Hassan Hosseinnia
email: hoseinnia@unex.es

Inés Tejado

Vicente Milanés
email: vicente.milanes@csic.es

Jorge Villagrá
email: jorge.villagra@csic.es

Blas Vinagre
email: bvinagre@unex.es

Y S H Chen

I Hosseinnia

B M Tejado

Vinagre

Experimental Application of Hybrid Fractional-Order Adaptive Cruise Control at Low Speed

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Experimental Application of Hybrid Fractional-Order

Adaptive Cruise Control at Low Speed S. Hassan Hosseinnia, Inés Tejado, Vicente Milanés, Jorge Villagrá, and Blas M. Vinagre

Abstract-This brief deals with the design and experimental application of a hybrid fractional adaptive cruise control (ACC) at low speeds. First, an improved fractional-order cruise control (CC) is presented for a commercial Citroën C3 prototype-which has automatic driving capabilities-at low speeds, which considers a hybrid model of the vehicle. The quadratic stability of the system is proved using a frequency domain method. Second, ACC maneuvers are implemented with two different distance policies using two cooperating vehiclesone manual, the leader, and the other, automatic-also at very low speeds. In these maneuvers, the objective is to maintain a desired interdistance between the leader and follower vehicles, i.e., to perform a distance control-with a proportional differential (PD) controller in this case-in which the previously designed fractional-order CC is used for the speed control. Simulation and experimental results, obtained in a real circuit, are given to demonstrate the effectiveness of the proposed control strategies.

Index Terms-Adaptive cruise control (ACC), fractional-order control (FOC), hybrid system and control, stability.

I. INTRODUCTION

T HE CONSIDERABLE increase in the number of vehicles for transportation of people or goods in recent decades have caused an increase in the number of road fatalities. Since more than 80% of road accidents are due to the human factor [START_REF]Motor vehicle traffic crash fatality counts and estimates of people injured for 2005[END_REF], it turns road transport into a suitable candidate to the application of autonomous or semiautonomous control systems to avoid-or reduce-driver errors.

During last years, significant advances have been carried out in this field. Although most of the commercial vehicles have included cameras or radars to detect pedestrians [START_REF] Llorca | Autonomous pedestrian collision avoidance using a fuzzy steering controller[END_REF] or a leading vehicle [START_REF] Heddebaut | Millimeter-wave communicating-radars for enhanced vehicle-to-vehicle communications[END_REF], or ultrasound sensors for parking assistance [START_REF] Agarwal | A cost-effective ultrasonic sensor-based driver-assistance system for congested traffic conditions[END_REF], or even warning devices as head-up displays and audible signals, the last decision remains on the driver. Therefore, next step is to turn from warning to automatic devices for accident reduction or mitigation, which is an open field of research. Concerning vehicle's automation, one can distinguish between the lateral-associated to the steering wheel-or longitudinal-associated to the brake and throttle pedals-actions. The work presented in this brief focuses in the latter.

Automatic speed control-well known as cruise control (CC) in the literature-was one of the first autonomous systems implemented on a vehicle. It involves in regulating the action over the throttle pedal to try to follow a desired speed. Subsequent step was the inclusion of the brake pedal in the speed control system. Based on this inclusion and the use of radar system for detecting the leading vehicle, adaptive CC (ACC) systems were implemented for freeways driving [START_REF] Naus | Design and implementation of parameterized adaptive cruise control: An explicit model predictive control approach[END_REF]. Current research line in speed control is based on vehicle-to-vehicle (V2V) communications to reduce the distance between vehicles. These control systems, called cooperative ACC, have been experimentally tested with prototype vehicles [START_REF] Milanés | Comparing Fuzzy and intelligent PI controllers in stop-and-go manuevers[END_REF]- [START_REF] Kianfar | Design and experimental validation of a cooperative driving system in the grand cooperative driving challenge[END_REF].

Controlling the speed of a vehicle is a classic application of control system theory and, as a matter of fact, most of the commercial systems are based on proportional-integraldifferential (PID) controllers because of the proper vehicle's behavior versus their easy implementation. Although PID can achieve adequate results, advanced control techniques capable of improving their benefits are required in the automotive field. In this context, in the past few years, fractional-order PID controllers, i.e., the generalization of traditional PID to noninteger orders, are recognized to guarantee better closed-loop performance and robustness with respect to the classical controllers-refer to [START_REF] Monje | Fractional-Order Systems and Controls. Fundamentals and Applications[END_REF] and [START_REF] Podlubny | Fractional-order systems and PI λ D μ controllers[END_REF] for fundamentals and benefits of fractional-order control (FOC).

One of the key issues in longitudinal control is the commutation between the throttle and brake pedals due to the significant differences between the accelerating and braking vehicle dynamics. In this context, hybrid control-because of switching between different controllers-can be an accurate approach to achieve stability and provide an effective mechanism to deal with these highly complex systems by combining the advantages of different controllers [START_REF] Hespanha | Encyclopedia of Life Support Systems (EOLSS)[END_REF]- [START_REF] Fierro | A framework for hybrid control design[END_REF]. Examples of hybrid controllers in the automotive field include applications for automated highway systems [START_REF] Lygeros | Verified hybrid controllers for automated vehicles[END_REF], motion planning [START_REF] Frazzoli | Robust hybrid control for autonomous vehicle motion planning[END_REF], [START_REF] Frazzoli | A maneuver-based hybrid control architecture for autonomous vehicle motion planning[END_REF], collision avoidance [START_REF] Mukai | A collision avoidance control for multi-vehicle using PWA/MLD hybrid system representation[END_REF], trajectory tracking [START_REF] Altafini | Hybrid Systems: Computation and Control[END_REF], [START_REF] Balluchi | Hybrid feedback control for path tracking with a bounded-curvature vehicle[END_REF], and so on. Even though, research in hybrid control has been the object of an intense and productive effort in the recent years in the automotive field, from the best of our knowledge, this is the first time that benefits of both FOC and hybrid control are used for ACC maneuvers.

At this point, let us formulate the final aim of this brief as follows. Consider a number of vehicles driving in a common area at low speeds with V2V communications and a control station capable of communicating with all of them through a wireless network. The control station will be responsible for sending each car its specific target speed so as to avoid the possibility of collisions. The objective of this brief is to develop a capable and efficient advanced driver assistance system on the basis of FOC to allow the control station modify the speed of the cars to keep safety for all maneuvers in the area, which can be divided into two items: 1) remote CC maneuvers, which were addressed in [START_REF] Tejado | Fractional network-based control for vehicle speed adaptation via vehicle-toinfrastructure communications[END_REF] and 2) ACC via networks. In this brief, we will focus on the first step of this second item, more particularly, on the adaptation of the system developed in [START_REF] Tejado | Fractional network-based control for vehicle speed adaptation via vehicle-toinfrastructure communications[END_REF] to local ACC applications. With these premises, the purpose of this brief was threefold.

1) Design two fractional-order PI controllers to act over the throttle and brake pedals independently, so as to adapt the control designed in [START_REF] Tejado | Fractional network-based control for vehicle speed adaptation via vehicle-toinfrastructure communications[END_REF] for CC to ACC maneuvers. 2) Implement a hybrid control law for the commutation between the action over each pedal in a safe and robust way. 3) Validate the proposed hybrid control experimentally considering two different strategies for generating the safe interdistance between vehicles. It is worth mentioning that the idea was to compare two widely used rules with a classical PD controller, but not to design a fractionalorder one-it will be addressed in future works. The rest of this brief is organized as follows. Section II briefly describes the follower vehicle and its dynamic longitudinal model obtained for this kind of maneuvers. Section III addresses CC maneuvers. In Section IV, ACC maneuvers and the interdistance policies considered for the experiments are described. Simulation and experimental results are given in Section V to validate the proposed hybrid fractional strategy for CC and ACC maneuvers. Finally, concluding remarks are included in Section VI.

II. AUTOMATIC VEHICLE

This section briefly summarizes the modifications performed in the follower vehicle-an automatic convertible Citroën C3 Pluriel, whereas the leader is an electric Citroën Berlingo-to act autonomously on the throttle and brake pedals for the experimental CC and ACC maneuvers, as well as its dynamic longitudinal model when accelerating and braking at very low speeds. Both follower and leader vehicles belong to the AUTOPIA Program at the Center for Automation and Robotics (CAR).

A. Description

The vehicle control system for automatic driving, following the classical perception-reasoning-action paradigm [START_REF] Onieva | Throttle and brake pedals automation for populated areas robotica[END_REF], [START_REF] Milanés | Clavileño: Evolution of an autonomous car[END_REF], is in charge of localizing as precisely and robustly as possible the vehicle. To that end, the following subsystems are embedded in the vehicle.

1) A double-frequency global positioning system (GPS) receiver running in real-time kinematic (RTK) carrier phase differential mode that supplies 2 cm of resolution positioning at a refresh rate of 5 Hz.

2) A wireless local area network (IEEE 802.11) support, which allows the GPS to receive both positioning error corrections from its base station and vehicle and positioning information from the preceding vehicle.

3) An inertial measurement unit (IMU) Crossbow IMU

300CC placed close to the center of the vehicle to provide positioning information during GPS outages. 4) Car odometry supplied by a set of built-in sensors in the wheels, whose measurements can be read by accessing the controller area network bus of the vehicle. 5) An on-board computer, which requests values from each of the on-board sensors with which to compute the controller's input values. Finally, the devices that make possible to act on the throttle and brake of the car are an electrohydraulic system, which is mounted in parallel with the original one, capable of injecting pressure into the car's antiblock braking system, and an analog card, which can send a signal to the car's internal engine computer to demand acceleration or deceleration. More details can be found in [START_REF] Milanés | Electro-hydraulic braking system for autonomous vehicles[END_REF].

B. Dynamic Longitudinal Model

To design the controllers for CC and ACC maneuvers at very low speeds, a model of the vehicle was obtained experimentally when accelerating and braking. It is worth mentioning that obtaining the exact vehicle longitudinal dynamics is not required in this application because of the kind of experimental maneuvers to be performed. Thus, simple linear models were considered-similar models have been also used in [START_REF] Rodriguez | Estimacion de posicion y control de vehiculos autonomos a elevada velocidad[END_REF] and [START_REF] Kamga | Speed, steering angle and path tracking controls for a tricycle robot[END_REF]. On the one hand, the vehicle speed when accelerating was simplified as

G 1 (s) 4.39 s + 0.1746 . ( 1
)
On the other hand, the vehicle dynamics when braking can be given by an uncertain first-order transfer function that depends on the voltage applied to the brake pedal [START_REF] Milanés | Electro-hydraulic braking system for autonomous vehicles[END_REF] G 2 (s)

1 τ s + 1 (2)
where the time constant varies in the interval τ ∈ [1.6, 3.1] sthe nominal value of τ was considered as 2.25. The validation of these models can be found in [START_REF] Tejado | Fractional network-based control for vehicle speed adaptation via vehicle-toinfrastructure communications[END_REF], [START_REF] Tejado | Low speed control of an autonomous vehicle by using a fractional PI controller[END_REF], and [START_REF] Hosseinnia | Low speed control of an autonomous vehicle using a hybrid fractional order controller[END_REF].

III. CRUISE CONTROL

This section presents the hybrid CC of the vehicle at low speeds based on the above-mentioned different dynamics. The design of the fractional-order controllers for the throttle and the brake is firstly given and then, the hybrid modeling, control, and stability analysis.

A. Design of the Fractional-Order Controllers

The most important mechanical and practical requirement of the vehicle to consider during the design process is to obtain a smooth vehicle's response so as to guarantee its acceleration to be less than the well-known comfort acceleration, i.e., less than 2 m/s 2 .

In [START_REF] Tejado | Fractional network-based control for vehicle speed adaptation via vehicle-toinfrastructure communications[END_REF], [START_REF] Tejado | Low speed control of an autonomous vehicle by using a fractional PI controller[END_REF], and [START_REF] Villagrá | Control basado en PID inteligentes: Aplicación al control de crucero de un vehículo a bajas velocidades[END_REF], some classical and fractional-order PI controllers were designed for CC maneuvers. In this brief, the fractional-order PI controller designed in [START_REF] Tejado | Low speed control of an autonomous vehicle by using a fractional PI controller[END_REF] will be used for the throttle action-it was designed to control the throttle and brake pedals, but neglecting the dynamics during braking-whereas the brake will be controlled by a robust fractional-order PI due to the system uncertainty described previously. The motivation of improving that design by considering a hybrid model of the vehicle mainly arises from its application to ACC maneuvers, in which commutation between the pedals plays a key role for the success of the whole control.

Consider a fractional-order PI controller of the form

C(s) = k p + k i s α . ( 3
)
Specifications related to phase margin, gain crossover frequency and output disturbance rejection are going to be considered. Let assume that the gain and phase crossover frequency of the open-loop system are given by ω gc and ω pc , the phase and gain margins are denoted by φ m and M g , and the output disturbance rejection is defined by a desired value of a sensitivity function S(s) for a desired frequencies range.

The three specifications to be fulfilled to achieve stability and robustness are the following. 1) Phase margin specification

arg(C( j ω gc )G( j ω gc )) = -π + φ m (4) arg(C( j ω pc )G( j ω pc )) = -π. (5)
2) Gain crossover frequency specification

|C( j ω gc )G( j ω gc )| = 1 ( 6 ) |C( j ω pc )G( j ω pc )| dB = 1/M g . ( 7
)
3) Output disturbance rejection

1 1 + C( j ω)G( j ω) dB ≤ -20 dB, ω ≤ ω s . ( 8
)
To tune the fractional-order PI controller (3) for the throttle, the set of ( 4)-( 6)-( 8) was solved with the MATLAB function fsolve for the following specifications: 1) φ m = 90°; 2) ω gc = 0.45 rad/s; and 3) ω s = 0.035 rad/s. The controller parameters were: 1) k p = 0.09; 2) k i = 0.025; and 3) α = 0.8-the full design of this controller can be found in [START_REF] Tejado | Low speed control of an autonomous vehicle by using a fractional PI controller[END_REF].

With respect to the control of the brake, a fractional-order PI controller robust to variations in the system time constant was required. Since the controlled system phase never crosses -π rad, and in accordance with the idea proposed in [START_REF] Monje | On fractional PI λ controllers: Some tuning rules for robustness to plant uncertainties[END_REF], the following specifications are considered instead of ( 5) and [START_REF] Bu | English adaptive and cooperative cruise control[END_REF]:

arg (C( j ω m )G( j ω m )) = p m (9) |C( j ω m )G( j ω m )| dB = 1/M m . ( 10
)
Thus, ( 9) and ( 10) are used to find the frequency ω m at the gain M m and the phase p m . Therefore, defining θ = απ/2, (4), ( 6), [START_REF] Kianfar | Design and experimental validation of a cooperative driving system in the grand cooperative driving challenge[END_REF], and (10) turned into the following set of four nonlinear equations with four unknown variables -k p , k i , α, and ω m :

tan -1 k p ω α gc sin θ k i + k p ω α gc cos θ -tan -1 (τ ω gc )+π -θ -φ m = 0 (11) tan -1 k p ω α m sin θ k i + k p ω α m cos θ -tan -1 (τ ω m ) -θ -p m = 0 (12) 20 log ⎛
⎝ (k i + k p ω α gc cos θ) 2 + (k p ω α gc sin θ) 2 ω α gc (τ ω gc ) 2 + 1 ⎞ ⎠ = 0 (13) 20 log ⎛ ⎝ (k i + k p ω α m cos θ) 2 + (k p ω α m sin θ) 2 ω α m (τ ω m ) 2 + 1 ⎞ ⎠ - 1 M m = 0. (14)
In this case, the MATLAB function fmincon was used to reach out its solution, which finds the constrained minimum of a function of several variables. Actually, (13) was considered as the main function to optimize with [START_REF] Podlubny | Fractional-order systems and PI λ D μ controllers[END_REF], [START_REF] Hespanha | Encyclopedia of Life Support Systems (EOLSS)[END_REF], and (14) as constraints. Considering φ m = 90°, p m = -100°, ω gc = 0.7 rad/s, and M m = 20 dB as specifications, the parameters obtained for the brake controller were k p = 0.7, k i = 1.1, α = 0.45, whereas ω m = 5.7 rad/s. This controller was tuned to be robust for the above-mentioned interval for τ . Fig. 1 shows the Bode diagrams of the vehicle when braking with the designed PI α controller. It can be observed that ω gc = 0.7 rad/s and φ m = 93°, which fulfill the design specifications with robustness to variations of system time constant τ .

B. Hybrid Control

Let us describe the system and the controllers by their transfer functions G q (s) = K q /s + T q and C q (s) = k p q + k i q /s α q , where q = {1, 2} refers to the throttle and brake actions, respectively, and with the parameters shown in Table I. Phase differences between the characteristic polynomials of the closed-loop system.

Thus, the closed-loop transfer function of the system can be written as

Y (s) R(s) = γ q s α q + β q s α q +1 + (T q + γ q )s α q + β q , q {1, 2} (15)
where γ q = K q k p q and β q = K q k i q .

To analyze the stability of the hybrid system, the frequency domain method proposed in [START_REF] Hosseinnia | Stability of fractional order switching systems[END_REF] is going to be used. To this respect, the system has to be described as a switching system. Therefore, assuming α q = N q /D q , the switching system can be represented as

D 1 Mq x = A q x ( 16
)
where A q , q = {1, 2}, are the switching subsystems and M q is lowest common multiple of the denominators of D q and N q .

Then, system ( 16) is quadratically stable if and only if

|arg(det(A 1 -j ωI )) -arg(det(A 2 -j ωI ))| < π 2 ∀ω (17)
where A q = -(-A q ) 1/2-M q , q = {1, 2}, and I is identity matrix with proper dimension. The characteristic polynomials of the controlled system for the throttle and the brake are d 1 = s 1.8 + 0.57s 0.8 + 0.11 and d 2 = s 1.45 + 0.76s 0.45 + 0.49, respectively. Thus, the corresponding fractional-order system can be represented in state space by

D 1 5 x = A 1 x = O 1,5 -0.57 O 1,3 -0.11 I 9,9 O 9,1 x D 1 20 x = A 2 x = O 1,20 -0.76 O 1,8 -0.49 I 29,29 O 29,1 x
where O l,m and I l,m denote matrix of zeros and identity matrix with dimension of l × m, respectively. Fig. 2 shows the graphic representation of condition (17) applied to this system. It can be observed that the maximum phase difference is 36.33 • independently of τ -less than 90 • -which prove the stability of the controlled system considering the uncertainty in the brake dynamics.

IV. ADAPTIVE CC

This section addresses ACC maneuvers with two different distance policies considering two cooperating vehicles-one manual, the leader, and another automatic-at very low speeds (see a scheme in Fig. 3). The objective is to act the throttle and the brake of the automatic vehicle to track as precisely as possible both a desired distance between the two vehicles (interdistance) and a target relative velocity. Actually, a classical PD controller will be designed to perform the interdistance control, whereas the previously designed hybrid fractionalorder control will be used for the longitudinal control of the automatic vehicle. Thus, at least two control law regimes are needed: one for the desired velocity tracking (problem studied in Section III) and the other which tracks a desired following distance between the leader vehicle and a detected lead vehicle.

A. Interdistance Policies

In ACC, it is necessary to set the interdistance in a safe distance, which is called safe interdistance, d r , and will be the reference distance for the control. Although different strategies have been proposed in the literature to obtain d r , we will focus on the distance policies reported in [START_REF] Zhou | Range policy of adaptive cruise control vehicles for improved flow stability and string stability[END_REF] and [START_REF] Martinez | A safe longitudinal control for adaptive cruise control and stop-and-go scenarios[END_REF] mainly due to their success.

In accordance with [START_REF] Zhou | Range policy of adaptive cruise control vehicles for improved flow stability and string stability[END_REF], d r has been calculated as the minimal distance to avoid a collision if the preceding vehicle were to act unpredictably

d r = hV + d c + l v ( 18
)
which is known as constant-time headway policy, where l v is the vehicle length, d c is the minimal interdistance to avoid collision, and V is vehicle velocity and h is the constanttime headway, which is specified by the driver. No collision can occur if it is satisfied h ≥ 2γ max /J max , where γ max and J max are the maximum attainable vehicle's acceleration and the maximum driver desired jerk, respectively [START_REF] Cook | Stable control of vehicle convoys for safety and comfort[END_REF].

On the other hand, a safe interdistance policy is proposed in [START_REF] Martinez | A safe longitudinal control for adaptive cruise control and stop-and-go scenarios[END_REF] in such a way control could be designed independently of the vehicle's model, permitting the additional control loop to only be responsible of the model-matching between the actual system and the desired reference dynamics. The dynamic reference model will provide a reference interdistance less than the 2-s headway rule if the allowed maximum acceleration is high enough. In particular, the interdistance reference model describes the virtual dynamics of a vehicle, which is positioned at a reference distance d r from the leading vehicle as follows [START_REF] Martinez | A safe longitudinal control for adaptive cruise control and stop-and-go scenarios[END_REF]:

ḋr = c(d 0 -d r ) 2 + ẋl (t) -[c(d 0 -d r (0)) 2 + ẋ f (0)] (19)
where d 0 is the nominal safe interdistance, c plays the role of a damping constant-from a nonlinear model-, x l is the position of the leading vehicle, and ẋ f is the velocity of the follower. Note that all l and f subscripts refer to leading and following vehicles, respectively.

It should be remarked that both interdistance policies ( 18) and ( 19) satisfy the following comfort and safety constraints: 1) d r d c ; 2) V f γ max ; and 3) V f J max . They are taken to represent the worst case scenario in an emergency and limitations on the response of the traction and braking systems in the vehicle, as well as what is physiologically tolerable for the occupants.

B. Design of the Interdistance Controller

In this section, classical PD controller is going to be designed to obtain the reference speed for the following vehicle and guarantee the tracking of d r , which will be generated with the aforementioned policies.

A block diagram of the closed-loop control to be performed in the vehicle is shown in Fig. 4. The inner loop system can be expressed as where C d ,G c , and G d denote the transfer functions of PD controller, the closed-loop longitudinal control and a traditional integrator, respectively, i.e., C d (s

F(s) = C d (s)G c (s)G d (s),
) = k p + k d s, G c (s) = C q (s)G q (s)/1 + C q (s)G q (s), and G d (s) = 1/s.
To design a unique PD for the two inner-loop systems because of the brake and throttle dynamics, the system with lower phase margin was considered: the dynamics when throttle is active. Considering the following design specifications for the inner loop:

arg(F( j ω gc )) = -π + φ m (20) |F( j ω gc )| = 0 dB ( 21
)
with φ m > 80°and 0.6 < ω gc < 1 rad/s, the parameters obtained for the PD controller were: k p = 0.7 and k d = 1.2.

V. SIMULATION AND EXPERIMENTAL RESULTS

The real experiments were carried out on the real vehicle in the CARs private driving circuit, which was designed with scientific purposes, so only experimental vehicles were driven in this area. Two vehicles were used for the experimental phase: a fully automated vehicle and a manually driven one. As commented, the former is a convertible Citroën C3 Pluriel and is equipped with automatic driving capabilities with hardware modifications made to the throttle and the brake pedal actions. The latter vehicle is an electric Citroën Berlingo van also equipped with automatic driving capabilities. For the purpose of this brief, it was driven by a human driver making the leading car's behavior as close to a real traffic situation as possible. Both vehicles were equipped with RTK-DGPS working at 5 Hz as the main sensor.

This section shows the goodness of the proposed fractional hybrid strategy through simulation and experimental results, grouped into CC and ACC maneuvers. First, the details of how to implement the fractional-order controllers digitally are given.

A. Digital Implementation of Fractional Order Controllers

Theoretically, a fractional-order controller is an infinitedimensional linear filter, and that all existing implementation schemes are based on finite-dimensional approximations. In practice, we use a digital method, specifically the indirect discretization method, which requires two steps: 1) obtaining a finite-dimensional continuous approximation for the integral part s -α and 2) discretizing the resulting s-transfer function. In our case, to preserve the integral effect, s -α was implemented as s -α = s -1 s 1-α ; actually, only the fractional part P(s) = s 1-α was approximated by the modified Oustaloup's method [START_REF] Monje | Fractional-Order Systems and Controls. Fundamentals and Applications[END_REF]. Thus, an integerorder transfer function that fits the frequency response of P(s) in the range ω ∈ (10 -3 , 10 3 ) rad/s was obtained with seven poles and seven zeros. Later, the discretization of this continuous approximation was carried out using the Tustin rule with a sampling period T s = 0.2 s-GPS sampling period. Considering both the throttle and the brake controllers, eight-order digital IIR filters of the form C q (z) = k p q +k i q (2/T s 1z -1 /1 + z -1 ) -1 P q (z) were obtained, where

P q (z) = 7 k=0 b k z -k /1 + 7
k=1 a k z -k and with the coefficients shown in Table II.

B. Results for CC Maneuvers

The designed hybrid controller for CC maneuvers was tested by MATLAB/Simulink simulations and on the real automatic vehicle for different low velocity references between 5 and 20 km/h. In simulation, a random noise with zero mean and variance of 0.85 was added to the nominal value of τ to show the efficiency of the robust controller.

Fig. 5 shows the behavior of the vehicle when applying the designed fractional-order hybrid controller; more precisely, velocity tracking, acceleration, and normalized control action are included. In Fig. 5(a), the solid and dash-dotted lines refer to the experimental and simulated responses, whereas the dotted lines is the velocity reference. First, it is worth mentioning that both the experimental and the simulated behaviors are quite similar, so the considered longitudinal dynamics of the vehicle is good enough for the maneuvers at low speeds. Furthermore, the simulated and experimental vehicle responses are stable and smooth and track the desired reference. In Fig. 5(c), both the throttle and the brake control inputs were normalized to the interval [-1, 1], where positive values mean throttle actions-solid line-and the negative, brake ones-dotted line. It can be observed that the acceleration and control action are met the desired intervals. One can also appreciate the soft action over vehicle's actuators obtaining a good comfort for car's occupants-this is reflected in the acceleration values.

To sum up, the fractional-order hybrid control may be useful for autonomous vehicles at low speeds to control both the brake and the throttle actions, specially due to its possibility of obtaining more adjustable time and frequency responses and allowing the fulfillment of more robust performances.

C. Results for ACC Maneuvers

To compare the control with the two interdistance policies in conditions as equal as possible, a predefined route was recorded. This route was first travelled over with the manually driven vehicle, and all the relevant variables to perform the control-position, speed and acceleration were stored. In this way, the human influence in two consecutive trials was removed. The distance between vehicles at the beginning of the test was set to 6 m. Once this distance was achieved with 1-cm accuracy using the RTK-DGPS positioning system, the test was initiated. The interdistance dynamic models were parameterized to provide: 1) a maximum speed of V max = 50 km/h; 2) a maximum acceleration of γ max = 2 m/s 2 ; 3) a maximum jerk of J max = 5 m/s 3 ; and 4) a constant-time headway of h = 0.8 s.

Figs. 6 and7 show the behavior of the automatic vehicle when using the reference interdistance given by ( 18)-with d c + l v = 6 m-and [START_REF] Altafini | Hybrid Systems: Computation and Control[END_REF] for ACC maneuvers, respectively. Figs. 6 and7(a) show the simulated-thinner red lines-and experimental-thicker blue lines-velocity of the following vehicle with respect to the leading one, which is considered as reference for the former. Only differences can be observed between the velocity of the leader and the follower, especially in simulation. In Figs. 6 and7(b), the desired and the experimental interdistances are represented. As observed, the actual interdistance tracks the reference interdistance adequately. Automatic vehicle's acceleration and jerk are shown in Figs. 6 and7(c) and (d), whose values are lower than the aforementioned prerequisites. Finally, Figs. 6 and7(e) show the normalized control action. As can be observed, the vehicle behaves efficiently during both acceleration and deceleration, even when the leading car reduces its speed significantly-at time 65 s, the following car properly follows the reference interdistance as at the same time it increases the speed.

To compare the results for the different interdistance policies, an error function was defined as,

J = 1/T T 0 (|e p | + |e v | + u s )dt, where e p = d -d r is the interdistance error (in m), e v = V f ref -V f
is the velocity error (in km/h) and u s = |du/dt| is the control smoothness. Table III shows the results obtained by both strategies. As can be observed, the interdistance policy given by ( 19) causes smoother interdistance and, consequently, the vehicle's behavior is smoother. On the contrary, using the rule [START_REF] Mukai | A collision avoidance control for multi-vehicle using PWA/MLD hybrid system representation[END_REF], the vehicle's performance is poor in comparison [START_REF] Mukai | A collision avoidance control for multi-vehicle using PWA/MLD hybrid system representation[END_REF] AND [START_REF] Altafini | Hybrid Systems: Computation and Control[END_REF] with the previous strategy, but may be acceptable for a range of speeds.

For comparison purposes with integer-order strategies, the experimental results in [START_REF] Milanés | Comparing Fuzzy and intelligent PI controllers in stop-and-go manuevers[END_REF] when applying a traditional PI controller were also considered, in which the same route was used for the tests with the interdistance policy [START_REF] Altafini | Hybrid Systems: Computation and Control[END_REF] (see the interdistance and the velocity comparisons in Fig. 8). As observed, there exist meaningful differences between the hybrid fractional strategy proposed in this brief and the classical PI control, especially in terms of interdistance error and tracking, mainly due to the fact that the fractional controller allows the vehicle to follow the interdistance reference with more accuracy. On the one hand, the greatest interdistance error-with a value of 3.67 m-is obtained with the PI controller at around 65 s, because the autonomous vehicle is driving around a curved stretch; at that time, the error obtained with the proposed controller is almost zero. In contrast, the higher interdistance error obtained with the fractional controller is 1.54 m at 90 s; at that time, the error with the PI is even greater, i.e., 1.61 m. On the other hand, considering the mean value of the interdistance error, the proposed controller also shows a significantly better performance in ACC against the traditional PI: 0.431 against 0.658 m, respectively. Concerning the velocity, it can be said that the PI controller follows the leading vehicle's speed with poorer results.

VI. CONCLUSION

In this brief, a fractional-order hybrid strategy has been designed to control both the throttle and the brake pedals for CC and ACC maneuvers at very low speeds. Simulated and experimental results, obtained for real vehicles in a real circuit, were given to demonstrate the effectiveness of the proposed hybrid control law. Since the vehicle has different dynamics during accelerating and decelerating, two fractional-order PI controllers were designed for controlling the throttle and the brake for CC maneuvers. A hybrid model of the controlled system was obtained and its quadratic stability was proved using a frequency domain method, modeling the system as a switching hybrid system. ACC maneuvers were performed by two different distance policies using two cooperating vehiclesone manual, the leader, and another automatic-in which the desired interdistance between the leader and follower is maintained by an additional PD controller.

Our future effort will focus on replacing: 1) the fractional hybrid controller by a robust fractional-order PI controller to be to both the throttle and the brake pedals and 2) the PD interdistance controller by a fractional-order version.

Fig. 1 .

 1 Fig. 1. Bode diagrams of the vehicle controlled by the fractional-order PI with different values of the time constant τ for the brake.

Fig. 3 .

 3 Fig. 3. Scheme of ACC maneuvers with two Citroën vehicles.

Fig. 4 .

 4 Fig. 4. closed-loop control of the automatic vehicle for ACC maneuvers.

Fig. 5 .

 5 Fig. 5. CC results. (a) Velocity. (b) Acceleration. (c) Normalized control action.

Fig. 6 .

 6 Fig. 6. ACC results using (18) as the reference interdistance (d c + l v = 6 m). (a) Velocity. (b) Interdistance. (c) Acceleration. (d) Jerk. (e) Normalized control action. (For the velocity, the reference corresponds to the velocity of the leading vehicle.)

Fig. 7 .

 7 Fig. 7. ACC results using (19) as the reference interdistance. (a) Velocity. (b) Interdistance. (c) Acceleration. (d) Jerk. (e) Normalized control action. (For the velocity, the reference corresponds to the velocity of the leading vehicle.)

Fig. 8 .

 8 Fig.8.Comparing ACC results of classic PI and proposed controller. (a) Interdistance (Rule[START_REF] Altafini | Hybrid Systems: Computation and Control[END_REF] was used as the reference interdistance policy). (b) Velocity. (For the velocity, the reference corresponds to the velocity of the leading vehicle.)

TABLE I SYSTEM

 I

AND CONTROLLER PARAMETER Fig. 2.

TABLE II COEFFICIENTS

 II OF THE APPROXIMATIONS OF THE FRACTIONAL-ORDER CONTROLLERS

TABLE III ACC

 III RESULTS WHEN USING THE REFERENCE INTERDISTANCE GIVEN BY

This work was supported by the Spanish MICINN under Project TRA2008-06602-C03-01 and Project TRA2008-06602-C03-02.


Olivier Aubert
email: olivier.aubert@univ-nantes.fr

Joscha Jaeger
email: joscha.jaeger@merz-akademie.de

Merz Akademie

Annotating Video with Open Educational Resources in a Flipped Classroom Scenario

A wealth of Open Educational Resources is now available, and beyond the first and evident problem of finding them, the issue of articulating a set of resources is arising. When using audiovisual resources, among different possibilities, annotating a video resource with additional resources linked to specific fragments can constitute one of the articulation modalities. Annotating a video is a complex task, and in a pedagogical context, intermediary activities should be proposed in order to mitigate this complexity. In this paper, we describe a tool dedicated to supporting video annotation activities. It aims at improving learner engagement, by having students be more active when watching videos by offering a progressive annotation process, first guided by providing predefined resources, then more freely, to accompany users in the practice of annotating videos.

Introduction

There exists a huge number of Open Education Resources (OERs) of various types, in numerous domains. OERs offer great pedagogical content, but somehow lack in articulation. One of the ways to enhance their pedagogical potential is to provide explicit links between resources, exposing some knowledge articulation, defining a path to follow or a graph of relations to explore. This activity is at the heart of knowledge work, but its realisation as a shareable and modifiable entity is not obvious to many people. One of the goals of current teaching should be to teach students how to explicitly link these resources between themselves, so as to add explicit relationships to the existing knowledge. Many OERs are text-based or image-based, but an increasing number relies on audiovisual content, in part due to the technological availability of capture means and the general capture policy carried out in some institutions. While hypertext links are now commonly used and understood, hypervideo links, i.e. links from/to fragments of video documents, are less common and raise a number of specific issues, given the dynamic nature of video documents. Thus while video documents are now more and more openly accessible and available, and constitute a learning material of great pedagogical value, their potential is not always fully exploited [START_REF] Hobbs | Non-optimal uses of video in the classroom[END_REF]. Bringing the learners to a more active attitude while watching video documents can be achieved through various pedagogical practices and tools [START_REF] Bossewitch | Teaching and Learning with Video Annotations[END_REF][START_REF] Zahn | Digital video tools in the classroom: empirical studies on constructivist learning with audio-visual media in the domain of history[END_REF][START_REF] Schwan | The cognitive benefits of interactive videos: Learning to tie nautical knots[END_REF]. We propose here a tool that can be used to promote video-based active learning, instead of passive watching, through the use of annotations, illustrated here through a flipped classroom scenario [START_REF] Strayer | The effects of the classroom flip on the learning environment: a comparison of learning activity in a traditional classroom and a flip classroom that used an intelligent tutoring system[END_REF]. In addition, collaboration features promote group activities in order to invite learners to build their own shared knowledge [START_REF] Scardamalia | Knowledge Building: Theory, Pedagogy, and Technology[END_REF].

In this article, we describe a software framework dedicated to supporting video annotation activities, which can be tested at http :// ocwc . open -hypervideo . org/. It aims at 1/ improving learner engagement, by having the students be more active when watching videos; 2/ offering a progressive annotation process, first guided then more free, to accompany the users in the practice of annotating videos and building hypervideos; 3/ promoting a constructivist approach by offering collaboration and discussion features.

Video annotations and usage

We consider here video annotations as pieces of information linked to a specific fragment of a video. They can be of different natures: textual comments, images, other audio or video resources, or more generally an URL to any resource. These contents are anchored to specific fragments of the original video document, specifying begin and end timecodes (which may be identical when the user only wants to annotate a specific point in the video instead of a durative fragment).

Depending on the usage context, annotations may also be associated with various metadata, such as information about their author or creation date, or some way of categorizing them. Annotations constitute essential metadata to enable audiovisual documents handling beyond basic playing. They are required to offer indexing capabilities, either through basic chaptering of audiovisual documents or full-text search through time-aligned transcriptions for instance. They also can be used as a navigational aid for interactive video usage. Hereafter, they also can form the basis for the production of new kinds of documents, combining audiovisual documents and its metadata, which can qualify as hypervideos [START_REF] Aubert | Advene: Active Reading through Hypervideos[END_REF]. Video annotation production and usage shares some common concerns with text or image annotation: all require anchoring schemes, raise issues around the combined evolution of both original data and its metadata, and introduce new licensing issues (which may target the document, its metadata or the combination of both). Moreover, the dynamic and temporal nature of audiovisual documents brings additional concerns, especially in annotation edition and visualisation. The complexity of generic annotation processes can thus require a fair expertise and involvement. That is why it is essential to propose more specific annotation tools, more fitted to specific tasks, in order to simplify their usage. We propose here such a tool, targeting a pedagogical context where pre-defined resources are provided and users have to assimilate them and associate them to appropriate fragments of a video.

Usage scenario

We will illustrate our proposal through an example usage scenario. In a science history course, a teacher records a lecture in order to use it in a flipped classroom setup: his students will have to watch the lecture recording by themselves, and they will later have a interactive session together where the teacher can answer questions. To support this flipped classroom setup, before publishing his lecture the teacher provides additional resources such as images, texts or web resources that he publishes along the lecture recording. The learner tasks are twofold: first, they have to link the provided resources to appropriate moments of the lecture, as an exercise, through a simple interface, presented in figure 1. Second, they can annotate the recording with free-text annotations, identifying and expliciting the parts of the recording that they would like to talk about in class. The first step of the process encourages learners to be more active when watching a video, by taking into account other existing, predefined resources and linking them to appropriate parts of the lecture. Moreover, in order to properly achieve the task, they have to examine every associated resource, and memorize part of their information. The second step of the process, free-text annotation of specific lecture fragments, involves explicitation of difficult parts or of emerging ideas to be discussed in the classroom, and is useful for the teacher as a feedback, but also for the learners as a way to express concerns or ideas. The outcome of this phase then consists, for each student, in an annotated video, where pedagogical resources are synchronized with the original recording. A collaboration activity can then be carried out, built up upon the produced material: the class is divided into smaller learner groups, where each member confronts his annotations (linked resources and comments) with the annotations of the other members, thanks to a simultaneous display of annotations, as shown in figure 2. Learners are then encouraged to debate on the correct timing for resources or links, in order to achieve some consensus that can be presented to the rest of the class. The integration of a revision history system could then bring a track of the different modifications, in order to possibly have the group reflect on its own group activity.

Developments and future work

The proposed tool is functional but still in development. It is built using the Open Hypervideo framework (described and available at http://www.open-hypervideo.org/) and will be published under an open-source license, making it freely reusable and modifiable, in order to be consistent with the OER idea. The architecture of the tool adopts a lightweight, componentized approach, so that it can easily be integrated into different platforms. To foster learner engagement and improve digital literacy, the tool itself is based on open web technologies and standards, enabling learners as well as teachers to use, study, remix and share the software itself as needed, as part of the outcome. Dependencies concerning the technical environment have been limited to the smallest extent possible. In this self-contained surrounding, the boundaries between creation and creational process are meant to shift, extending the definition of work to the authoring environment. The interface provides different view modes, in which a set of options is made available based on user tasks and roles. By default, users can view the video and browse existing timebased annotations. When learners log in, the Annotate Video mode shows an overview of existing resources and facilitates adding, editing and removing annotations through a simple drag-and-drop interface. The outcome of this task is a personalised annotation set for the current video sequence, which can be exported and shared with the teacher. An additional view mode (Manage Annotations) enables importing, comparing and managing multiple annotation sets. This view mode is used to collaboratively select and merge annotations from all learner sets into one main timeline.

The view modes described above do not interfere with the video playback or time-based events. They rather provide their respective options on-the-fly, while the video continues to play. The video area is thereby always visible, scaling to provide the space needed for other interface elements. On the technical side, the tool already supports additional means of including time-based resources, such as spatio-temporal overlays on top of the video as well as collections of linked video sequences. Designing appropriate editing interfaces for these components will be an important part of future developments. Our final goal is to expand the editing means from an annotation framework down to the filmic material. Following the principles described above, teachers and learners shall be capable of editing and remixing the underlying video sequences from within the tool. In the end, this concept leads to an agglomeration of open media fragments, assembled by programming code and thus in a constantly unfinished state. For example, a film sequence would consist of several fragments of video files, customizable overlays like text inserts or time-based effects, as well as spatiotemporal links to external media fragments. What emerges is a time-based, extendable and interactive knowledge network that seamlessly integrates with the World-Wide-Web as technical and, more importantly, as social environment.

Discussion

This project focuses on interface issues. However, finding appropriate open educational resources is quite time-consuming and would greatly benefit from some support from other research projects such as the LinkedUp project [START_REF] Dietze | LinkedUp -Linking Web Data for Education Project[END_REF], which aims at developing tools and methods for the exploitation of public, open data available on the Web, in particular by educational institutions. A semi-automatic approach based on semantic metadata about existing OERs could be leveraged to facilitate the finding of resources by teachers and students. To this end, our resource creation and annotation interface should be augmented to add components that assist authors in finding appropriate resources through recommendations based on semantic metadata. By working with semantic concepts and linked open data, authors will also be able to discover previously unknown relationships during the process of gathering adequate resources. Evaluating possible interfaces and interaction methods for these tasks will be part of future developments. Video annotation is not an end in itself: it is one of the tools that is now becoming available on the pedagogical palette. Beyond video documents, annotation of any kind of document is an integral part of any scholarly work, and tools should be provided to accompany this practice on a variety of medias. Moreover, beyond the availability of such tools, appropriate integration in pedagogical scenarios and practices must be experimented and studied [START_REF] Sankey | Using technology to enable flipped classrooms whilst sustaining sound pedagogy[END_REF].

Conclusion

We propose a new open-source tool aiming at the development of new pedagogical practices, taking advantage of existing audiovisual OERs. In order to make learners more familiar with the practice of video annotation, a guided approach is proposed in a first phase, based on predefined resources proposed by the tutor. Then, learners can engage in a more open and flexible way with the video document by producing their own annotations, and carry out a collaborative activity around them. After the design and implementation phase, basic initial tests are encouraging and we are looking for more experimentation opportunities to validate our initial ideas.

Figure 1 :

 1 Figure 1: resource linking interface -predefined resources have to be associated by the learners at appropriate moments of the reference video document.

Figure 2 :

 2 Figure 2: collaborative comparison interface -the annotations produced by the different learners or groups are displayed simultaneously, in order to foster debate and discussion. This process leads to a consolidation of annotated resources in a main timeline, generating a joint group work that can be presented and shared with other learners.

Acknowledgement This work was partly funded by a French government support granted to the COMIN Labs excellence laboratory and managed by the National Research Agency in the "Investing for the Futures" program ANR-JO-LABX-07-0J. License and Citation This work is licensed under the Creative Commons Attribution License http :// creativecommons . org / licenses / by /3.0/. Please cite this work as: Aubert, O. and Jaeger, J. (2014). Annotating Video with Open Educational Resources in a Flipped Classroom Scenario. In Proceedings of OpenCourseWare Consortium Global 2014: Open Education for a Multicultural World.


Susete Alves Carvalho

Raluca Uricaru

Jorge Duarte

Claire Lemaitre

Nathalie Rivière

Gilles Boutet

Alain Baranger

Pierre Peterlongo

Reference-free high-throughput SNP detection in pea: an example of discoSnp usage for a non-model complex genome

From them:

 1,920 genotyped with an Illumina Golden Gate assay and 84% succeeded.

 1,340 mapped on a Pea consensus genetic map and their reference contigs anchored to the model species M.truncatula physical map.  The quality of discoSnp results in association with its very low memory needs and low time footprints led us to choose this software for a SNP discovery and direct Genotyping By Sequencing project on a set of 48 pea genomic DNA libraries from a recombinant inbred lines subpopulation sequenced with Illumina HiSeq2000 technology. The analysis enabled to identify 88,851 SNP polymorphs on this population, from which around 60k SNPs will be genetically mapped (Boutet et al. 2014).

SNPs data by

  defined in-silico from normalized cDNA sequencing (454 GF-FLX sequencer) of 8 pea genotypes.

Duarte et al. 2014

 Research SNPs from any number of raw NGS dataset(s)  No reference genome, data assembly or specific annotations needed  Composed by two modules to detect SNPs and improve their robustness.  Availability: http://colibread.inria.fr/software/

discosnp/ 42,645 SNPs defined in-silico. discoSnp software

  discoSnp software offers the advantage to find robust SNPs without the need to perform assembly. It can therefore be successfully applied to non-model unsequenced genomes(Quillery et al. 2014).

 In conditions of unsequenced genomes and low sequencing coverage, different tools on the same data can generate complementary SNPs sets.



Conclusions and Prospects

Uricaru et al. (2014). Submitted Duarte et al. (2014). BMC Genomics 15:126 Quillery et al. (2014). Molecular Ecology Ressources 14(2) Boutet et al. (2014). IFLRC VI 2014; Canada; Oral Communication

 From 1,340 SNPs mapped on a Pea consensus genetic map: 929 found by discoSnp and 432 found by Bowtie2+GATK.

→ The three methods each provide between 35k and 40k SNPs but only 6k SNPs are common between the three sets. Between 16k and 26k SNPs belong to only one detection method specifically.

→ The reason why SNPs specifically generated by either method were lost in the genotyping process may be due to: i/ filtering parameters including low coverage of the sequencing data, ii/ the large "kmer" size (especially for discoSnp, it does not to detect SNPs that are too close one from others).