , d 1 , d 2 , ..., d n }, ii) velocity v = {v min : ∆v : v max }, and iii) driving mode m = {Skid4, Single4, Dual4, Skid2, Single2, Dual2}. Each point in the grid is obtained with respect to all constraints described in equation (4.1a); as shown in Fig. 4.5. In this approach, arc-length is segmented according to the geometrical criteria, which is usually a non-uniform segmentation. The sampling step of the velocity ∆V is about 0.5 km/h. Unlike the dynamic programming, Dijkstra algorithm finds the optimal global solution without covering all possible edges in the graph [LaValle 2006]. A * algorithm is a modified Dijkstra algorithm with a heuristic function, which minimizes the following function:

f (n) = g(n) + h(n),
where n is the last vertex on the path, g(n) is the cost of the path from the starting vertex to the n th one, and h(n) is a heuristic that estimates the cost of the cheapest path from vertex n to the goal. The choice of a good heuristic is very important to reduce the time calculation. In this work, a heuristic function h(n) is proposed, based on the curvature of the trajectory. The heuristic function h(n), is defined as the cost of energy from any point of the trajectory to the end with a curvature equal to zero in Cs plane, corresponding to a straight line in the xy plane.

Results and discussion

The following assumptions are taken into consideration for the proposed algorithm: i) only 2D road geometry is considered, ii) the URV has a constant acceleration in each segment, and iii) the switching between any two driving modes is possible. The developed algorithm is applied for the real trajectory of the University of Lille campus, as shown in Fig. 3.4. In Fig. 4.7 and 4.8, the optimal velocity profile and the optimal driving mode for minimum energy consumption are presented for each segment of the filtered trajectory in sv and X -Y planes, respectively. The constraint of traveling time is set to less than 40 min. The fluctuations in velocity and mode distribution are due to the noise in data acquisition and trajectory filtering. The algorithm shows that Single2 and Single4 modes are the best for the given optimal velocity profile as shown in Fig. 4.9. Moreover, the algorithm suggests a combination of Single2, Single4, Dual2, and Dual4 in sharp turns with a variation of velocity (Fig. 4.8). However, the transition from one mode to another mode is not appropriate at the sharp turns for the vehicle in real autonomous navigation. Hence, we make some correction in mode selection at sharp turns, and it is suggested to use only one steering mode as shown in Fig. 4.11 and Fig. 4.10. In the same purpose, in Fig. 4.12,Fig. 4.13,Fig. 4.14,and Fig. 4.15 the optimal velocity profile and the optimal driving mode for minimum energy consumption are presented for each segment of the filtered trajectory with time constraints of 30 min and 20 min, respectively. These results show that time constraint affects the optimal driving mode and the optimal velocity profile, but are almost the same on the sharp turns.

A comparison of energy consumption for different driving modes is given in Table 4.2. It can be observed that with the same optimal velocity profile, the energy consumption is reduced by using the optimal driving mode during the autonomous navigation of the URV. Moreover, it is corrected with the proposed post-processing at the sharp turn which leads to an increased value of energy consumption.

In Table 4.3, the time cost of the global optimization algorithms in different steps is summarized. The time taken for the construction of the 3D grid is big, which is around 99 percent of the total time. It can be noticed that A * takes very less time than Dijkstra and dynamic programming.

Conclusion

This chapter presents a methodology for the energy planning of an overactuated URV. Data-learning qualitative method (ANFIS) is utilized for power consumption estimation. The latter is calculated for different driving modes of the redundant steering system of the URV. Three optimization algorithms are tested and compared to obtain the global optimization of the velocity and the driving mode of the URV for each segment of the trajectory with the time constraint. The results show that dynamic programming, Dijkstra and A * give the global optimum, but A * is faster when a useful heuristic function is selected. For future work, the energy planning methodology is to be extended to manage URV's faults. Besides, some dynamic constraints can be added to the model to consider other road users in a dynamic environment. Discrete energy planning methodology depends on the number of segments of the path, according to its geometry, and the length of the considered path. If the path is very long, the computation time of the optimization algorithm will increase accordingly. For this case, continuous planning of the energy can be very useful to solve this optimization problem with short computation time.

particularly on the topics of design, control and planning among the fundamental issues addressed in this framework, power consumption evaluation, and management during tasks execution. In fact, despite the numerous advantages of autonomous vehicles, their limited source energy constitutes an essential constraint that should be handled carefully for rational exploitation.

The need to plan and manage the available batteries power has prompted the researchers to open new research axes. The effective estimation of vehicle power consumption is the main issue. It is addressed to establish an accurate model that permits to avoid the situation of battery discharge during the autonomous navigation. In addition to power consumption estimation modeling, it is essential to have a good methodology for energy planning. Indeed, the main objective of energy planning is to optimize energy consumption and the travel time of the URV for a given trip. Many researchers developed discrete methods for energy optimization strategies. Dynamic programming has been used to obtain the optimal energy consumption of vehicles [START_REF] Ozatay | [END_REF]], [START_REF] Zhang | [END_REF]]. Moreover, authors developed energy optimization methods using model predictive control (MPC) and compared with dynamic programming based methods [START_REF][END_REF]], [Quaglia 2016]. Furthermore, the power management has been studied by using control allocation for an over-actuated URV, based on parametric torque distribution [START_REF] Dizqah | [END_REF]]. But this approach considered only vehicle dynamics and not the road profile.

Chen et al. [START_REF][END_REF]] estimated the optimal velocity profile and torque using the dynamic programming method for a URV considering its front steering. In [Zhang 2017], neural network and MPC based method are developed for energy optimization and compared with dynamic programming algorithm. In [Liu 2017], quadratic programming is used to develop energy optimization for a URV. In a previous work of the authors [START_REF] Bensekrane | [END_REF]], a discrete energy planning methodology has been developed for over-actuated URVs with the geometrical segmentation. The discrete methodology can be very greedy in time calculation according to the number of segments of the considered path. Extending to that work, and to improve the time calculation, this work presents a continuous energy planning methodology. For most of the existing algorithms, continuous energy planning is not considered, and the influence of the curvature smoothing is not discussed.

Main contributions

Based on the above literature review, the main contributions of this work can be summarized as follows:

• A continuous energy planning methodology based on a multi-objective optimization technique is applied to each driving mode of the URV, while the considered road path is smoothed using two different methods to evaluate the effect of the path smoothness (curvature) on the energy planning methodology. The road path is modeled by using two smooth geometrical combinations: the first one is "lines, clothoids, and arcs", and the second one is "lines and Pythagorean Hodograph (PH) curves"

• A composite velocity profile is constructed based on specific points selected from the generated Pareto fronts corresponding to the different driving modes. Each selected point represents the optimum of compromise between energy consumption and the travel time. Furthermore, a Directed weighted Graph is built to achieve the optimal velocity profile and the corresponding driving mode distributions.

The main advantage of the proposed approach is its ability to generate, for the considered URV on an assigned road path, an optimum smooth velocity profile defining the adequate transitions between the driving modes.

2, 2, 1 The proposed methodology for energy planning is briefly described in Fig. 5.2. The energy planning methodology is divided into three main phases. In the first phase of pre-processing, a power consumption model is developed using a set of input data related to the terrain, vehicle, and the assigned task. The second phase concerns the path smoothing, where the generated path is obtained from filtered GIS data, according to geometrical criteria. These data are then modelled by using two smooth geometrical combinations: the first

T S R N N     2 S   2, 1, 0 T S R N N     1 S   2, 0, 1 T S R N N      0 S   4, 2, 3 T S R N N     2 S   4, 1, 2 T S R N N     1 S   4, 0, 1 T S R N N     0 S  
(δ s = 1, δ R = 2) 4 1(front) Dual4 (δ s = 2, δ R = 3) 4 2 Single2 (δ s = 1, δ R = 0) 2 1(front) Dual2 (δ s = 2, δ R = 1) 2 2
one is lines, clothoids, and arcs, and the second one is lines and Pythagorean Hodograph (PH) curves. Finally, the optimization phase gives an optimal composite velocity profile and the corresponding driving modes. hereafter, the vector of cost functions includes URV's energy and travel time. Additionally, the problem is treated under a set of constraints inherent to the vehicle's kinematic and dynamic performances and the path characteristics. In a Geographical Information System (GIS), a road is represented by polylines [START_REF] Jakkula | [END_REF]], describing the central axis of its surface. Each point of this polyline is defined by the 3D geographic coordinates (longitude, latitude, and altitude). This discrete representation is not always appropriate for realistic simu-lation or path planning. A continuous representation, often parametric, is necessary to estimate all the parameters required for the calculation (contact angle of yaw, the radius of curvature, etc.) in each point of the curve. To simplify this representation, the road path is decomposed into horizontal and vertical curves representing respectively the roads mapped onto the plane (Fig. 5.3). In this work, we use the cubic spline interpolation approach for polylines describing the considered trajectory [Ahlberg 1967].

Task data Vehicle data Terrain data

Power consumption modeling

Energy management strategy

The GIS data for real road is often tainted by errors of acquisition systems, which explains the fluctuations presented in the estimated curvature of the 2D trajectory. In this work, the following two methods are used to make a smooth path.

Method 1:

A discrete filter is developed to construct the road with its main components, namely, lines, arcs, and clothoids. The discrete filter takes one point among n s samples if the curvature is bounded between 0 and a predefined threshold e g of the curvature. If the curvature is higher than the threshold value, then only one point is selected from n t samples.

1/n t 0 ≤ C <e g 1/n s C ≥ e g (5.1)
The curvature of the trajectory can take three forms:

C i =    0 Straight line Constant Arc as + b Clothoide (5.2)
where, s represents the arc length; while a and b are constant parameters of clothoid in Cs plane. The estimated and filtered curvature for the campus of the University of Lille is shown in Fig. 5.4 (Cs plane), where e g = 0.05m -1 , e d = 20m, n s = 5, n t = 2, and total of 138 segments.

Method 2:

The road path is smoothed using lines and Pythagorean Hodograph (PH) curves. PH curves are synthetic parametric curves. These curves were introduced by Farouki and Sakkalis [START_REF] Rida | Pythagorean hodographs[END_REF]] in 1990 to overcome the drawbacks of the previously used curves, e.g., Bezier, B-splines, NURBS, etc. The most notable properties of these curves are, their arc-length has closed form solution, and they possess rational offset curves. Since then, PH curves have been used in many fields such as 3D path planning and obstacle avoidance of Unmanned Aerial Vehicles (UAVs) [Shanmugavel 2007], [Shah 2010].

In [Bruyninckx 1997], PH curves are used for path planning of mobile robots.

In this work, we exploit PH curves to generate a smooth path. In this case, the curvature of the trajectory can take two forms:

C i = 0 Straight line V ariable PH curve
(5.3) A PH curve r(h) can be constructed using the four known variables P s (position vector at the start point), d s (direction vector at the start point P s ), P f (position vector at the end point) and d f (direction vector at the end point P f ) as shown in Fig. 5.5.

P s (x s , y s ), d s (d xs , d ys ) r(h) → P f (x f , y f ), d f (d xf , d yf ) (5.4)
where, h represents the curvilinear coordinate along the curve. Fig. 5.6 shows the real curvature and the smoothed curvature using PH curves for the real road path. The objective functions to be minimized for the trajectory X(t) between initial and final states are generally expressions containing significant physical parameters related to the URV's behavior and to the efficiency of the system. Hereafter, we particularly consider the following functions :

F 1 = T, F 2 = E k (5.5)
where, T is the task duration, E k represents the consumed energy which is linked to power consumption P k , for a driving mode M k , as follows:

E k = T 0 P k dt (5.6)
The set of feasible motions is restricted by numerous constraints reflecting the physical limitations on URV's performances.

Physical limitation

The velocity profile evaluated at the center of gravity is limited with upper and lower limits as follows:

V min ≤ V ≤ V max (5.7)
The acceleration is also limited, In case of four wheels drive the limits are given by A 1min , A 1max , while the limits for the two wheels drive are given by A 2min and A 2max .

A 1min ≤ A 1 ≤ A 1max A 2min ≤ A 2 ≤ A 2max (5.8)
The different driving modes M k considered for this work are:

M k =        δ s = 1, δ R = 0 Single2 (Over-actutaed) δ s = 2, δ R = 1 Dual2 (Over-actutaed) δ s = 1, δ R = 2 Single4 (Over-actutaed) δ s = 2, δ R = 3

Energy optimization methodology

In Fig. 5.7, the proposed methodology for the continuous energy planning of an over-actuated URV is presented. The methodology is divided into three steps.

The first step includes the calculation of a set of optimum velocity profiles for different driving modes on smoothed paths, obtained using two path smoothing methods described in the previous section. This is achieved using the NSGA-II algorithm [Deb 2001], which is one of the popularly used evolutionary algorithms which attempt to find multiple Pareto-optimal solutions in a multi-objective optimization problem. From each generated Pareto front, corresponding to individual driving modes, a set of solutions (objective points) are selected to generate a set of velocity profiles. Finally, the different driving modes are combined to obtain a composite velocity profile by using a digraph representation. Dynamic programming is used to obtain the optimal solution from the constructed digraph. A PH based interpolation is used to smooth the resulting velocity profile in the different nodes of the digraph.

Pareto front generation

The procedure for generating optimal Pareto fronts regrouping the compromise URV velocity profiles is described in Fig. 5.8. As discussed earlier, we already have a smoothed path using two different methods. The algorithm aims to find, for each driving mode, solutions ensuring the compromise between the final time T f and the consumed energy E. This phase is based on a parametrization of the velocity profile using a cubic spline interpolating a set of intermediate control points uniformly distributed along the time scale [0, T f ], as shown in Fig. 5.9. The positions of these control points are investigated within the limits imposed by kinematic constraints in equations 5.7 and 5.8. The ANFIS model calculates then the power consumption for each solution candidate. Note that, a Pareto front is generated for each driving mode, thus the algorithm of Fig. 5.8 is repeated for each mode. In order to combine the different velocity profiles obtained from the selected objective points, we superimpose the different velocity profiles for various driving modes as shown in the example of Fig. 5.11. The different velocity profiles are plotted according to their arc-length to have the same reference. A directed graph is then generated to support this process (Fig. 5.12). The digraph is a weighted directed graph, where the edges have directions assigned to them [START_REF] West | Introduction to graph theory[END_REF]]. The directed graph is an ordered pair G = (V e, Ed), where V e is a set of vertices representing the different intersection points in the different velocity profiles, and Ed is a set of edges representing the connection The developed digraph is used to find the minimum energy between the starting and ending points by applying dynamic programming. A PH curve interpolation is finally applied to the constructed composite velocity profile at the intersection points.

Start End

Velocity

() Vt t f T 0 max V 1 V 2 V 3 V 4 V 5 V m V 6 V 7 V 1 t 2 t

Experimental data-based results with virtual point

control for an indoor TOMR

Robot Modeling

In this work, we consider Three-wheeled Omnidirectional Mobile Robot (TOMR) structure on a flat XY-surface. Thus, we concentrate on longitudinal and yaw dynamics, but the approach is general and allows taking into account motions such as lateral skid, pitch, and roll. Fig. 5.13 represents the three-wheeled omnidirectional mobile robot structure, that is driven by three identical DC motors. q = x y θ T represents the robot coordinates, where x and y denote the linear coordinates relative to the global frame and θ its orientation with respect to X axis. The kinematics equations of Robotino can be expressed as follows:

  V 1 V 2 V 3   =   -sin θ cos θ b -sin( π 3 -θ) -cos( π 3 -θ) b sin( π 3 + θ) -cos( π 3 + θ) b     ẋ ẏ θ  (5.10) Where V 1 V 2 V 3
T is the vector of the linear velocities of wheels. The linear and angular velocities of the robot can be obtained from Fig. 5.13 as: By combining equations (5.10) and (5.11) the equation establishing the relationship between the velocities of the wheels and those of the robot is derived.

  V 1 V 2 V 3   =   0 b -sin( π 3 ) b sin( π 3 ) b   v ω (5.
12)

The forces acting on CoG are represented by F x and F y in the longitudinal and lateral directions, respectively. The yaw moment of CoG is represented by M z . The effects of the suspensions are neglected on the overall dynamics because the TOMR is moving with low velocity and on a plane area.

Let [x(t), y(t), z(t), α(t)] represent respectively XYZ-positions of the center of mass and orientation (yaw angle) of the TOMR in an inertial coordinate system at time t. We assume that at all time z(t) = 0. Correspondingly v x = ẋ, v y = ẏ, v z = 0 are the coordinates of the heading vector

v = [v x , v y , v z ]
and ω is a yaw rate vector which is perpendicular to XY-plane, ω = ω = α.

Namely, let r c (t) be a radius vector from instant center of rotation of the TOMR on XY-plane to its center of mass. Then velocity vector for the center of mass is v = ω × r c (t).

The angular velocity vector ω and velocity vector v of the center of the TOMR are related as the vector 5.13) where R c = r c . The center of instant rotation location can be expressed via XY-position of the TOMR center, normal unit vector n to the velocity v ( n ⊥ v) and radius of rotation R c as

ω = r c × v R 2 c , (
r c = -nR c = -n 1 k , (5.14)
where k = R -1 c is the trajectory curvature. The TOMR can move on trajectory curvature k, with velocity vector v = [v x , v y , 0] T direction angle θ = atan( vy vx ) and the yaw angle α. The kinematic equations of the TOMR are

ẋ = v cos(θ) ẏ = v sin(θ), (5.15)
where

v = v = v 2 x + v 2 y . v and ω are related v = R c ω.
The equations of translational and yaw dynamics are 5.16) where m is the TOMR mass, I zz is inertia moment with respect to Z-axis, F is the force along v vector, and τ is the yaw torque.

m v = F I zz ω = τ, (
The force F and the torque τ can be expressed via torques applied to respective wheel τ 1 , τ 2 , τ 3 and resistance forces.

Velocity planning using kinetic energy planning

Let us consider a smooth path on XY-plane defined parametrically as x = X(s) y = Y (s),

(5.17) where 0 ≤ s ≤ L is a distance along the path. So, .18) We also assume that the curvature k

[X (s)] 2 + [Y (s)] 2 = 1. ( 5
(s) = X (s)Y (s) -Y (s)X (s) is a continuous function of s.
The velocity plan V (s) along the path is based on the following assumption: the TOMR constrained on the path should be moving in such a way that α = θ = tan -1 Y (s) X(s) , i.e. its center line is collinear with the heading vector as well as tangent vector to the path at all times. Let Ω(s) is the angular velocity at s then Ω(s) = V (s)k(s).

We assume that the time to reach the destination is fixed T . .19) On the other hand, the kinetic energy of the TOMR moving on such path is .21) In our development, we will consider an electric TOMR without energy recuperation, so any braking results in energy loss.

T = L 0 ds V (s) . ( 5
E kin (s) = mV 2 2 + I zz Ω 2 2 = 1 2 [m + I zz k 2 (s)]V 2 (s). (5.20) So, V (s) = 2E kin (s) m + I zz k 2 (s) . ( 5
Let us assume for a minute that there is no resistance for the TOMR moving along this path. Then neglecting the time to reach certain energy level and braking (this is a valid assumption for longer paths) it is easy to see that the optimal power saving methodology is to reach energy level E 0 such that 5.22) and then this kinetic energy should remain constant until the end of the path since slowing down results in unrecoverable energy loss. Using this quasi optimal methodology the velocity plan along the path is .23) As can be seen, increase in curvature of the path results in decrease of velocity and vice versa that is "natural" behavior of the TOMR.

E 0 = 1 2 1 T L 0 m + I zz k 2 (s)ds 2 (
V (s) = L 0 m + I zz k 2 (ξ)dξ T m + I zz k 2 (s) . ( 5
In reality, the TOMR following this path will encounter resistance that includes friction, aerodynamic drag, etc., but following such preplanned velocity profile will ensure that the TOMR energy is spent only on overcoming resistance.

Virtual Point Following Methodology

Our approach to control the TOMR so that it follows robustly the planned velocity profile derived in the previous section is based on the idea of sliding mode control and virtual point following.

Let us consider a virtual point on the path with coordinates X(s * ), Y (s * ) following the path according to the following differential equation: ṡ * (t) = V (s * (t)).

(5.24)

The equation 5.24 guarantees that the velocity of the virtual point at every s is equal to the plan V (s). Now we will derive a control for the TOMR that follows the virtual point. If x(t), y(t) is current position of the TOMR (that is not necessarily on the path) then the coordinates of the deviation error from the virtual point are e x (t) = x(t) -X(s * (t)), e y (t) = y(t) -Y (s * (t)). Differentiating and using 5.15 we have

ėx = v cos(α) -X (s * ) ṡ * = v cos(α) -X (s * )V (s * ) ėy = v sin(α) -Y (s * ) ṡ * = v sin(α) -Y (s * )V (s * ).
(5.25)

Let us consider the following relations that will be considered as desired manifold in the system state space:

v cos(α) -X (s * )V (s * ) + λe x = 0 v sin(α) -Y (s * )V (s * ) + λe y = 0, (5.26)
or v = v des , where (5.27) This can be separated into two relations one of them concerns steering: .28) and other concerning velocity

v des = [X (s * )V (s * ) -λe x , Y (s * )V (s * ) -λe y , 0] T .
α = tan -1 X (s * )V (s * ) -λ(x -X(s * )) Y (s * )V (s * ) -λ(y -Y (s * )) . ( 5
v= √ [X (s * )V (s * )-λ(x-X(s * ))] 2 +[Y (s * )V (s * )-λ(y-Y (s * ))] 2 .
(5.29)

If these equations are valid then ėx = -λe x ėy = -λe y .

( 5.30) where λ > 0. It implies that e x → 0, e y → 0 when t → ∞. The relations 5.23, 5.24, 5.28, 5.29 represent the control algorithm. Practical implementation may include additional features taking into account steering actuator dynamics as well as TOMR and engine dynamics, but the main idea remains the same: maintaining relations 5.26, or equivalently 5.27.

Energy Model of Robotino

The energy estimation model of Robotino can be expressed as follow [START_REF] Liu | [END_REF]]: 5.31) where E Total , E Motor , and E Other denote the total energy of the robot, motor energy and static energy respectively. µ, b, and Γ represent the friction coefficient, the distance between the wheel and CoG, and the angular acceleration respectively, while P s represents the static power consumption of the embedded PC and different sensors.

E Total = E Motor + E Other = t m max{V (t)A(t), 0} + I zz max{Ω(t)Γ(t), 0} +2µmg max{|V (t)| , |bΩ(t)|} dt + P s t (

Experimental Results And discussion

Description of holonomic robot Robotino

The Robotino robot is supplied with two 12V batteries which permit a running time of up to two hours. The robot's dimensions are 450 mm in diameter and 290 mm in height with an overall weight of approximately 21kg. The platform embeds numerous application programming interface layers. While the Linux layer provides standard user space, the platform can also be controlled by external PC via the wireless communication, by using the real time Linux layer. Experimental tests were performed by using a set of external Motion Capture Systems called OptiTrack. A total of 8 OptiTrack cameras (4 Prime-13 + 4 Prime-13W), are used to give the position and orientation of the robot with an error of 0.13mm. The path is generated inside an area of 4m x 6m as shown in Fig. 5.15.

Constant kinetic energy approach

The experiments are done for Robotino with constant kinetic energy E kin = 0.117J. The results of the path following are given in Fig. 5.16, Fig. 5.17 and Fig. 5.18. Refer to Fig. 5.16 and Fig. 5.18. we notice that the virtual control point algorithm shows a very good accuracy in path tracking and following the given velocity profile from constant kinetic energy. Fig. 5.17 represents a comparison Comparison of power consumption of Robotino with estimated model. The estimated model has some errors in estimation. These errors can be due to the non-uniform nature of the ground.

Multi-criteria optimization

The results for optimal velocity profile obtained from NSGA-II are presented in Fig. 5.19,Fig. 5.20 and Fig. 5.21 Fig. 5.19 and Fig. 5.21 represents a comparison of path tracking and velocity following with virtual control point for the optimal velocity profile obtained from the NSGA-II. The obtained results show the robustness of the proposed controller. Fig. 5.21 represents a comparison Comparison of power consumption of Robotino with the estimated model. We notice that the errors are reduced. The remaining errors are due to the non-uniform surface of the ground. The following assumptions are considered for the proposed algorithm: i) the elevations in the road profile are neglected, ii) the switching between any two driving modes is possible, and iii) the maximum velocity of URV is 16km/h which ensures the stability along a given path. The developed algorithm is applied on a real path.

The proposed optimization procedure is applied in the case of four driving The optimal velocities corresponding to selected compromise points from each Pareto front corresponding to each driving mode are superimposed in Fig. 5.30, Fig. 5.31 for smoothed paths using method 1 and method 2. The intersection points among different velocity profiles are identified.

Therefore, using these intersection points a digraph is constructed and dynamic programming is applied. In consequence, we obtain the optimal composite velocity profile with the optimal distribution of driving modes for smoothed paths using method 1 and method 2 as shown in Fig. 5.32 and 5.33, respectively. Fig. 5.34 represents the results of optimal velocity profile and optimal driving modes for a discrete energy planning methodology with dynamic programming as discussed in [START_REF] Bensekrane | [END_REF]]. In this figure, we notice that the mode switching and acceleration rate cannot be reasonable for some turns in the path (e.g. turns between arc lengths [1250,1500]). While, using the proposed continuous energy planning methodology, a smooth and reasonable profile of optimal velocity and modes are obtained (Fig. 5.32 and 5.33). Figures 5.35 and 5.36 shows the comparison of Experimental and ANFIS power consumption for optimal distribution of driving modes for method 1 and method 2 respectively. Refer to Table 5.2, a comparison of energy con- sumption and travel time for method 1 and method 2 is given for all selected points corresponding to each driving mode and for a combined velocity profile along with the experimental energy and travel time. This comparison is done to show that the methods used to smooth the path effects the energy planning methodology. From a combined velocity profile, it is also noticed that for method 1, the energy consumption is less but the travel time is more important. cussed in [START_REF] Bensekrane | [END_REF]]. It can be observed that the DP method in [START_REF] Bensekrane | [END_REF]] presents only one global solution for energy optimization, unlike the continuous energy planning methodology having multiple optimal solutions with different optimal energy consumption and optimal traveling times.

Conclusion

This chapter presents a continuous energy planning methodology for an overactuated URV based on power consumption estimation model. The power consumption is estimated using ANFIS model for different driving modes of the URV. The tracked path is generated using two different smoothing meth-ods. Also, NSGA-II algorithm is then applied to generate Pareto fronts regrouping compromise solutions between travel time and the consumed energy, for each driving mode. Finally, a weighted digraph has been made in order to find the optimal velocity profile taking benefit from the various URV driving modes. The obtained results highlighted that the proposed approach is efficient and allows to generate smooth reference velocity profile for the considered URV on the assigned path, that accounts of the over-actuation and the existence of many driving modes. The choice of the smoothing method affected considerably the overall energy consumption and the travel time of a URV. For future work, it is intended to extend the proposed energy planning methodology in case of presence of actuation's faults.

Chapter 6 The main objective of this thesis is to provide a methodology for energy planning of an autonomous over-actuated URV. Generally, in the literature, the energy management is developed through an optimal control problem. However, the energy planning consists to plan the available energy in an optimal way before the execution of the autonomous navigation algorithms for the URV. In a simple case, energy planning consists of finding an optimal velocity profile. However, in the consideration of the characteristics of an over-actuated vehicle, the problem becomes more complex, where the energy planning needs to find the optimal configuration associated with the velocity profile and the driving modes, along the predefined path. The proposed methodology is validated experimentally on over-actuated URV, and it is also compared with the different methods.

Conclusion and Prospective

Summary of Conclusions

First, a concise and a complete view of the field of autonomous driving of vehicles is presented, after discussion of the different types of robots according to their kinematic parameters. The main interesting problems addressed in the framework of this PhD thesis are:

1. Power consumption modeling of over-actuated URVs, 2. Energy planning methodology for over-actuated URVs.

Due to the actuation redundancy of over-actuated URVs and the derivatives of the different driving configuration, the modeling of power consumption estimation plays a vital role. The positioning of the energy planning methodology for URVs has been made compared to existing algorithms for autonomous driving. Also, the redundancy in terms of traction or in the steering is optimized along the path as one of the specifications for the proposed contribution.

To reach the global optimization of energy and to plan energy for vehicles for predefined road path, it is essential to have a precise model of energy power consumption estimation, which will allow us to avoid a sudden stop situation or to disrupt vehicle traffic. First, the model of power consumption estimation is formulated for different configuration separately. The total power consumption is decomposed into three elements of power estimation including inertia power, rolling resistance power, gravitational power, and the static power caused by various electrical components. The main consumption power is caused by the rolling resistance which has a relation with the curvature of the trajectory C, the degree of steerability δs, and the degree of redundancy δ R .

A generic analytic formulation of power consumption estimation is developed including different kinematic parameters, geometrical parameters, and dynamic parameters for six driving modes of the URV. The different contact forces are estimated by the magic formula of Pacejka and kept unchangeable for all the offline energy planning. This generic formulation does not cover all the non-linearities present in the different components of the URV, located at the mechanical chain, the electric chain, and the battery. To overcome these non-linearities in the power consumption modeling estimation, a qualitative model is developed. Thus, an Adaptive Neuro Fuzzy Inference System (ANFIS) is proposed. The inputs of the ANFIS model are the curvature of the path, the velocity and the acceleration of the URV, and the output of the neuronal model is the overall power consumption. ANFIS model was validated experimentally with real URV and it shows a better accuracy for the different driving modes, comparing to the analytic model.

The proposed energy planning is decomposed on three steps:

1. Pre-processing phase: Both quantitative and qualitative models of power consumption estimation are used to find an accurate model of power consumption for the over-actuated URV.

2. Optimization phase: it concerns the use of optimization algorithms to solve a given objective function.

3. Post-processing phase: In this step, a correction of distribution of driving modes is considered for a specific segment of the road path.

In the optimization phase, discrete and continuous optimization algorithms are used. The discrete approach of optimization is based on the discretization (filtering) of the road profile according to geometrical criteria {Lines, Clothoids, and Arcs}. This filtering divides the path into multiple segments according to its geometrical nature. An energy digraph is then constructed, by associating the graph nodes to the starting and ending point of each segment, and the cost value of each vertex in the digraph represents the consumed energy in each segment and for each driving mode. This operation will elabo-6.2. Future works 115 rate on different layers in the digraph, where each layer corresponds to a given driving mode. When the energy digraph is constructed with different driving modes, we use search graph algorithms to find the global optimal solution. The used algorithm in the search graph to find a global solution is Dynamic Programming. The global solution is presented as a couple of velocity profile and the driving mode, associated with each segment of the considered road profile. In terms of the time consuming, Dijkstra and A * are compared with dynamic programming. we noticed that A * is faster than Dijkstra and dynamic programming in case of discrete optimization. The continuous method was developed to resolve the energy planning problem in the presence of a smooth velocity profile and smooth changes of driving modes. To reach this goal, a multi-objective algorithm based on genetic algorithms (NSGAII) is used. The choice of multi-objective optimization rather than mono-objective algorithms is the importance of the energy and travel time compromise. The path was smoothed using two sets of curves, smooth{Lines, Clothoids, and Arcs} and {Lines, Pythagorean Holograph (PH)}. A Pareto front was developed for each driving mode and for each smoothed path. Finally, a digraph structure is proposed to combine the different optimal velocities obtained from the ideal point from each Pareto front. Our conclusion in terms of discrete and continuous optimizations, used in this work, is that the discrete one is appropriate for short paths, where the time consuming of the algorithm is high, with an accurate discrete road profile. However, the continuous optimization is suitable for long paths, where the time consuming is relatively low and the road profile is continuous and less accurate.

Future works

The possible extensions in the current work regarding the energy planning strategies for URVs are numerous:

1. Doing the online energy planning of the URV, by considering the changes in the environment, in terms of parameters variation of the external efforts of the wheel-ground contacts, as a result of the change of weather for example.

2. According to the planning energy baseline, in case the URV is operating in normal condition, it is important to study the performance of this planning in the case of faults occurrence. The aim is to make the energy planning in critic situations in the case of a fault in actuators or a puncture in the wheel tire,..etc. This allows to make a power planning tolerant to faults.

3. Another prospective of this realized work is to develop coordination between offline energy planning and online energy management. In that case, it is interesting to make the path planning, the trajectory planning, the task allocation and the routing of the URV, not based only of the short path/trajectory, the optimal velocity,..., but also the optimal energy to be consumed in accordance with specified constraints. • Evaluation of human driver performance and behavior,

• Driver fatigue, sleepiness, Hypo vigilance, drugs and alcohol effects,

• Ergonomics,

• Traffic safety,

• Infrastructure and transportation studies,

• Human Machine Interface (HMI) and ADAS,

• System prototyping and integration.

A.1.1 Massive simulation

SCANeR TM virtual platform enables driver assistance systems (ADAS) and autonomous driving functions to be endlessly tested and validated. The use of virtual testing to complement track or road testing provides safer test condition and reduced costs and time. This use case relies on exclusive SCANeR TM features:

• Modeling of the vehicle, sensors, driver and environment,

• Complex scenario and critical events representative of real driving situations,

• Automated tests edition program, The experimental results for characterization of RobuCAR motor are seved with a frequency of 0.01s. The efficiency maps for free load, 10% of load, 20% of load, 30% of load, 40% of load, 50% of load are presented in Fig. A.8,Fig.A.9,Fig.A.10,Fig.A.11,Fig.A.12,and Fig.A.13 respectively.

Résumé

Dans cette thèse, une planification énergétique pour les véhicules routiers sans conducteur (URV), suractionnés avec une direction redondante est proposée. En effet, des indicateurs sur la géométrie de la route, la redondance des actionnements, le profil de la vitesse optimale et le mode de conduite sont identifiés pour chaque segment de la trajectoire de l'URV. Ainsi, un modèle d'estimation de la consommation d'énergie d'un URV sur-actioné est développé. Deux méthodes de modélisation de la consommation d'énergie sont considérées. La première méthode est basée sur un modèle analytique de consommation d'énergie prenant en compte le degré de steerabilité, le degré de mobilité et le degré de redondance dans l'actionnement. La deuxième méthode utilisée pour la modélisation de la consommation d'énergie repose sur la méthode qualitative d'apprentissage des données, à savoir: le système d'inférence neuro-floue adaptatif (ANFIS). Cette dernière a été considérée pour répondre à la présence des incertitudes paramétriques de l'URV et aux incertitudes sur son interaction avec l'environnement. La validation de l'estimation de la consommation énergétique a été appliquée à un véhicule autonome réel appelé RobuCar. La stratégie de la planification énergétique a été élaborée selon deux approches: discrète et continue. L'approche discrète repose sur la construction d'un digraphe d'énergie avec toutes les configurations possibles, tenant compte des contraintes cinématiques et dynamiques basées sur une grille 3D, selon: la vitesse, la longueur de l'arc, le mode de conduite. Dans ce graphe orienté et pondéré, les arêtes décrivent l'énergie consommée par l'URV le long d'un segment de la trajectoire. Un algorithme d'optimisation est appliqué sur le digraphe pour obtenir une solution globale optimale combinant le mode de conduite, la consommation électrique et le profil de vitesse de l'URV. L'approche continue repose sur une stratégie d'optimisation multicritères utilisant des algorithmes génétiques (NSGA-II). Ensuite, un chemin réel est considéré et modélisé, en utilisant deux types de courbes constituée d'un ensemble de géométriques lisses: la première est lignes, clothoides et arcs, et la seconde regroupe des lignes et courbes de Hodograph de Pythagore. La stratégie de planification énergétique est ensuite appliquée aux chemins générés. En outre, un graph orienté est construit pour synthétiser le profil de vitesse optimale qui minimise la consommation énergétique globale tout en prenant en compte tous les modes de conduite. Les résultats sont comparés à ceux donnés par la méthode de programmation dynamique pour une optimisation globale hors ligne. Mots clés: Panification énergétique, Consommation d'énergie, Redondance, Sur-actionné, Conduite autonome.

Towards an Energy Planning Strategy for Autonomous

Driving of an Over-actuated Road Vehicle

Abstract

In this thesis, an energy planning for over-actuated unmanned road vehicles (URVs) with redundant steering configurations is proposed. In fact, indicators on the road profile geometry, the redundancy of actuation, the optimal velocity profile and the driving modes are identified for each segment of the URV's trajectory. Thus, a power consumption estimation model of an over-actuated autonomous driving vehicle is developed. Two methods for power consumption modeling are considered. The first method is based on an analytic model of power consumption, taking into account the degree of steerability, the degree of mobility and the degree of actuation redundancy. The second method used for power consumption modeling is based on data-learning qualitative method, namely: Adaptive Neuro Fuzzy Inference System (ANFIS). The latter has been considered in case of the presence of unknown dynamic parameters of the URV and uncertainties of interaction with the environment. Validation of the estimation of the power consumption has been applied on a real autonomous vehicle called RobuCar. Energy planning strategy has been built using two approaches, discrete and continuous. The discrete approach depends on the construction of an energy digraph with all feasible configurations taking into account kinematic and dynamic constraints based on a 3D grid map setup, according to the velocity, the arc-length,and the driving mode. In this weighted directed graph, the edges describe the consumed energy by the URV along a segment of a trajectory. An optimization algorithm is applied on the digraph to get a global optimal solution combining the driving mode, the power consumption and the velocity profile of the URV. The continuous approach is based on a multi-criteria optimization strategy using genetic algorithms (NSGA-II). Then a real road path is considered and modelled by using two smooth geometrical combinations: the first one uses lines, clothoids and arcs, and the second one uses lines and Pythagorean Hodograph (PH) curves. The energy planning strategy is then applied to the generated paths. Also, a directed graph is built to synthesis the optimal velocity profile that minimizes the overall energy consumption while accounting for all driving modes. Results are compared with those given by the dynamic programming method for global offline optimization.

Keywords:

Energy Planning, Power consumption, Redundancy, Over-actuated, Autonomous driving.

  between experimental and simulated longitudinal acceleration for each wheel. . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.10 Comparison between experimental and simulated steering angles for each wheel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.11 Comparison between experimental and simulated lateral acceleration for each wheel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.12 Comparison between (a) battery voltage, (b) battery current, and (c) Power consumption of Real Vehicle and simulated model in SCANeR TM 60 3.13 Comparison of the power consumption of URV using ANFIS and experiment with (a) Skid4 and (b) Skid2 configurations. . . . . . . . 61 3.14 Comparison of the power consumption of URV using ANFIS and experiment with (a) Single4 and (b) Single2 configurations. . . . . . 62 3.15 Comparison of the power consumption of URV using ANFIS and experiment with (a) Dual4 and (b) Dual2 configurations. . . .

Figure 1 . 1 :

 11 Figure 1.1: Organization of the works developed within the group MOCIS

Figure 1 . 2 :

 12 Figure 1.2: Different driving modes (steering configurations) of one considered UAV with m = 6.

FigureFigure 2 . 3 :

 23 Figure 2.2: Configuration of Steered Standard Wheel

Figure 2 . 6 :

 26 Figure 2.6: Steering type of Vehicle [Jazar 2017]

Fig. 3 .

 3 Fig. 3. UTDrive setup and sample synchronous data (two video streams, three audio streams, gas and brake ped

Figure 2 . 8 :

 28 Figure 2.8: Sensors in URV [Takeda 2011]

Figure 5 :

 5 Figure 5: Influence of Different Rover Parameters on Total Required Battery Energy to Accomplish a 2km Traverse

Figure 2

 2 Figure 2.9: Influence of Different URV Parameters on Total Required Battery Energy to Accomplish a 2km Traverse [Hou 2019].

Figure 14 .

 14 Figure 14. Percentage of power. (a) Power percentage of the three systems; (b) Smooth running power percentage.

Figure 14 .

 14 Figure 14. Percentage of power. (a) Power percentage of the three systems; (b) Smooth running power percentage.

Figure 2 .

 2 Figure 2.10: Percentage of Power Consumption for URVs [Hou 2019].

Figure

  Figure 2.11: Nomad URV.

Figure

  Figure 14: Experimental Results of Radius vs. Power for Nomad

Figure 2 .

 2 Figure 2.13: Power consumption for Nomad Vehicle [Shamah 1999] IV. EXPERIMENTAL SETUP The Khepera III mobile robot (127x123x70 mm 3 , Fig 4), produced by the K-team Corporation, has an inbuilt smart battery monitoring system providing the current state of the battery (voltage, current, capacity remaining, and temperature)and hence this robot was selected to start with our experiments so that no additional hardware module (e.g. current sensor) was needed.

Fig. 4 :

 4 Fig. 4: Khepera mobile robot Khepera III powered by a rechargeable Li-polymer battery pack of 1400 mAh, has 2 DC brushed servo motors, 11 infrared sensors and 5 ultrasonic sensors. Korebot II, a minicomputer (extension module) that hosts Bluetooth and Wi-Fi communication modules is added to the Khepera III robot. The voltage and current values are recorded at a sampling frequency of 20 Hz.As soon as the robot is started, the power consumed by various components is recorded by activating or controlling the components one by one. Programs for deriving the power models from a series of operations (Fig.4, right) and calculating the energy consumption of each component (by determining the duration for which each component was active) were written in MATLAB and tested with the robot's datasets created during the experiments. Initially the computer is turned on and hence P comp is calculated. Then, the controllers are activated and the power P con is noted. Each other component's power consumption is calculated by subtracting from the previous power value after the activation of the respective components.Since all sensors data were needed during teleoperation to ensure safety of the robot and surroundings, all the sensing

  Where, the parameter C I depends on the its inertia.The power consumption of static com to be almost constant (average values ar speed used in teleoperation experiments With the measurement of motion power speed and payload of the robot (Fig3a) the equation 14 can be applied to the m at the following equation.P i motion = 2.4 • υ i + 0.22 • mThe generated power model (Fig 3c prediction modelling system. It can be Fi module consumes significantly high components. To verify the accuracy of the energy p conducted two different type of tasks wi from point A to point B (Fig 5a). For total time for completing the task t n = Power (sensors, controller, computer) 2. Static + Bluetooth Module 3. Static + WiͲFi Module 4. Static + WiͲFi + Motion at minimum speed (28 mm/s, 0g payload) 5. Static + WiͲFi + Motion at maximum speed (138 mm/s, 0g payload) 6. Static + WiͲFi + Motion at minimum speed (28 mm/s, 576g payload) 7. Static + WiͲFi + Motion at maximum speed (138 mm/s, 576g payload)

Figure 2 .

 2 Figure 2.14: Khepera robot [Parasuraman 2014]

Chapter 2 .Fig. 4 .Fig. 5 .

 245 Fig. 4. Mobile robot Auriga-β and a minihelicopter landing on its selfstabilized platform.

Fig. 6 .

 6 Fig. 6. Two rubber belt types.TABLE I MAXIMUM POWER CONSUMPTION OF THE COMPONENTS OF AURIGA-β

  (a) Auguira URV [Morales 2009] Figure 8. Experiment Platform: the iRobot Packbot

  Fig. pow exp

Figure 2 .

 2 Figure 2.15: Tracked vehicles

Fig. 3 .

 3 Fig. 3. Drive system scheme of Quadriga mobile robot.4771

Fig. 1 .

 1 Fig. 1. Left: Custom-built robot used in our experiments. Right: Attopilot voltage and current measurement circuit from SparkFun Electronics.

  Figure 2.16: Wheeled mobile robots

Fig. 6

 6 Fig. 6 Forces acting on the skid-steered vehicle during a steady state turn. Only the tyre forces acting on the front outer and the rear inner tyres are shown

Fig. 14

 14 Fig. 14 Forces acting on the Ackermann-steered vehicle during a steady state turn. Only the tyre forces acting on the front outer and the rear inner tyres are shown

  Chapter 2. Power Management of Autonomous Road Vehicles r an energy optimal control strategy for a obotic Electric Vehicle (ROboMObil) is is a development of the Robotics and (which is part of the German Aerospace several research topics, like energy or remote controlled driving for future lications. Since saving electric energy is a rating a battery electric vehicle (like the eveloped a new approach for energy over-actuated electric car. The focus of s in the model based minimization of the ower consumption for driving along a y to optimize the overall efficiency. The a real-time capable nonlinear control rithm, using quadratic programming, object oriented modeling language ization objectives are analyzed and the ted by simulation results. Finally an CA dynamic inversion is discussed, which is the different time constants of the . INTRODUCTION

Fig. 1 :

 1 Fig. 1: ROMO -the robotic electric vehicle in front of DLR Techlab.

  Mono-Objective Methods Multi-objective Methods Graph search methods . . .

Figure

  Figure 2.19: Optimal Autonomous Driving

Figure 2 .

 2 Figure 2.21: Components Of Optimal Control

  Figure 2.22: MRTA schemes

  Figure 2.23: Optimization Techniques

Fig. 5 . 4 .

 54 Fig. 5. All kinds of employed energy management strategies. Fig. 4. Distribution of research subjects.

Figure 2 .

 2 Figure2.24: All EMS[Zhang 2015]

Figure 3 . 1 :

 31 Figure 3.1: URV schematic diagram in Dual configuration

Figure 3 .

 3 Figure 3.2: ANFIS architecture.

Figure 3 . 3 :

 33 Figure 3.3: Flowchart for the estimation of the power consumption.

Figure 3 . 4 :

 34 Figure 3.4: Trajectory from the Campus of University of Lille

Figure 3 . 7 :Figure 3 . 9 :Figure 3 .

 37393 Figure 3.5: Curvature of the trajectory

Figure 3 .

 3 Figure 3.11: Comparison between experimental and simulated lateral acceleration for each wheel.

Figure 3 .Figure 3 .Figure 3 .Figure 3 .

 3333 Figure 3.12: Comparison between (a) battery voltage, (b) battery current, and (c) Power consumption of Real Vehicle and simulated model in SCANeR TM

4. 2 .

 2 Descrete Energy Planning for Autonomous Navigation of the URV 67

Figure 4 . 1 :

 41 Figure 4.1: methodology for URV energy planning.

  Figure 4.2: Energy planning schema.

Figure 4 . 3 :

 43 Figure 4.3: Real and filtered curvature.

Table 4 . 1 :

 41 Constraints of driving mode for each type of road segment.

Figure 4 . 4 :

 44 Figure 4.4: Real and filtered trajectory.

Figure 4 . 6 :

 46 Figure 4.6: Driving pattern during sampling intervals.

Figure 4 . 7 :

 47 Figure 4.7: Optimal velocity profile for the campus trajectory (t < 40min).

Figure 4 . 8 :

 48 Figure 4.8: Optimal mode distribution for the campus trajectory (t < 40min) (zoom in at sharp turn).

Figure 4 . 9 :

 49 Figure 4.9: Percentage of modes use before correction in campus trajectory with traveling time (t < 40min).

Figure 4 .Figure 4 .Figure 4 .

 444 Figure 4.10: Percentage of modes use after correction in campus trajectory with traveling time (t < 40min).

Figure 4 .Figure 4 .Figure 4 .

 444 Figure 4.13: Optimal driving modes for campus trajectory with traveling time (t < 30min).

5. 1 . 1

 11 Related Work5.1.1.1 Energy Planning of a URV

Figure 5 . 1 :

 51 Figure 5.1: Different driving modes of RobuCAR

  Figure 5.2: The proposed methodology for power consumption estimation and energy planning.

Figure 5 . 3 :Figure 5 . 4 :

 5354 Figure 5.3: Campus trajectory of the University of Lille

Figure 5 . 5 :Figure 5 . 6 :

 5556 Figure 5.5: Basic conditions to generate a PH curve

Figure 5 . 7 :

 57 Figure 5.7: Energy optimization methodology.

Figure 5

 5 Figure 5.8: Generation of Pareto Fronts of velocity profiles

Figure 5

 5 Figure 5.9: Generation of motion profile candidate

Figure 5 .

 5 Figure 5.11: Example for superposition of velocity profiles

3 EvFigure 5 .

 35 Figure 5.12: Example of digraph

  Figure 5.13: Three-wheeled omnidirectional mobile robot structure

Figure 5 .

 5 Figure 5.14: Robotino3 mobile robot

Figure 5 .

 5 Figure 5.16: Comparison of Robotino path with reference path

5. 9 .Figure 5 .Figure 5 .

 955 Figure 5.20: Comparison of power consumption of Robotino with the estimated model

Figure 5 .

 5 Figure 5.22: Pareto front for method 1 smoothing for Dual2.

5. 9 .Figure 5 .

 95 Figure 5.23: Pareto front for method 1 smoothing for Dual4.

Figure 5 .Figure 5 .

 55 Figure 5.24: Pareto front for method 1 smoothing for Single2.

Figure 5 .Figure 5 .

 55 Figure 5.26: Pareto front for method 2 smoothing for Dual2.

Figure 5 .Figure 5 .Figure 5 .Figure 5 .Figure 5 .

 55555 Figure 5.28: Pareto front for method 2 smoothing for Single2.

Figure 5 .Figure 5 .

 55 Figure 5.33: Optimal velocity profile and optimal distribution of driving modes for Method 2.

Contents 6 . 1

 61 Summary of Conclusions . . . . . . . . . . . . . . . . . . . . . 113 6.2 Future works . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Figure A. 3 :

 3 Figure A.3: Different lighting for driving

•

  Coaxial reducer: raio 1-29 (RobuCAR AT) • Nominal torque: 32 Nm • Radial load: 2040 Nm in the middle of the motor shaft • Mass: 8 kgA.2.2 Test bench for motor characterizationIn order to characterize the RobuCAR motor, a test bench is set up as shown in the Fig.A.5. The purpose of this characterization is to plot the motor efficiency map by measuring the ratio of mechanical power and electric power for different loads. The latter is introduced in the specific field of the electric motor in the dynamic model under SCANeR TM . This operation is done to guarantee a better representation of the motor and to have a dynamic model of RobuCAR URV very close to real URV. Fig. A.6 represents the load variation on RobuCAR motor, and Fig.A.7 show the acquisition setup with a real-time embedded industrial controller called CompactRio and voltage and current sensors.

Figure A. 8 :

 8 Figure A.8: Map efficiency with free load

Figure A. 9 :

 9 Figure A.9: Map efficiency with 10% load

Figure A. 11 :

 11 Figure A.11: Map efficiency with 30% load

Figure A. 13 :

 13 Figure A.13: Map efficiency with 50% load

  4.11 Post-processing with correction in mode distribution at sharp turn. . 76 4.12 Optimal velocity profile for campus trajectory with traveling time (t < 30min). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.13 Optimal driving modes for campus trajectory with traveling time (t < 30min). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.14 Optimal velocity profile and for campus trajectory with traveling time (t < 20min). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.15 Optimal driving modes for campus trajectory with traveling time (t < 20min). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 List of Tables 1.1 Parameters describing URV driving configurations for m = 6. . . . . 3.1 Mean errors in power estimation . . . . . . . . . . . . . . . . . . . . 4.1 Constraints of driving mode for each type of road segment. . . . . . 4.2 Comparison of energy consumption with traveling time (t < 40min) 4.3 Time consumed for the different steps in the algorithm (t < 40min) . 5.1 Parameters describing driving modes of RobuCAR . . . . . . . . . . 5.2 Comparison of energy consumption . . . . . . . . . . . . . . . . . . . 5.3 Comparison of energy consumption . . . . . . . . . . . . . . . . . . . Framework and context of the thesis . . . . . . . . . . . . . . 5 1.2 General Introduction . . . . . . . . . . . . . . . . . . . . . . .

		List of Tables	3
	IPOPT Interior Point OPTimizer ST Single Task	List of Abbreviations Chapter 1
	MOCIS Méthodes et Outils pour la Conception Intégrëe des Systémes SVM support vector machine General Introduction
	A-PMP approximate Pontryaginâs Minimum Principle MPC Model Predective Control TA Time extended Assignment
	ADEA Adaptive Differential Evolution Algorithm MR Multi-Robot TD Temporal Difference
	ANFIS Adaptive Neuro-Fuzzy Inference System MRTA Multi-Robot Task Assignment TO Trajectory Optimization
	BA MT Multi-Task Bees Algorithm TOMR Three-wheeled Omnidirectional Mobile Robota Contents
	CA NDP Neuro-dynamic Programming Control Allocation TOP Trajectory Optimization Problem 1.1
	CRIStAL Centre de Recherche en Informatique, Signal et Automatique de Lille NLP Nonlinear Programming URV Unmanned Road vehicle
	CVRP Capacited Vehicle Routing Problem NN Neural Network URVTAP) URV Task Assignment Problem
	DDP Deterministic Dynamic Programming NSGA Nondominated Sorting Genetic Algorithm VRP Vehicle Routing Problem
	DOF Degree of Freedom NSGA-II Non-dominated Sorting Genetic Algorithm-II
	DOM Degree of Mobility OC Optimal Control
	DOMS Degree of Maneuverability OEM Optimal Energy Management
	DOS Degree of Steerability PA Power Allocation
	DP PCOA Parallel Chaos Optimization Algorithm Dynamic Programming
	EA PH	Evolutionary Algorithm Pythagorean Hodograph
	ECMS Edge Cloud Management Controller PMP Pontryaginâs Minimum Principle
	EM PP	Energy Management Path Planning
	EOM Equations of Motion PSO particle swarm optimization
	ES QP	Extremum Seeking Quadratic Programming
	FDP Fast Dynamic Programming RGA Real-valued Genetic Algorithm
	GA RRT Exploring Random Trees Genetic Algorithms
	SA	GPS Global Positioning System Simulated Annealing
	GT SEUMRE Space Exploration and Unimodal Region Elimination Game Theory
	HEV Hybrid Electrical Vehicles SOC State of Charge
	IA SQP Sequential Quadratic Programming Instantaneous Assignment
	SR	IDP Iterative Dynamic Programming Single Robot

. . . . 63 4.1 methodology for URV energy planning. . . . . . . . . . . . . . . . . . 68 4.2 Energy planning schema. . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.3 Real and filtered curvature. . . . . . . . . . . . . . . . . . . . . . . . 70 4.4 Real and filtered trajectory. . . . . . . . . . . . . . . . . . . . . . . . 71 4.5 Energy digraph in 3D grid. . . . . . . . . . . . . . . . . . . . . . . . 71 4.6 Driving pattern during sampling intervals. . . . . . . . . . . . . . . . 72 4.7 Optimal velocity profile for the campus trajectory (t < 40min). . . . 74 4.8 Optimal mode distribution for the campus trajectory (t < 40min) (zoom in at sharp turn). . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.9 Percentage of modes use before correction in campus trajectory with traveling time (t < 40min). . . . . . . . . . . . . . . . . . . . . . . . 75 4.10 Percentage of modes use after correction in campus trajectory with traveling time (t < 40min). . . . . . . . . . . . . . . . . . . . . . . . 75 6 1.3 Thesis objective . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . 8 1.5 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.6 Disseminated Results . . . . . . . . . . . . . . . . . . . . . . . 11 1.7 Manuscript organization . . . . . . . . . . . . . . . . . . . . . 12 1.1 Framework and context of the thesis This PhD thesis has been prepared within the research group Méthodes et Outils pour la Conception Intégrée de Systèmes (MOCIS) 1 , of the Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) (UMR CNRS 9189) 2 .

•

  Bensekrane, I., Kumar, P., Melingui, A., Coelen, V., Amara, Y., Chettibi, T. & Merzouki, R. Energy Planning for Autonomous Navigation of an Overactuated Road Vehicle", IEEE/ITS Intelligent transportation system,2019.

	Accepted with Minor Revision
	2018, October) Bond
	Graph-based Power Consumption Estimation of a Non-holonomic Wheeled
	Mobile Robot with Multiple Driving Modes. In 2018 IEEE International Con-
	ference on Systems and Control (ICSC). IEEE.
	• P. Kumar, I. Bensekrane and R. Merzouki. (2018, December) "Modeling of the Multi-domain Steering System with Hybrid Dynamics for an Over-

• Bensekrane, I.,

Kumar, P., Melingui, A., Chettibi, T., Singh, I.,

Singh, M. & Merzouki, R., "Energy Planning for Autonomous Driving of an Unmanned Road Vehicle on Smooth Paths", IEEE/TVT Transactions on Vehicular Technology, 2019. Under Revision • Kumar, P., Bensekrane, I., Merzouki, R., "Estimation of Power Consumption of Wheeled Mobile Robots with Multiple Kinematics: A Bond Graph Approach", IEEE/ASME Transactions on Mechatronics, 2019. Under Revision International conferences • Bensekrane, I., Kumar, P., Amara, Y., & Merzouki, R. (2017, December). Towards adaptive power consumption estimation for over-actuated unmanned vehicles. In 2017 IEEE International Conference on Robotics and Biomimetics (ROBIO) (pp. 92-97). IEEE. • Datouo, R., Motto, F. B., Zobo, B. E., Melingui, A., Bensekrane, I., & Merzouki, R. (2017, December). Optimal motion planning for minimizing the energy consumption of wheeled mobile robots. In 2017 IEEE International Conference on Robotics and Biomimetics (ROBIO) (pp. 2179-2184). IEEE. • Bensekrane, I., Kumar, P., Melingui, A., Coelen, V., Amara, Y., & Merzouki, R. (2018, August) Energy Planning for Unmanned Over-actuated Road Vehicle. In 2018 IEEE Vehicle Power and Propulsion Conference (VPPC). IEEE. • Kumar, P., Bensekrane, I., Singh, M., & Merzouki, R. (actuated Autonomous Vehicle," IEEE International Conference on Robotics and Biomimetics (ROBIO), (pp. 2514-2519). IEEE.

  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Kinematic Properties of Unmanned Road Vehicles (URVs) 14 2.2.1 Degree of freedom . . . . . . . . . . . . . . . . . . . . . . . .

	Chapter 2
	Power Management of
	Autonomous Road Vehicles
	Contents
	2.1

16 2.2.2 Degree of mobility . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2.3 Degree of steerability . . . . . . . . . . . . . . . . . . . . . . . 17 2.2.4 Degree of manoeuverability . . . . . . . . . . . . . . . . . . . 17 2.2.5 Holonomy Constraint . . . . . . . . . . . . . . . . . . . . . . 18 2.2.6 Omni-directional Property . . . . . . . . . . . . . . . . . . . . 18 2.3 Power Consumption and Energy Management of URVs . . 19 2.3.1 Energy Consumption of URVs: . . . . . . . . . . . . . . . . . 20 2.4 Optimal autonomous driving of URVs . . . . . . . . . . . . . 30 2.4.1 URV path planning problem . . . . . . . . . . . . . . . . . . 30 2.4.2 Trajectory optimization problem of URVs . . . . . . . . . . . 33 2.4.3 URV routing problem . . . . . . . . . . . . . . . . . . . . . . 36 2.4.4 URV task assignment problem . . . . . . . . . . . . . . . . . 37 2.4.5 URV energy planning . . . . . . . . . . . . . . . . . . . . . . 43 2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

Total Charge Energy Residue Battery Energy Steering Motor Controller Power Electronics Drive Motor Transmission Propulsion Work Power Electronics Loss Drive Motor Loss Battery Steering Device Steering Motor Wheels Steering work Tire Deformati- on Soil-wheel Interaction Internal Friction Steering Motor Loss Steering Motor Controller Loss Controller, Sensor, Radio, … … Communi- cation Sensing Computing Robotics Steering Wheels Tire Deformati- on Soil-wheel Interaction Internal Friction Propulsion

	394	Chapter 2. Power Management of Autonomous Road Vehicles 7. Steering Dynamics
		Ackerman	 1 % Parallel	2 % 	Reverse
	FIGURE 7.15. By increasing the speed at a turn, parallel or reverse steering is
	needed instead of Ackerman steering.			3 % 
					4 % 
					5 % 
		Figure 2.5: Energy Utilization for URVs [Xiao 2014]
			.

TABLE I PACKET

 I LOSS RATES FROM DIFFERENT SPEECH CODERS.

	VoIP Bit Rate iLBC 13.33 kb/s iLBC 15.20 dB/s GSM AMR 12.2 kb/s GSM AMR 7.4 kb/s GSM AMR 4.75 kb/s G.729 8 kb/s MELP 2.4 kb/s	Speech PLR Video PLR 14.23% 14.01% 20.70% 20.84% 16.80% 17.62% 14.27% 14.84% 15.86% 16.38% 20.34% 20.53% 13.78% 13.62%	Speech Frame Length (ms) 30 20 20 20 20 10 22.5

TABLE I LOCAL

 I COORDINATES OF THE CENTER OF GRAVITY FOR THE FULL AND EMPTY TANK CASES.

		Full	Empty
	x (cm)	0.05	-0.06
	y (cm)	2.02	0.89

TABLE II PARAMETERS

 II

FOR CLOSED-LOOP SY a small number of experiments are ne coefficients of friction and shear moduli

Table 3 .

 3

			1: Mean errors in power estimation
		Skid4	Single4	Dual4	Skid2	Single2	Dual2
	DS	400965 264634 262079 541280 264119	263802

  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

	Chapter 4
	Discrete Approach of Energy
	Planning Methodology
	Contents
	4.1

4.1.1 Main contributions . . . . . . . . . . . . . . . . . . . . . . . . 66 4.1.2 Problem formulation . . . . . . . . . . . . . . . . . . . . . . . 66 4.2 Descrete Energy Planning for Autonomous Navigation of the URV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.2.1 Pre-Processing Phase: Power Consumption Estimation . . . 67 4.2.2 Optimization Phase: Energy planning . . . . . . . . . . . . . 68 4.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . 73 4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Table 4 .

 4 2: Comparison of energy consumption with traveling time (t < 40min)

	Energy (J)	loss (%)

Table 4 .

 4 3: Time consumed for the different steps in the algorithm (t < 40min)

		Computing time (s)
	3D grid construction	12642.504
	Digraph construction	5.32224
	Dynamic programming	30.924936
	Dijkstra	13.503235
	A star	0.038087

Table 5 .

 5 1: Parameters describing driving modes of RobuCAR Tractive actuators Steering actuators Single4

Table 5

 5 In Table5.3, a comparison of energy and travel time is shown for the methods presented in this chapter and the discrete method dis-

		.2: Comparison of energy consumption
		Smoothing Method1: Line, Arc, Clothoid
		Dual2	Dual4	Single2	Single4 Combined
	Energy (J) 1.397e 5 1.312e 5	1.320e 5	1.346e 5 9.4394e 4
	Time (s)	1543	2203	1423	1571	3953
		Smoothing Method 2: Line, PH
		Dual2	Dual4	Single2	Single4 Combined
	Energy (J) 1.356e 5 1.331e 5	1.315e 5	1.319e 5 1.0333e 5
	Time (s)	1695	1740	1119	1803	2056

Figure 5.36: Comparison of Experimental and ANFIS power consumption for optimal distribution of driving modes for Method 2.

Table 5 .

 5

		3: Comparison of energy consumption
		Method 1 Method 2 Method in [Bensekrane 2018]
	Experimental Energy (J) 9.765e 4 1.0439e 5	7.6589e 4
	Experimental Time (s)	3920	2086	1390
	Simulated Energy (J)	9.4394e 4 1.0333e 5	1.0426e 5
	Simulated Time (s)	3953	2056	1411.9

Thèse de Ismail Bensekrane, Université de Lille, 2019 © 2019 Tous droits réservés. lilliad.univ-lille.fr

https://www.cristal.univ-lille.fr/?rubrique27&eid=24

https://www.cristal.univ-lille.fr/ Thèse de Ismail Bensekrane, Université de Lille, 2019 © 2019 Tous droits réservés. lilliad.univ-lille.fr

Thèse de Ismail Bensekrane, Université de Lille, 2019 © 2019 Tous droits réservés. lilliad.univ-lille.fr 1.2. General Introduction

Thèse de Ismail Bensekrane, Université de Lille, 2019 © 2019 Tous droits réservés. lilliad.univ-lille.fr 1.6. Disseminated Results

Thèse de Ismail Bensekrane, Université de Lille, 2019 © 2019 Tous droits réservés. lilliad.univ-lille.fr 2.3. Power Consumption and Energy Management of URVs

Thèse de Ismail Bensekrane, Université de Lille, 2019 © 2019 Tous droits réservés. lilliad.univ-lille.fr5.2. Path Smoothing

Thèse de Ismail Bensekrane, Université de Lille, 2019 © 2019 Tous droits réservés. lilliad.univ-lille.fr 5.9. Experimental data-based results for an outdoor over-actuated URV 107

Thèse de Ismail Bensekrane, Université de Lille, 2019 © 2019 Tous droits réservés. lilliad.univ-lille.fr 5.9. Experimental data-based results for an outdoor over-actuated URV 109

Acknowledgments

• Improve the validation process and tests coverage rate,

• High performance computing on premises or in the cloud,

• Metrics and performance analysis and reports,

• Validate functional safety.

A.1.2 Vehicle Dynamics

SCANeR TM includes CALLAS model A.4 and offers a virtual proving ground for various civil, military and motorsport vehicle dynamics applications: vehicles concepts and design, performance, homologation, advanced chassis control, consumption and pollution optimization, etc.

30/06/2019

Applications -AVSimulation

Vehicle Dynamics

SCANeR ™ studio includes CALLAS model and offers a virtual proving ground for various civil, military and motorsport vehicle dynamics applications:

vehicles concepts and design, performance, homologation, advanced chassis contrai, consumption and pollution optimization, etc.

::::::1: m::111

A.2 RobuCAR Motor Characterization

The motor of RobuCAR is an electric motor manufactured by MBR company under the reference CFB0.120F1-48V 22 A 3200T/Mn 900W. It has the following characteristics: