Cette thèse considère principalement trois problèmes dans le domaine du contrôle distribué coopératif des systèmes multi-agents(SMA): le consensus, la navigation en formation et le maintien en formation d’un groupe d’agents lorsqu’un agent disparait. Nous proposons 3 algorithmes pour résoudre le problème du calcul distribué d’un consensus à partir de l’approche leadeur-suiveur dans le contexte SMA à dynamique non-linéaire. La référence est définie comme un leader virtuel dont on n’obtient, localement, que les données de position et de vitesse. Pour résoudre le problème du suivi par consensus pour les SMA à dynamique non-linéaire, nous considérons le suivi par consensus pour SMA de premier ordre. On propose des résultats permettant aux suiveurs de suivre le leadeur virtuel en temps fini en ne considérant que les positions des agents. Ensuite, nous considérons le suivi par consensus de SMA de second. Dans le cas de la planification de trajectoire et la commande du mouvement de la formation multi-agents. L’idée est d’amener la formation, dont la dynamique est supposée être en 3D, d’une configuration initiale vers une configuration finale (trouver un chemin faisable en position et orientation) en maintenant sa forme tout le long du chemin en évitant les obstacles. La stratégie proposée se décompose en 3 étapes. Le problème du Closing-Rank se traduit par la réparation d’une formation rigide multi-agents "endommagée" par la perte de l'un de ses agents. Nous proposons 2 algorithmes d’autoréparation systématique pour récupérer la rigidité en cas de perte d'un agent. Ces réparations s’effectuent de manière décentralisée et distribuée n’utilisant que des informations de voisinage / This dissertation focuses on distributed cooperative control of multi-agent systems. First, the leader-following consensus for multi-agent systems with nonlinear dynamics is investigated. Three consensus algorithms are proposed and some sufficient conditions are obtained for the states of followers converging to the state of virtual leader globally exponentially. Second, the consensus tracking for multi-agent systems with nonlinear dynamics is investigated. Some consensus tracking algorithms are developed, and some sufficient conditions are obtained. Based on these consensus tracking algorithms and sufficient conditions, it is shown that in first-order multi-agent systems all followers can track the virtual leader in finite time, and in second-order multi-agent systems the consensus tracking can be achieved at least globally exponentially. Third, the path planning and motion control of multi-agent formation is studied, where a practical framework is provided. In order to find a collision-free and deadlock-free feasible path for the whole formation, an optimizing algorithm is given to optimize the path generated by A* search algorithm. In order to realize the cohesive motion of a persistent formation in 3-dimensional space, a set of decentralized control laws is designed. Finally, the formation keeping problem is studied. We mainly focus on the closing ranks problem, which deals with the addition of links to a rigid multi-agent formation that is “damaged" by losing one of its agents, in order to recover rigidity. Some graph theoretical results are obtained, and some systematic ’self-repair’ operations are proposed to recover the rigidity in case of agent removals

Cooperative control problems for multiple vehicle systems can be categorized as either formation control problems with applications to mobile robots, unmanned air vehicles, autonomous underwater vehicles, satellites, aircraft, spacecraft, and automated highway systems, or non-formation control problems such as task assignment, cooperative transport, cooperative role assignment, air traffic control, cooperative timing, and cooperative search. The cooperative control of multiple vehicle systems poses significant theoretical and practical challenges. For cooperative control strategies to be successful, numerous issues must be addressed. We consider three important and correlated issues: consensus seeking, formation keeping, and trajectory tracking. For consensus seeking, we investigate algorithms and protocols so that a team of vehicles can reach consensus on the values of the coordination data in the presence of imperfect sensors, communication dropout, sparse communication topologies, and noisy and unreliable communication links. The main contribution of this dissertation in this area is that we show necessary and/or sufficient conditions for consensus seeking with limited, unidirectional, and unreliable information exchange under fixed and switching interaction topologies (through either communication or sensing). For formation keeping, we apply a so-called "virtual structure" approach to spacecraft formation flying and multi-vehicle formation maneuvers. As a result, single vehicle path planning and trajectory generation techniques can be employed for the virtual structure while trajectory tracking strategies can be employed for each vehicle. The main contribution of this dissertation in this area is that we propose a decentralized architecture for multiple spacecraft formation flying in deep space with formation feedback introduced. This architecture ensures the necessary precision in the presence of actuator saturation, internal and external disturbances, and stringent inter-vehicle communication limitations. A constructive approach based on the satisficing control paradigm is also applied to multi-robot coordination in hardware. For trajectory tracking, we investigate nonlinear tracking controllers for fixed wing unmanned air vehicles and nonholonomic mobile robots with velocity and heading rate constraints. The main contribution of this dissertation in this area is that our proposed tracking controllers are shown to be robust to input uncertainties and measurement noise, and are computationally simple and can be implemented with low-cost, low-power microcontrollers. In addition, our approach allows piecewise continuous reference velocity and heading rate and can be extended to derive a variety of other trajectory tracking strategies.