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Multi-Robot Systems Classification
Given the variety of designs of multi-robot systems, it is useful to have them organized. [19], [18],[1], developed the taxonomy of these systems. Farinelli’s [1] classification relies on the coordinative nature of the robot set. This taxonomy is represented by the hierarchical structure shown by Figure 2.1. At the cooperative level, we can distinguish cooperative systems from noncooperative ones. A cooperative system is composed of robots that operate together to perform some global task. Farinelli’s work, also considers the coordinative level. Coordination is a cooperation in which the actions performed by each robotic agent takes into account the actions executed by the other robotic agents in such a way that the whole ends up being a coherent and high-performance operation. Organization level introduces a distinction in the forms of coordination, distinguishing centralized approaches from distributed ones. In particular, a centralized system has an agent (leader) that is in charge of organizing the work of the other agents; the leader is involved in the decision process for the whole team, while the other members can act only according to the leader’s directions. In contrast, a distributed system is composed of agents that are completely autonomous in the decision process with respect to each other; there is no leader in such cases. The classification of centralized systems can be further refined depending on the way the leadership of the group is played. Specifically, strong centralization is used to characterize a system in which decisions are taken by the same predefined leader agent throughout the entire mission, while in a weakly centralized system more than one agent is able to take the role of the leader during the mission. Instead of a classification based on coordination as proposed by Farinelli et al; the classification of Cao et al. [18] relies on the structure of the robot set. According to this classification, a multi-robot system can be homogeneous or heterogeneous. A group of robots is said to be homogeneous if the capabilities of the individual robots are identical, and heterogeneous otherwise.
Leader-Follower
The Leader-follower strategy was first introduced in control system by the German economist Heinrich Freiherr von Stackelberg who published Marktform und Gleichgewicht in 1934 which described this model (see [43]). These control methodologies, also known as Stackelberg strategies, are appropriate for classes of system problems where there are multiple criteria, multiple decision makers and decentralized information. In these strategies, the follower control actions are based on the leader’s state and control. The leader-follower concept has been widely used in multi-robot control. Feddema et al [44], studied the observability and reachability of leader-follower based control of cooperative mobile robots. Other leader-follower applications in multi-robot systems have been presented for terrestrial vehicles” [45], [22], [46], aerial autonomous multi-robot systems [47],[48] and unmanned underwater vehicle platoons [49],[50]. In the leader-follower approaches, each robot agent is positioned in the formation by the relative geometry with respect to its predefined neighbour. Each robot follows its predefined leader with a certain geometrical relationship. Using this leader-follower relationship, a geometrical pattern of n robots can be obtained. Typically, there is a single leader of the formation. This single leader does not follow any other robot in the set, but a predefined trajectory. The stability of leaderfollower-based multi-unicycle robot systems was studied by Lechevin et al., [51]. The stabilization was proposed for a formation of unicycles where the relative angle between the robots remained constant in time. Also using the leader-follower approach, Desai et al. [52], proposed a stabilization strategy of multiple autonomous nonholonomic robots. A framework based on graph theory for transitioning from one geometrical pattern to another was presented. Among the applications of the leader-follower strategies, the work of Dasset al. [22]: proposed vision-based stabilization of the formation of car-like vehicles.
Centralized Motion Planning
Another point of view in motion planning for multi-robot systems are the centralized planning strategies. In general, a reference trajectory is defined for the platoon then the single robot paths are computed with respect to this reference trajectory. Such of use of a reference point for all robots this strategy can be considered as a centralized approach, all robots should be able to know their distance to this reference point. Among this strategy, Barfoot and Clark [3], propose a planning approach for mobile robot in formation, as formation they refer to certain geometrical constraints which are imposed on the relative positions and orientations of the robots throughout their travel. For platoons of nonholonomic robots keep the geometrical pattern for some manoeuvering is not possible, such of that the Barfoot and Clark work proposed to control the formation in a curvilinear coordinates rather than in the original rectilinear coordinate system. This takes advantage of the non-holonomic constraint imposed on each robot. It also ensures that for a static formation which does not turn sharper than a threshold curvature, the individual robot trajectories will not collide. They introduce an arbitrary reference point, within the formation whose coordinates serve as a single set of reference coordinates for the group. This point could be the center of the formation, one of the robots in the formation, or any other point. All robots in the formation will be described relative to this reference point (but in curved space).
Landmark-based Navigation
In a landmark-based navigation system, the robot relies on its onboard sensors to detect and recognize landmarks in its environment to determine its position. The navigation system depends on the kind of sensors being used, the types of landmarks and the number of landmarks available. Vision by means of cameras has been applied to localize reference point in the environment. Apart of vision other sensors have bern used in position estimation, including laser, ultrasonic beacons, GPS, and sonars. As no sensor is perfect an landmarks may change none of these method is adequate to operate autonomously in the real world [64]. Global Positioning System: Among the positioning strategies for autonomous mobile robots in outdoor application is the global positioning system (GPS), [65]. The GPS was developed in 1970 by the United States Department of Defense for military applications. In 1983, President Reagan established a horizontal accuracy of 100 metres for civil users worldwide. In 1989, a new satellite group was put into service (Group II), and in 1991 the civil application signal was intentionally degraded (selective availability, SA). Selective availability was then suppressed under the Clinton administration (1996) and the accuracy of 100 metres was thus improved by a factor of 10; that is, 10 metres of horizontal accuracy for civil applications. The GPS consists of 24 satellites in six different orbits. Four satellites are positioned in 6 different orbits. the same orbit to assure worldwide covering. Thus, every point on the earth is visible from four to ten satellites The GPS is composed of three subsystems: spatial (Space), terrestrial (Control) and User. The Space subsystem consists of all 24 satellites, orbiting the earth every 12 hours in six orbital planes, at an altitude of 20,200 km inclined at 550 to the equator in a sun-synchronous orbit. There are often more than 24 operational satellites as new ones are launched to replace older satellites. The orbit altitude is such that the satellites repeat the same track and configuration over any point approximately every 24 hours (4 minutes earlier every day). The satellites are oriented in such a way that from any place on earth, at any time, at least four satellites are available for navigational purposes. The Control subsystem consists of a group of four ground-based monitor stations, three upload stations and a master control station. The master control facility is located at Schriever Air Force Base in Colorado. The monitor stations track the satellites continuously and provide data to the master control station. They measure signals from the satellites, which are incorporated into orbital models for each satellite. The master control station calculates satellite ephemeris and clock correction coefficients and forwards them to an upload station; Figure 2.9 shows the localization of the terrestrial Control subsystem. The upload stations transmit the data to each satellite at least once a day. The satellites then send subsets of the orbital ephemeris to GPS receivers over radio signals.
Robot Model and Flat Outputs
Differentially flat systems constitute a broad class of dynamical systems. They are the simplest possible extension of controllable linear systems to the nonlinear systems domain. Flat systems have a finite set of differentially flat outputs or outputs that do not satisfy nonlinear differential equations, so that all system variables, including the control inputs, can be exclusively written in terms of algebraic functions of such differentially independent outputs. Flat systems were first introduced by Fliess et al, [72], and further development and some mechanical examples were presented in the Martin’s work [39].
Leader-Follower Convergence Conditions
In order to ensure the trajectory generation convergence, we show that the value of the linear velocity of the desired follower position |vd foll(t)| has to be less than the maximal robot velocity value Vmax. The aim of this section is to obtain the imposed follower desired velocities into the formation. We suppose the robot formation as a rigid body, then, by the geometrical desired pattern and the formation leader trajectory we can obtain the desired linear velocities of each follower. Finally we can obtain the speed velocity restrictions that will ensures the convergence of all follower robots to is desired positions, under any maneouvring of the leader of the formation. To obtain the desired follower positions and their variations in time, we consider the robot formation as a rigid body, or in simpler terms, that the robot set pattern is not deformed for any formation leader movement. Then, for any formation leader displacement, we can obtain where the followers desired positions are, by means of the rigid body mechanics relationships.
Real-time Considerations
In section (3.6), we presented a nonlinear trajectory generator. This trajectory generator is based on real-time path generation. As the algorithm of optimization, we proposed the feasible nonlinear programming solver CFSQP [78]. An ideal solution in critical real-time trajectory problem is to obtain a feasible solution a each iteration, obtaining a feasible solution is better than none at all. In this section, we show the simulations of trajectory generation to study the computing time. We present the trajectory generation method for a single robot. This robot has to displace from an initial state to a final one while avoiding obstacles. The aim of these simulations is to contrast the solutions for different computing time restrictions in order to validate the results of the feasible nonlinear programming solver in bounded computing time conditions. In the first simulation, we see the trajectory when there are no computing time restrictions (Fig. 4.8-b)
Securing Link Communication
The quality of the received WiFi signal is a function of the power, distance and transmission medium. Every robot can measure the RSS by using its WiFi devices. In order to avoid communication losses, we have to maintain the received signal power above a security level that ensures the quality of the communication for each robot. A constraint of minimal signal power reception must be included in the solution strategy. To maintain the communication links between robots, we propose to include a term in the performance index that penalizes the loss of power in the received signal.
Trajectory Tracking Control
The trajectory tracking problem can be defined as follow: Given a feasible trajectory, of the relative position between the leader i and its follower j: rdi j(t) with t ∈ R+, regulate the state error εr = ri j(t)−rdi j(t) asymptotically to the origin, subject to the leader-follower model (3.7): r˙i j = fi j(ri j,vj). To solve this problem, we propose to linearize the model system (3.7) around the feasible trajectory rdi j(t), then regulate the error εr to the origin by using a optimal linear quadratic feedback regulation (LQR). In 1960 Kalman, [105],introduced an integral performance index that had a quadratic penalty on output errors and control magnitudes, and he used the calculus of variations to show that the optimal controls were linear feedbacks of the state variables.
Communication as Positioning System
We validate the use of a wireless communication network to secure the links between robots. A model to estimate the relative positions between the formation robots is proposed and validated by simulations and experiments. The positions are estimated using the received signal strength, RSS, and the direction of the maximal RSS. This last task was not studied experimentally, but some simulations are presented to validate the general approach. Wireless RSS can be used not only to ensure the links between robots, but also to build an obstacle avoidance strategy. If a robot is following the maximal RSS and an obstacle modifies the RSS field, the robot can use this information to avoid the obstacle.
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Table des matières
1. Introduction
1.1 Approach
1.2 Problem Definition
1.3 Contribution
1.4 Thesis Outline
2. State of the Art
2.1 Cooperative Multi-Robot Systems
2.1.1 Multi-Robot Systems Classification
2.2 Nonholonomic Systems
2.2.1 Control of Nonholonomic Systems
2.3 Motion Coordination
2.3.1 Artificial Potentials
2.3.2 Leader-Follower
2.3.3 Centralized Motion Planning
2.3.4 Redundant Manipulator Techniques
2.4 Collision-free Motion of Robots
2.4.1 Reactive Control
2.4.2 Planning and Reactive Control
2.5 Localization
2.5.1 Absolute methods
2.5.2 Relative Methods
3. Distributed Trajectory Generator
3.1 Introduction
3.2 Robots Coordination Modeling
3.2.1 Formation Topology
3.3 Open-loop Control Problem
3.4 Optimal Trajectory Definition
3.4.1 Real-time Trajectory Planning
3.5 Trajectory generator Algorithm
3.5.1 Robot Model and Flat Outputs
3.5.2 Trajectories with B-splines Parameterization
3.5.3 Transcription into a Nonlinear Programming Problem
3.6 Time-Optimal Trajectories
3.7 Convergence Conditions
3.7.1 Leader-Follower Convergence Conditions
3.7.2 Leader-Follower Implementation Considerations
3.7.3 Single Leader-Follower Example
3.7.4 Multiple Leader-Follower Example
3.8 Final Remarks
4. Obstacle Avoidance
4.1 Introduction
4.2 Deformable Virtual Zone
4.3 Deformable Virtual Zone in the Trajectory Generator
4.3.1 DVZ in the Trajectory Generator
4.4 Real-time Considerations
4.5 Final Remarks
5. Wireless Communication for Relative Positioning in Multi Mobile Robots Formation
5.1 Introduction
5.2 RSS-Based Location Estimation
5.2.1 Propagation Phenomena
5.2.2 RSS Propagation Model Identification
5.3 Position Estimation via Extended Kalman Filter
5.3.1 Simulations
5.3.2 Experimental Validation
5.4 Securing Link Communication
5.5 Final remarks
6. Single Vehicle Closed-Loop Control
6.1 Introduction
6.2 Trajectory Tracking Control
6.2.1 Linearized Leader-Follower Model
6.2.2 Controllability Conditions
6.2.3 Simulations
6.3 Final Remarks
7. Conclusions
7.1 Multi-robot Coordination
7.2 Obstacle Avoidance
7.3 Communication as Positioning System
7.4 Outgoing Work
8. Résumé
8.1 Introduction
8.2 Stratégie de commande décentralisée
8.2.1 Introduction
8.2.2 Positionnement leader-follower
8.2.3 Génération de trajectoires en temps réel
8.3 Evitement d’obstacles
8.4 Positionnement grâce au niveau de réception
8.5 Conclusions
BIBLIOGRAPHY
I.1 PUBLICATION ACTIVITIES
I.1.1 Journals
I.1.2 International Conferences
I.1.3 National Conferences
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