Naresh Marturi

Brahim Tamadazte

Sounkalo Dembélé

Nadine Piat

Visual Servoing-Based Approach for Efficient Autofocusing in Scanning Electron Microscope

Fast and reliable autofocusing methods are essential for performing automatic nano-objects positioning tasks using a scanning electron microscope (SEM). So far in the literature, various autofocusing algorithms have been proposed utilizing a sharpness measure to compute the best focus. Most of them are based on iterative search approaches; applying the sharpness function over the total range of focus to find an image in-focus. In this paper, a new, fast and direct method of autofocusing has been presented based on the idea of traditional visual servoing to control the focus step using an adaptive gain. The visual control law is validated using a normalized variance sharpness function. The obtained experimental results demonstrate the performance of the proposed autofocusing method in terms of accuracy, speed and robustness.

I. INTRODUCTION

Over the past few decades, micro-nanosystems have received much attention due to their significant potential for development and use in different industrial domains (telecoms, automotive, aeronautics) and biomedical applications (manipulation of oocytes, non-invasive surgery, nanomedicine). The consequence of this strong demand is the emergence of an active research area concerning the development of assembly and handling technologies on a micro-nanoscale. In the case of nanoelectromechanical systems (NEMS) manufacturing, it is essential to master positioning, transfer, handling or assembling nanometric objects. To be able to visualize these type of objects, it is necessary to use a specific imaging system, the SEM. Compared to the optical microscopes, a SEM produce images of a sample by raster scanning the sample surface with a focused beam of electrons. Therefore, it is characterized by high resolution (better than 1 nanometer), high magnification (up to 500,000×) and a large depth-of-field.

In general, the automation of nanohandling tasks inside a SEM vacuum chamber with nanometric accuracy requires, the use of SEM vision feedback in control laws [START_REF] Wich | Nanohandling automation within a scanning electron microscope[END_REF]. Such control strategies require efficient image processing algorithms to extract visual features in designing the control laws. Hence, it is essential to use high quality and sharp images to ensure nanometric precision when extracting visual features. To obtain a sharp image and to use the SEM at its maximum This work is conducted with a financial support from the project NANOROBUST (ANR-11-NANO-006) funded by the Agence Nationale de la Recherche (ANR), France. It is also performed in the framework of the Labex ACTION (ANR-11-LABX-01-01) and the Equipex ROBOTEX (ANR-10-EQPX-44-01) projects. It is also partially supported by UFC-BQR project.

Naresh Marturi, Brahim Tamadazte, Sounkalo Dembélé, and Nadine Piat are with Automatic control and Micro Mechatronic Systems (AS2M) department, Institute FEMTO-ST, Besanc ¸on, France naresh.marturi at femto-st.fr potential, it is necessary to apply an efficient, accurate, robust and fast autofocus before nanohandling processes.

Basically in vision systems, focusing is defined as a process of obtaining maximum sharpness in the images by adjusting the objective lens. In general, autofocusing methods are classified into two types: active and passive [START_REF] Colour | Understanding camera autofocus[END_REF]. At first hand, active methods are commonly seen in the modern day cameras where the system uses a different measurement system to find the distance between the object and lens. Autofocusing is achieved by adjusting the optical system. On the other hand, passive methods determine the best focus by analyzing the image recorded at the sensor. The developed autofocusing technique in this work is a passive method that uses SEM secondary electron images.

Traditional autofocusing methods are mostly concentrated on selecting an optimal sharpness function and applying it over total range of focus steps to find the maximum sharpness point (i.e. maximum focus score). A comparison of different sharpness functions has been performed in [START_REF] Groen | A comparison of different focus functions for use in autofocus algorithms[END_REF], [START_REF] Sun | Autofocusing algorithm selection in computer microscopy[END_REF]. For SEM, with a high range of focus, applying the sharpness function at each focus step and finding the sharp image is a time-consuming process. To overcome this problem, many works have used the iterative search approaches to find the best focus point [START_REF] Batten | Autofocusing and astigmatism correction in the scanning electron microscope[END_REF], [START_REF] Rudnaya | Iterative autofocus algorithms for scanning electron microscopy[END_REF]. A Fourier transform-based autofocusing method is also presented in [START_REF] Ong | A robust focusing and astigmatism correction method for the scanning electron microscope[END_REF]. In order to provide a dynamic autofocus, a reliable and accurate method has to be developed. In this paper, we present a real-time method where the best focus is achieved by controlling the focus step using an adaptive gain.

In the remainder of this paper, section II presents the experimental setup along with the details of focusing process in a SEM. Various sharpness functions are presented in section III. The proposed visual servoing-based autofocusing approach is presented in section IV. The experimental results are reported in section V.

II. EXPERIMENTAL SETUP

The experimental setup architecture used for this work is shown in Fig. 1. It consists of a JEOL JSM 820 SEM along with two computers. The cross-section diagram of our SEM is shown in Fig. 2. Its electron column contains: an electron gun with tungsten filament, an anode, an objective aperture strip with 4 apertures of diameters 100, 70, 50, and 30 µm , respectively, a secondary electron (SE) detector, two scan coils, an objective lens and a vacuum chamber equipped with a movable platform to place the sample. The primary computer (Intel Pentium 4, CPU 2.24 GHz and 512 MB of RAM) is solely responsible for SEM control and it is connected to the SEM electronics and an image acquisition system (DISS5 from Point Electronic GmbH). The second PC (Intel Core 2 Duo, CPU 3.16 GHz, and 3.25 GB of RAM) is connected to the primary one using an Ethernet crossover cable. The communication between the two PCs is accomplished by implementing a client-server model using TCP/IP protocol, where the server program runs on the primary computer. The server is mainly responsible for setting the focus step and receiving images from the acquisition system. Image client receives these images from server and transmits them to the control server. Later, sharpness analysis and calculations are performed by the control server and a focus control command is issued to the image server via client. The possible magnification with the SEM ranges from 10× to 100, 000× with an achievable resolution of 3 nm.

A. Focusing in SEM

The two sets of electromagnetic lenses that contribute towards the focusing in SEM are condenser and objective lenses. The condenser lenses lying above the aperture strip are mainly responsible for controlling the spot size. Initially, these lenses converges the electron beam to a spot. Later, this beam flares out again and passes through the aperture, where low energy and non-directional electrons are filtered out. The objective lenses that are present below the aperture converges the beam once again and focus it onto the sample surface. Coarse focusing of the sample surface is performed by adjusting the electronic working distance that is attained by modifying the current passing through the objective lenses. This distance is electronically measured between the focused plane (on the sample surface) and the lower pole piece of the objective lens (electron column) and is not to be confused with the sample stage height which can be controlled externally. Fig. 3(a) shows the focusing geometry in SEM. At a distance D/2 on both sides of the focus plane for a selected magnification, the beam diameter is two times the pixel diameter and produces a blur image. Over the distance D (depth of focus), the image appears to be acceptably in focus. The depth of focus D is given by ( 1).

D = rZ AM [µm] (1)
So, focus is mainly dependent on the size of the aperture (A) and working distance (Z) at any given magnification (M ) and resolution (r). Fig. 3(b) reports the three main scenarios in the focusing procedure (i.e. focus, over focus and under focus).

The JEOL SEM is installed with a dynamic focusing module that modifies the current passing through the objective lens and thus the electronic working distance can be preselected. As stated earlier the DISS5 system has been used for this work, it provides a simple control for the focus by linking the electronic working distance with a series of focus steps (i.e. each focus step modifies the working distance to get a focused image). The relation between focus steps and electronic working distance is shown in Fig. 4. Subsequently, the value of working distance (Z) for any given focus step (F ) can be computed by using the curve equation obtained by approximating it with a polynomial given in [START_REF] Colour | Understanding camera autofocus[END_REF].

Z =      50, if F ≤ 813 1, if F ≥ 1713 p 1 F 4 + p 2 F 3 + p 3 F 2 + p 4 F + p 5 , otherwise (2)
where, p 1 . . . p 5 are the polynomial coefficients.

III. IMAGE SHARPNESS FUNCTIONS

In the context of this work, various sharpness measures that have been used in many focusing algorithms are studied [START_REF] Sun | Autofocusing algorithm selection in computer microscopy[END_REF], [START_REF] Rudnaya | Evaluating sharpness functions for automated scanning electron microscopy[END_REF] and [START_REF] Subbarao | Focusing techniques[END_REF]. The principle of accomplishing autofocusing based on the computed sharpness score using a sharpness function is shown in Fig. 5. It is considered that the image with best focus has the maximum value of sharpness score. Different sharpness functions are explained below using the following notations: sharpness function S, image I M ×N where M and N are the width and height, intensity I(u, v) where u and v are pixel coordinates.

A. Derivative-based sharpness functions

Derivative-based sharpness functions are widely used in many experiments. The underlying principle behind these methods is that the focused images have high differences between the neighboring pixels than in out-of-focus images.

1) Laplacian: This function convolves the image with a Laplacian edge detection mask given by L = [-1 -4 -1; -4 20 -4; -1 -4 -1] to compute the second derivative d(u, v) of the image. The sharpness function is given by [START_REF] Groen | A comparison of different focus functions for use in autofocus algorithms[END_REF].

S L = M N |d(u, v)| (3)
2) Brenner: Brenner's function uses the difference between a pixel value and its second neighboring pixel value.

S B = M N |I(u, v) -I(u + 2, v)| (4)

B. Statistics-based sharpness functions

Usually, the statistics-based measures are less sensitive to image noise and are widely used in many autofocusing algorithms.

1) Variance: This function computes the variations in the grey level intensities among the pixels.

S V = 1 M N M N (I(u, v) -µ) 2 (5)
where, µ is the image mean intensity and is given by [START_REF] Rudnaya | Iterative autofocus algorithms for scanning electron microscopy[END_REF].

µ = 1 M N M N I(u, v) (6)
2) Normalized variance: This function normalizes the final value by the pixel mean intensity.

S N V = 1 M N 1 µ M N (I(u, v) -µ) 2 (7)
Objective lens

Z

Best focus

Sample surface

Direction of scan

Sharpness function

Fig. 5. Autofocusing principle in SEM.

3) Correlation: Two focusing measures using the correlation technique have been proposed. One is based on the autocorrelation function (ACF) and the other is based on standard deviation function. The ACF-based sharpness function is given by [START_REF] Rudnaya | Evaluating sharpness functions for automated scanning electron microscopy[END_REF].

S AC = M -1 u=1 N v=1 I(u, v) I(u + 1, v)- M -2 u=1 N v=1 = I(u, v) I(u + 2, v) (8)
The standard deviation-based function is given by [START_REF] Subbarao | Focusing techniques[END_REF].

S std = M N I(u, v) I(u + 1, v) -M N µ 2 (9)
C. Wavelets-based sharpness functions

Various sharpness functions have been proposed using the wavelet transform [START_REF] Yang | Wavelet-based autofocusing and unsupervised segmentation of microscopic images[END_REF].

1) Wavelet-1: It applies both high-pass (H) and lowpass (L) filters to an image and divides it into four subimages LL, LH, HL and HH. Focus score is computed by summing the absolute values in HL, LH and HH regions.

S W 1 = M N |W HL (u, v)| + |W LH (u, v)|+ |W HH (u, v)| (10)
2) Wavelet-2: This function sums the variances in HL, LH and HH regions. The mean values in computing the variances for each region are computed using the absolute values.

S W 2 = 1 M N M N (|W HL (u, v)| -µ HL ) 2 + (|W LH (u, v)| -µ LH ) 2 + (|W HH (u, v)| -µ HH ) 2 (11)
The evaluation results of the different sharpness functions are shown in Fig. 6. It is noticed that all the functions have achieved a maximum value at the same focus image with more or less efficiency. Out of all, the normalized variancebased method resulted in a curve with less noise and a welldefined peak in less time. Thus, in the design of the visual servoing-based autofocusing, we choose this method as our sharpness function for estimating the sharpness score.

IV. VISUAL SERVOING-BASED AUTOFOCUSING

A. Traditional visual servoing approach

Visual servoing refers to the control of a robot's motion using the continuous image feedback information [START_REF] Chaumette | Visual servo control. I. basic approaches[END_REF]. To achieve this, a set of visual features are derived from the images and are compared with the visual features from the reference image. In the basic approach of visual servoing, a control law is designed such that the robot will move to a desired pose p * , having s * visual features, using the computed visual features s, at the current pose p. The main goal lies in minimizing the error function, e given by ( 12).

e = s -s * (12)
For designing the vision-based control scheme, an interaction matrix L that links the time variation of the current visual features ṡ with the camera instantaneous velocity v c is required. The relationship is then given by ṡ = Lv c . Using e and ṡ, the camera velocity is given by [START_REF] Marchand | Control camera and light source positions using image gradient information[END_REF].

v c = -λL † ė (13)
where, λ is the gain to assure an exponential decrease in the error, L † is the pseudo-inverse of the L and ė is the time variation of e. For a 2D point feature m(u, v) in the image frame that is a projection of the 3D point M (X, Y, Z) in the camera frame, the interaction matrix L associated with m is given by ( 14).

L = -1 Z 0 u Z uv -(1 + u) 2 v 0 -1 Z v Z -(1 + v) 2 -uv -u (14)

B. Autofocusing using visual servoing

This work has been performed utilizing the idea of basic visual servoing technique. Instead of minimizing the error function, the proposed method maximizes the normalized variance sharpness function given by [START_REF] Ong | A robust focusing and astigmatism correction method for the scanning electron microscope[END_REF]. Rather than computing the local visual features, the global image information is used in this work. This type of visual servoing is called as direct visual servoing [START_REF] Tamadazte | A direct visual servoing scheme for automatic nanopositioning[END_REF]. Most importantly, no reference image or features are used; instead, the method converges to a best focus position i.e. when the sharpness function reaches its maximum value.

If our goal is to maximize the sharpness function, it is first required to observe the variation of its behavior with respect to the focus steps i.e. with the change in electronic working distance. Fig. 7(a) shows this behavior of the sharpness function at two different magnifications. It is then observed that, for a specific range of working distance (inside the peak) we get images with some details and the rest are dark or bright images with varying noise. From this, the primary goal is to drive the control to reach the focus range. Keeping this in mind, the initial control law has been designed using an adaptive gain that changes with the sharpness score. The corresponding vision-based objective function (C) is given by (15).

C = λ S S (15)
where, λ is the adaptive gain given by ( 16).

λ = α S0 S 2 , if S0 S < 1, α, elsewhere. ( 16
)
where, α is a positive integer, S 0 and S are the sharpness scores computed from first image and the current image. The unit vector

S S

provides the driving direction. Using (16), the primary task function T 1 now takes the form given in (17).

T 1 = F c + C (17)
where, F c is the current focus step. The underlying idea is to have a maximum amount of gain at the region far from the focus. This ensures that the focus step is big enough to reach the focus region. Next, to have a minimum amount of gain at the region near focus such that the focus step is small. As the primary task can only drive the focus step using sharpness information, it does not have any direct linking with the working distance. In visual servoing, if the primary task does not constrain all degrees of freedom, a secondary task can be added as it has no effect on the primary task [START_REF] Marchand | Control camera and light source positions using image gradient information[END_REF]. So, for this problem of autofocusing using visual servoing, a secondary task (T 2 ) has been realized, that links the electronic working distance (Z) with the gradient of sharpness function. Later, it has been used as a stopping criterion for the overall process.

The secondary task function is given by (18).

T 2 = ∂S ∂Z L z (18)
where, ∂S ∂Z is the gradient of the sharpness function with respect to the working distance Z and L z is the interaction matrix that links the gradient with the working distance.

Here, assuming the change in the Z is small (especially near best focus point), the gradient has been treated as the difference between consecutive sharpness scores given by (19). The interaction matrix L z = -1 Z where, the Z value at a specific focus step is obtained from [START_REF] Colour | Understanding camera autofocus[END_REF].

∂S ∂Z = S i -S i-1 Z (19)
Using ( 17) and (18), the final control law to control the focus step is given by (20). The relationship between the sharpness score and the secondary task functions at 1000× magnification is depicted in Fig. 7(b). The secondary task function thus provides the derivative information of the sharpness score. When the sharpness function reaches it maximum, the secondary task function crosses zero and hence the overall process can be stopped at this point. Because of the presence of noise in the images, the secondary task function have some peaks near zero, to avoid this effect a value of -0.001 has been treated as the stopping limit in this work.

F = F c + λ S S

V. EXPERIMENTS WITH THE SYSTEM

This work has been performed to investigate and find a fast and reliable autofocusing method for SEM. Many experiments are performed to evaluate the proposed approach of autofocusing based on the visual servoing technique. The sample used for imaging is a microscale calibration template containing chessboard patterns that is fabricated at FEMTO-ST institute. The acceleration voltage used to produce the beam is 15 kV . All experiments are carried out using the secondary electron images with a size of 512 × 512 pixels.

A. Evaluation of the method

Initial experiments have been performed to validate the proposed method at different magnifications. The tests are conducted using an aperture size of 50 µm and α = 400 at 300× and 1000× magnifications. The brightness and contrast levels are set to the optimal values. The dwell time i.e. the time to scan one pixel is set to 360 ns to achieve an acquisition speed of 2.1 frames per second. Fig. 8(a) and Fig. 8(b) show the sharpness scores given by ( 7) and the corresponding gain values at 300× and 1000× magnifications respectively. Fig. 9 shows the secondary task function at 300× and 1000× magnifications. From the obtained results, it can be noticed that the focusing process stopped precisely at the maximum of sharpness function i.e. at this point the secondary task function reached -0.001.

B. Speed and accuracy test

The performance of the proposed autofocusing method is evaluated by comparing with the traditional search-based algorithms at different experimental conditions. An iterative search approach has been employed for this purpose. The search-based method is implemented over the total range of focus steps using three iterations. For each iteration, the total range of focus steps is divided into four subregions and searched for the global maxima with a fixed step size. The region containing the maximum value is then used for the next iteration. The step sizes used for each iteration are 50, 20 and 1, respectively. The maximum value found after the final iteration is the best focus point. The accuracy obtained by this method has been treated as the best accuracy, since it scans each step for the best focus in its final iteration. Hence, the focus step returned by this method is used as the reference step for computing the step error.

The proposed method is compared to the iterative searchbased approach in terms of total time taken and accuracy of focusing at different magnifications. Here, the total time taken also includes the time taken to acquire and transfer the images. The obtained results using optimal values of brightness, contrast and scan speed are summarized in Table I. Table II shows the results obtained with an increase in brightness. Table III summarizes the results achieved with a changed dwell time of 180 ns. This change in the dwell time increases the noise levels in the images. Table IV shows the results obtained using a silicon dioxide sample containing the microparts. The main reason behind this test is that the surface of this sample is not a good conductor. Due to this, charges are accumulated on the sample surface resulting in the images with grey level fluctuations. All these tests are performed using α = 300. Finally, Table V summarizes various speeds that can be achieved with proposed visual servoing-based method by changing the α value. Fig. 10 shows some of the screenshots captured during various tests. The obtained results show the repeatability, robustness and speed of the proposed method regardless of the operating conditions.

Fig. 1 .

 1 Fig. 1. Experimental setup architecture.

Fig. 2 .

 2 Fig. 2. Cross section diagram of JEOL JSM 820 SEM.

Fig. 3 .

 3 Fig. 3. (a) Depth of focus in SEM (b) Various focusing scenarios in SEM.

Fig. 4 .

 4 Fig.4. Relationship between the focus step and working distance.

Fig. 6 .

 6 Fig.6. Performance of various sharpness functions.

  Fig. 7. (a) Sharpness score variation with respect to focus steps at 300× and 1000× magnifications (b) secondary task variation with respect to the focus steps.

Fig. 8 .Fig. 9 .

 89 Fig.9. Secondary task function at 300× and 1000× magnifications.

TABLE I TIME

 I TAKEN AND ACCURACY AT OPTIMAL CONDITIONS.

	Mag (×)	Time (s)	Accuracy (Focus steps) (Focus step 0.3 mm)
		proposed	search	proposed search	step error
	300	42.703	117.97	1222	1219	3
	500	48.5	109.62	1220	1218	2
	800	43.46	112.03	1221	1219	2
	1000	48.42	109.4	1222	1219	3

TABLE II TIME

 II TAKEN AND ACCURACY AT CHANGED BRIGHTNESS.

	Mag (×)	Time (s)	Accuracy (Focus steps) (Focus step 0.3 mm)
		proposed	search	proposed search	step error
	300	42.06	110.64	1217	1213	4
	500	49.48	118.06	1218	1213	5
	800	48.29	111.6	1215	1212	3
	1000	51.37	111.74	1216	1213

ACKNOWLEDGMENT

Authors would like to thank Mr. Joel Agnus of AS2M, FEMTO-ST for his support in fixing the problems with SEM.

VI. CONCLUSION In this paper, new, fast and robust visual servoing-based autofocusing method for SEM has been presented. Unlike the traditional methods, the developed method performs the focusing by controlling the size of the focus step using an adaptive gain. The secondary task used in the control law precisely stops the overall process, when a best focus position is reached. For this work, a normalized variance sharpness function has been selected to produce the sharpness score of the images. Based on the sharpness score, the value of the gain is adjusted such that a best focus position is ensured. Obtained experimental results prove the fastness of the developed method over existing search-based and precision in finding the best focus. The proposed autofocusing approach has also been validated at different experimental conditions and the obtained results prove the robustness of the method. Future work will be devoted to use this technique in performing the autonomous nanoparts handling application using SEM.


A Mayzaud

R Badonnel

I Chrisment

Monitoring and Security for the Internet of Things

The concept of Internet of Things involves the deployment of Low power and Lossy Networks (LLN) allowing communications amongst pervasive devices such as embedded sensors. A dedicated routing protocol called RPL has been designed to consider the constraints of these LLN networks. However, the RPL protocol remains exposed to many security attacks that can be very costly in time and energy. In this paper, we propose to exploit risk management methods and techniques to evaluate the potentiality of attacks and to dynamically reduce the exposure of the RPL protocol while minimizing resources consumption.

Introduction and Challenges

The growing interest for the Internet of Things has resulted in the large-scale deployment of Low power and Lossy Networks, such as wireless sensor networks and home automation systems. These networks have strong constraints in terms of resources (energy, memory, power) and their communication links are by nature characterized by a high loss rate and a low throughput. Moreover the traffic patterns are not simply point-to-point, but in many cases the devices communicate according to a point-to-multipoint or multipoint-to-point schema. Existing routing protocols for wired networks (OSPF, IS-IS) and for ad-hoc networks (AODV, OLSR) are not suitable to deal with all these requirements. The IETF ROLL1 working group has proposed a new routing protocol called RPL (Routing Protocol for Low power and Lossy Networks) based on IPv6 and specifically designed for these environments [START_REF] Winter | RPL: IPv6 Routing Protocol for Low-Power and Lossy Networks[END_REF]. These RPL-based networks may be exposed to a large variety of attacks [START_REF] Tsao | Security Framework for Routing over Low power and Lossy Networks[END_REF], but the deployment of security mechanisms may also be quite expensive in terms of resources. In that context, we propose to exploit risk management methods and techniques to detect and prevent attacks while preserving resources in these networks. Risk management allows to dynamically adapt the selection of security countermeasures with respect to the observed threats. In the following of the paper, we will give an overview of the RPL protocol and its security issues, and then describe how risk management can be applied to these networks.

The RPL protocol is a distance-vector routing protocol based on IPv6, where devices are interconnected according to Destination Oriented Directed Acyclic Graphs (DODAG) [START_REF] Gaddour | RPL in a Nutshell: a Survey[END_REF]. An illustration of such a network is given in the lower plane of Figure 1. A network is composed of one or several DODAGs grouped into a RPL instance which is associated to an objective function. An objective function computes the best path for a set of metrics or constraints. A RPL node can join several instances at the same time but it can only join one DODAG per instance. For example in Figure 1, the node 11 is part of the RPL instances 1 and 2 in the DODAGs 2 and 3. These multiple instances enable the protocol to perfom different optimizations, such as quality-of-service. A set of ICMPv6 control messages is defined to exchange RPL routing information. A DODAG is built from a root which is the data sink of the graph. A rank is associated to each node and corresponds to its location in the graph with respect to the root. The node rank is always increasing in the downward direction, as illustrated in the DODAG 2 of Figure 1.

This procotol is exposed to multiple security attacks such as traffic interception, node resource exhaustion or denial of service [START_REF] Boumessouer | Analysis of Vulnerabilities and Attacks in the RPL Routing Protocol[END_REF]. For instance, a malicious node can voluntarily decrease its rank value to get closer to the root and intercept more traffic. A malicious node can also simply refuse to route messages, provide incorrect routing information data, or flood the network to perform denial of service. RPL already defines several mechanisms contributing to its security. It integrates local and global repair mechanisms to detect and avoid loops. It also considers two potential security modes. The pre-installed mode consists in having nodes with pre-installed keys in order to send secured messages. The authenticated mode considers that nodes with pre-installed keys can only join a DODAG as leaf, and must obtain a key from an authenticated authority to join the graph as a router. Complementary security mechanisms from regular protocols can also be envisioned to cover a larger variety of attacks, such as distributed denial-of-service attacks. The deployment of such security mechanisms (envisioned or not by the protocol) can be quite expensive in terms of network resources and may impact on the overall performances.

Risk Management applied to RPL-based Networks

Risk management offers new perspectives to dynamically activate or deactivate security mechanisms in RPL-based networks, in order to prevent attacks while maintaining network performances. We propose in this paper to investigate risk management methods and techniques for addressing the trade-off between security and cost in the Internet of Things. The risk level is traditionally defined as a combination of the probability of the attack and its consequences but may also be decomposed as given by Equation 1 [START_REF]An Introduction to Computer Security: The NIST Handbook[END_REF].

R(a) = P (a) × E(a) × C(a) (1)
Let consider a security attack noted a. The risk level R(a) depends on the potentiality P (a) of the attack, the exposure E(a) of the RPL network, and the consequences C(a) on the network if the attack succeeds [START_REF] Dabbebi | Managing Risks at Runtime in VoIP Networks and Services[END_REF]. Risk management is a process consisting in monitoring, prioritizing and controlling risks [START_REF] Bedford | Probabilistic Risk Analysis: Foundations and Methods[END_REF]. For instance, when this process observes a high potentiality P (a), it may activate security mechanisms (being aware of their costs) to reduce the exposure E(a) and maintain the risk level R(a) to a low value [START_REF] Gehani | RheoStat : Real-Time Risk Management[END_REF]. As depicted on the upper plane of Figure 1, the process is composed of two main activities: risk assessment and risk treatment. Risk assesment consists in quantifying the potentiality of attacks. For that, it is necessary to evaluate the performance of detection techniques (based on anomalies or known signatures) in these RPL environments, and to identify the network nodes able to perform this activity. Risk assessment aims also at quantifying the consequences of successful attacks. The objective is to assess the relative importance of nodes in the RPL network, and to analyze how the attack against a given node may impact on the functioning of the overall network.

The risk treatment activity consists then in selecting and applying the security mechanisms that are needed. The activities of suspicious nodes can be mitigated, or the nodes can be (partially) excluded from the RPL network. For instance, the number of requests from them may be restricted over time, or the considered RPL nodes may not be allowed to act as routers anymore. The selection of countermeasures takes into account the costs induced by their activation on the RPL network. As previously mentioned, this cost is often not negligeable in such a critical environment. A typical illustration of this statement has been given in [START_REF] Xie | Routing Loops in DAG-Based Low Power and Lossy Networks[END_REF] where the authors showed that the traffic generated by a loop avoidance mechanism was higher than the one generated by the loops themselves most of the time.

The Internet of Things is typically based on the deployment of Low power and Lossy networks. Those ones have scarce resources in terms of energy, power and memory, and rely on limited communication links. Their development has led to the specification of a dedicated protocol, called RPL, by the IETF ROLL working group. These networks are exposed to multiple attacks. While security mechanisms are available or could be adapted, their activation may degrade the network performance. We propose to apply risk management methods in these networks in order to address the trade-off between security and cost. The objective is to dynamically adapt the network exposure with respect to the threat potentiality, through the activation or deactivation of dedicated countermeasures.

As future work, we plan to classify the different security mechanisms available (or potentially applicable) for these networks and to analyze their cost and their coverage against current security attacks. We are also interested in other attacks such as diversion attacks. We will then work on the design, the implementation and the evaluation of our risk management strategy through proof-of-concept prototyping and simulations using Cooja or ns-3 [START_REF] Bartolozzi | ns-3 RPL Module: IPv6 Routing Protocol for Low Power and Lossy Networks[END_REF].

Fig. 1 .

 1 Fig. 1. Risk Management Applied to RPL Networks

Routing Over Low power and Lossy networks

Acknowledgements. This work was funded by Flamingo, a Network of Excellence project (ICT-318488) supported by the European Commission under its Seventh Framework Programme.


Donald Selmanaj

Matteo Corno

Olivier Sename

Sergio Savaresi

Advantages of rear steer in LTI and LPV vehicle stability control

Keywords: LPV controller, four-wheel steering, rear braking torques, yaw stability control

In this paper, the advantages of the rear wheel steer in robust yaw stability control of four wheeled vehicles are shown. A MIMO vehicle dynamic stability controller (VDSC) involving front steer, rear steer and rear braking torques is synthesized. The comparison between a vehicle with and without rear steer is done on avoidance maneuver using both LTI and gain-scheduling LPV controller. Both robust H ∞ controllers are built by the solution of an LMI problem. To better evaluate the influence of the rear steer on the performance time domain indexes are introduced. The simulation results show that active rear steer enhances vehicle handling on a low friction surface.

I. INTRODUCTION

In the last years active safety systems are widely spread in commercial light vehicles and several solutions to global chassis control can be found in literature. They can be classified by control structure and actuators used to ensure stability. The number of available actuators (control variables) is imposed by the mechanical layout. In brake-based studies (see, e.g., [START_REF] Corno | Advanced yaw control of four-wheeled vehicles via rear active differential braking[END_REF], [START_REF] Tondel | Control allocation for yaw stabilization in automotive vehicles using multiparametric nonlinear programming[END_REF], [START_REF] Panzani | Designing on-demand four-wheel-drive vehicles via active control of the central transfer case[END_REF]) the vehicle behavior is controlled through torque distribution to the four wheels. Brake-based solutions imply a relatively simple mechanical layout, however the induced vehicle behavior presents a strong dependence on the longitudinal velocity. Furthermore solutions involving both braking and active front steering (AFS) have been proposed (see [START_REF] Changfang | Asymptotic decoupling control with active front steering and electronic differentials in four wheel steering vehicles[END_REF], [START_REF] Yang | Coordinated control of afs and dyc for vehicle handling and stability based on optimal guaranteed cost theory[END_REF]). The combined management of these actuators leads to improved vehicle handling and stability, however the interaction between the front active steer controller and the driver might influence the driveability of the vehicle. To take full advantage of the tire grip, four wheel steering (4WS) architectures combined with brake-based architectures have been proposed. Mainly due to increased mechanical complexity, these solutions are not spread in commercial light vehicles, however many studies have evaluated the advantages introduced by an active rear steering. In [START_REF] Marino | Input-output decoupling control by measurement feedback in four-wheel-steering vehicles[END_REF] and [START_REF] Yang | Control strategy for four-wheel steering vehicle handling stability based on partial decoupling design[END_REF] decoupling control architectures have been proposed in order to reduce the interaction between the yaw rate and lateral dynamics, while in [START_REF] Yin | A study on µ-synthesis control for four-wheel steering system to enhance vehicle lateral stability[END_REF], [START_REF] Du | Robust control study for four-wheel active steering vehicle[END_REF], [START_REF] Ba Guvenc | Robust yaw stability controller design and hardware-in-the-loop testing for a road vehicle[END_REF] and [START_REF] Yin | Improving handling stability performance of four-wheel steering vehicle via µ-synthesis robust control[END_REF] robust control architectures are introduced in order to overcome external disturbances, such as wind forces and parameter variations due to the running vehicle condition. Among The present work is an extension of the previous one in [START_REF] Fergani | Global chassis control using coordinated control of braking/steering actuators[END_REF] and [START_REF] Poussot-Vassal | Vehicle dynamic stability improvements through gain-scheduled steering and braking control[END_REF] where a collaborative control of active front steer and rear brake torques is proposed. Two kinds of controllers are implemented: an LTI (Linear Time Invariant) controller and an LPV (Linear Parameter-Varying) controller. The LTI controller uses all available control variables in every condition while the LPV controller allows to choose whenever activate or deactivate a control input. The Activation criteria can depend on the vehicle running condition or it can depend on a fault detection system. For instance, if a failure occurs and an input is not available anymore, the LPV controller can switch to a different configuration still ensuring the stability of the system. It is worth noting that an LTI controller does not guarantee the system stability and performance if an actuator fails.

Here the vehicle architecture is extended introducing the active rear steering (ARS). Afterwards a LTI and a LPV controller are designed in the H ∞ framework, and the performance of both controllers and both types of vehicles (with and without rear steering action) are compared in a critical driving condition. The aim of the work is to identify the advantages introduced by the rear steering action in the yaw rate stability control and to emphasize the differences between the 2 types of controllers.

II. CONTROL ARCHITECTURE

The control structure is represented in Fig. 1 and derived from [START_REF] Poussot-Vassal | Vehicle dynamic stability improvements through gain-scheduled steering and braking control[END_REF]. It is a two-layer architecture. In the first layer the VDSC generates the desired steering angles and wheel torques; in the second level the ABS actuators at the rear axle and the steering actuators generate the actual control values. The control strategy implements a yaw reference tracking philosophy where the desired yaw is generated by a nominal model (here a bicycle model but some steady state evaluations could be done). The front active steering input is superimposed to the driver steering input. Two VDSC controllers are designed: an LTI controller employing all the available actuation and a LPV gain scheduled controller designed to better coordinate the available actuation (as explained later). Both controllers are designed following the H ∞ paradigm applied to the following extended bicycle model:

β ψ = µ -C f -C r mv 1 + l r C r -l f C f mv 2 l r C r -l f C f Iz -l 2 f C f -l 2 r C r vIz β ψ + C f mv C r mv 0 0 0 l f C f I z -l r C r I z 1 I z C λ t r 2I z - C λ t r 2I z       δ f δ r M dz T rl T rr       ( 1
)
where β is the vehicle slip angle, ψ is the yaw rate, δ f and δ r are the front and the rear steering angles respectively, T rl , T rr are the rear breaking torques and M dz is the yaw rate disturbance (lateral wind effect for instance). Fig. 2 shows the chosen H ∞ control configuration, including some weighting functions that represent the desired closedloop performances and handle the different limitations on the control inputs.

• W T br j ( j = l, r) limits the use of the braking actuators at high frequencies (10Hz). • W δ f is a band-pass filter witch allows the control to act below the actuator bandwidth frequency (10Hz) and above the drivers acting range of frequencies (we consider [0, 1]Hz). • W δ r penalizes the use of the rear steering actuator at high frequencies (10Hz).

• W e ψ ensures the tracking performances at low frequency • W β penalizes high side slip angles at low frequency. It is worth noting that, in Fig. 2, the bicycle model and the weighting functions are LTI systems. Nevertheless K will be either an LTI controller as an LPV one. The first case naturally arises following the control configuration in Fig. 2. On the other hand an LPV controller will be designed imposing a specific parameter dependent structure to the controller state space representation (as presented in [START_REF] Fergani | Global chassis control using coordinated control of braking/steering actuators[END_REF]).

A. LTI controller structure

The output feedback LTI controller serves as a benchmark. It is a fixed structure controller using all the control variables in every situation. Two different versions of the controller are designed, LTI1 uses front wheel steering and the brake actuators; LTI2 uses in addition the rear wheel steer. Fig. 3 shows the sensitivity functions of the two closed loop systems (controller + bicycle model).The rear wheel steering (which concerns only the LTI2) does not seem to improve the closed loop nominal performances.

B. LPV controller structure and parameters choice

The LTI controller employs all the control variables indifferently. Therefore all the actuators are used simultaneously, which could be not optimal in an energetic sense, and could be too obscure for car manufactures since the use of the control actions are not related to the driving situations. As shown preliminary in [START_REF] Fergani | Global chassis control using coordinated control of braking/steering actuators[END_REF] the LPV approach is a solution to a better coordination of the different control inputs (braking and steering) since it allows to activate the actuators only when requested by the driving situation (for instance the vehicle state behavior). Here the control strategy extends the previous works including the use of the rear steering actuators. An LPV controller is then designed here, whose parameters weight the use of the actuators. Indeed the resulting output feedback LPV controller is chosen of the form:

K (ρ 1 , ρ 2 , ρ 3 ) :                      ẋc (t) = A c (ρ 1 , ρ 2 , ρ 3 ) x c (t) + B c (ρ 1 , ρ 2 , ρ 3 ) e ψ (t)     δ + f δ + r T * brl T * brr     =     ρ 1 0 0 0 0 ρ 2 0 0 0 0 ρ 3 0 0 0 0 (1 -ρ 3 )     U(ρ) C 0 c (ρ 1 , ρ 2 , ρ 3 ) x c (t) (2)
Rem. Note that U (ρ) is chosen and implies that K is LPV.

If U (ρ) = I 4 the K will be LTI.

It depends on three parameters. ρ 1 and ρ 2 weight the front and rear steer respectively, and ρ 3 switches the torque action from the left rear to right rear wheel and vice versa.

In the present work they take value 0 or 1 according to the following criteria:

• ρ 1 : allows to activate the front steer (0 → no steering action, 1 → full steering action); • ρ 2 : the rear steer is only activated in critical con- ditions, namely when the stability index (S index = 9.5β + 2.49 β ) is above a threshold limit (if S index > 0.3 ρ 2 = 1 otherwise ρ 2 = 1); • ρ 3 : handles the over/under steering situations. Depend- ing on the sign of the yaw rate error only one of the two braking torque is allowed to act. Namely if e ψ > 0 → ρ 3 = 1 otherwise ρ 3 = 0 The LPV controller structure (2) is very generic. It allows an adaptive use of the front and rear steering actions. Only the distribution of the left/right rear breaking torques is imposed by the value of ρ 3 . In this paper a specific choise of the parameters values is considered to emphasize the additional use of the rear steering control action. The LPV controller design problem can be cast into a set of LMI's [START_REF] Scherer | Multiobjective output-feedback control via lmi optimization[END_REF] defined over the vertices of the polytope identified by the parameter space. The employed criteria effectively reduce the number of parameter to 2, yielding 4 vertices. Each vertex represent a specific combination of the parameters. The final LPV controller is a combination of four controllers, one for each of the vertices considered in the parameter choice. In this following analysis (in simulations) we have considered that the front steering is always active (ρ 1 = 1). Then the control is obtained as follows:

δ + f δ + r T * brl T * brr T =ρ 2 ρ 3 K(, ρ 2 , ρ 3 ) + ρ 2 (1 -ρ 3 )K(ρ 2 , ρ 3 ) + (1 -ρ 2 )ρ 3 K(ρ 2 , ρ 3 ) + (1 -ρ 2 )(1 -ρ 3 )K(ρ 2 , ρ 3 ) (3)
The set of LMI's are solved using SeDuMi and Yalmip [START_REF] Lofberg | Yalmip : a toolbox for modeling and optimization in matlab[END_REF]. For further information and details about the LMI optimization for H ∞ synthesis refer to [START_REF] Poussot-Vassal | Vehicle dynamic stability improvements through gain-scheduled steering and braking control[END_REF] [16] [START_REF] Scherer | Multiobjective output-feedback control via lmi optimization[END_REF] [17] [START_REF] Gahinet | Affine parameter-dependent lyapunov functions and real parametric uncertainty[END_REF] On the other hand to more easily assess the advantages of rear wheel steering two controllers have been designed: LPV1 without rear wheel steering and LPV2 with rear wheel steering. Fig. 4 plots the sensitivity functions in the nominal design case for all vertices of the parameter space polytope. Two observation are in place: • The fact that no difference can be observed among the sensitivity function at the vertices means that the LPV design is indeed successful in maintaining the specified performances throughout the parameter space. • In the nominal case the addition of the rear wheel steering does not bring any advantage. As long as frequency responses are concerned (of the closed loop system with LPV controllers and DRY road) we don't see any relevant differences between vehicle with and without rear steer.

III. VALIDATION

In this section the proposed control strategies are validated in simulation using a full vehicle simulation model, whose parameters are described in [START_REF] Poussot-Vassal | Vehicle dynamic stability improvements through gain-scheduled steering and braking control[END_REF] and [START_REF] Poussot-Vassal | Robust multivariable linear parameter varying automotive global chassis control[END_REF] and have been validated on a real Renault Mégane vehicle. Unlike the bicycle model the full model includes a nonlinear tire characteristic, a nonlinear lateral and longitudinal dynamics together with a nonlinear vertical dynamics. For the purpose of this article the full model has been extended with the rear steer input. An obstacle avoidance maneuver is illustrated. The driver input is shown in Fig. 5 and the vehicle initial speed is 90km/h. The simulation has been performed in 3 different road conditions: DRY (µ = 1), WET (µ = 0.5) and ICY (µ = 0.3). This will emphasize the intrinsic robustness property of the proposed approach.

A. Avoidance maneuver on icy road

To better understand the advantages and differences caused by the use of the rear steering it is useful to analyze in details one maneuver in the time domain. The obstacle avoidance presented maneuver on icy road is this in what follows. Fig. 6 shows the absolute value of yaw rate error, vehicle velocity and the side-slip angle for the LTI case. Comparing the results of the LTI controllers with the ones of the LPV controller presented in Fig. 8 it is evident that the LTI controller achieves better performance. At the same time Fig. 7 and Fig. 9 show the huge difference in the actuator usage between the two types of controllers. While there is no relevant difference in the peak values reached by the wheels torques, the steering angles behavior between LTI and LPV controllers is highly different. It is worth noting that the LPV controllers through the coordination of the control actions, induce a reduced use of the actuators. Indeed the maximal rear steering angle reaches 3deg for the LPV with rear steering controller and 10deg for the LTI with rear steering. Moreover the front steering angle is less than 1deg for the LPV rear controller and it reaches almost 3deg for the LT I rear . Hence the interference with the driver action is also reduced thanks to the LPV front and rear steering strategy.

0 0.5 1 1.5 2 2.5 3 3

B. Performance indexes

To better show the advantages of the rear steer we introduce three time domain indexes [START_REF] Changfang | Asymptotic decoupling control with active front steering and electronic differentials in four wheel steering vehicles[END_REF].

e ψindex = t end t 0 |e ψ (t) | dt (4a) β index = max t β (t) (4b)
V index = V 0 -min t (V (t)) (4c)
The first index quantifies the yaw rate tracking error. The second index penalizes high side-slip angles. It is well known that non professional drivers cannot manage high side-slip angle. The third index penalized loss of velocity, ideally one would want to be able to stabilize the obstacle avoidance maneuver without reducing the vehicle velocity. For all performance indexes, a lower value is to be preferred. comments can be drawn:

• All controllers considerably improve the yaw rate reference tracking in all conditions. • All the controllers cause a velocity reduction at the end of the maneuver. This is mainly caused by the use of the brakes. • In order to generate higher tire side slip (i.e. higher lateral tire force) all the controllers cause higher vehicle slip angle (in this case, the uncontrolled car is indeed not able to remain in the trajectory bound). • As predicted by the sensitivity analysis, rear wheel steering does not bring any advantage on dry road. • For both the LPV and LTI cases the use of rear wheel steering proves advantageous on low friction surfaces.

The farther the vehicle is from the nominal design condition, the more an additional lateral dynamics control variable is useful. In particular, as expected, the LTI controllers offer better reference tracking performance. This is due to the fact that they can access to all control variables, however this freedom comes at the cost of reduced velocity at the end of the maneuver. The LPV controllers achieve a slightly worse reference tracking, but on the other side also a reduced loss of velocity. This is due to the retarded use of the braking actuator.

IV. CONCLUSIONS

In this paper the advantages for the rear wheel steering action on the global chassis control was studied. The work involved 2 kind of controllers: an LTI controller that uses all the actuator simultaneously and an LPV controller that switches between different configuration of the actuators in relation to the driving situation. The main results can be summarized as follows:

• The advantages of the rear steering action have been emphasized in the yaw control case with avoidance maneuver. Moving from a nominal condition (i.e. high grip road surface) to a more critical one (i.e. ICY road) the rear steering action becomes more relevant. It could be further emphasized in harder driving situations like braking and avoidance maneuver in a curve at high speed.

• Still with more complex architecture (like the one with rear steering) the LPV controller, compared to the LTI allows lower and customizable usage of the actuators leading to lower power consumption and lower interaction with the driver action.

1 D

 1 . Selmanaj, M. Corno, S. Savaresi are with the Dipartimento di Elettronica, Informazione e Bioingegneria. Politecnico di Milano. Italy. corno at elet.polimi.it 2 O. Sename is with GIPSA-Lab., Control Systems Department, ENS E3-BP46, 38402 Saint Martin d'Mres Cebey, France. O. Sename is supported by the Region Rh ône-Alpes those tire cornering stiffness is a key influencing factor on maneuverability.

Fig. 1 .

 1 Fig. 1. Control architecture. AS are the active steering actuators and ABS+EMB are the wheel torque actuators (at the left/right rear wheels).

Fig. 2 .

 2 Fig. 2. Generalized plant used for synthesis.

Fig. 3 .

 3 Fig. 3. LTI controller, frequency response: LTI1 (black dotted), LTI2 (black dashed). Weighting functions 1/W e ψ ,1/W β ,1/W δ + r (black solid).

Fig. 4 .

 4 Fig. 4. LPV controller, frequency response: LPV1 (black dotted), LPV2 (black dashed). Weighting functions 1/W e ψ ,1/W β ,1/W δ + r (black solid)

Fig. 5 .

 5 Fig. 5. Driver input: avoidance maneuver.

Fig. 6 .

 6 Fig.6. Yaw rate error, speed and body slip angle: LTI (dotted), LTI with rear steer (dashed). Uncontrolled vehicle (black)

Fig. 7 .

 7 Fig. 7. Control inputs: LTI (dotted), LTI with rear steer (dashed).

Fig. 8 .

 8 Fig.8. Yaw rate error, speed and body slip angle: LPV (dotted), LPV with rear steer (dashed). Uncontrolled vehicle (black)

Fig. 9 .

 9 Fig. 9. Control inputs: LPV (dotted), LPV with rear steer (dashed).

Fig. 10 .

 10 Fig. 10. LTI controller: indexes comparison

Fig. 11 .

 11 Fig. 11. LPV controller: indexes comparison