Research On Cooperative Control And Analysis Of Stability For Multi-Agent Robots

The problem of collective motion of multi-agent robots attracts attention of the scientists from different research fields. From physics, biology, computer science to control science, scientists try to understand how a group of moving creatures such as flocks of birds, schools of fish, colonies of bacteria, crowds of people, or man-made mobile autonomous agents, can cluster in formations only by local cooperative rule without centralized coordination. This is mainly due to broad applications of multi-agent robots systems in many areas including cooperative control of unmanned air vehicles (UAVs), formation control of multi-robot, flocking of multi-agent robots, distributed sensor networks, attitude alignment of clusters of satellites, and congestion control in communication networks.This thesis mainly investigates flocking motion control of multi-agent robots, consensus problem of multi-agent robots and a nonlinear model for multi-robot formations. Details are as follows:The multiple mobile agents with double integrator dynamics followed by a leader to achieve flocking motion formation is studied. We model the interaction and/or communication relationship between agents by algebraic graph theory. A class of control laws for a group of mobile agents is proposed. Stability analysis is achieved by using classical Lyapunov theory in fixed network topology, differential inclusions and nonsmooth analysis in switching network topology respectively.Flock with double integrator dynamics to achieve flocking motion formation in directed networks is studied. A class of decentralized control laws for a flock of mobile agents is proposed. Theoretical analysis show that the weakly connectedness of directed graph and a class of directed graphs, called balanced graphs, play a crucial role in stability analysis.A novel procedure is presented for control and analysis of multiple autonomous agents with point mass dynamics achieving flocking motion in high-dimensional space. Four distributed control laws are proposed for a group of autonomous agents to achieve flocking formations related to two different centers (mass center and geometric center) of the flock. The first two control laws are designed for flocking motion guided at mass center and the others for geometric center. Smooth adjacency matrix and smooth potential function are introduced to overcome the difficulties in theoretical analysis. Under some reasonable assumptions, theoretical analysis is established to indicate the stability (cohesiveness, collision avoidance and velocity matching) of the control systems.A new notion, called weighted average-consensus, is proposed. Firstly, multi-agent achieving global weighted average-consensus in undirected dynamic networks is studied, linear and nonlinear distributed cooperative control laws are proposed for multi-agent systems to achieve weighted average-consensus. Secondly, the consensus problem in directed networks of multi-agent is studied. A class of distributed controller is applied to achieve global asymptotically weighted average-consensus in networks of multi-agent with fixed and switching topology. It is proved theoretically that the strongly connectedness of directed graph and a class of directed graphs, called balanced graphs, play a crucial role in solving weighted average-consensus problems.Vicsek's model is further discussed. Firstly, multi-agent achieving consensus asymptotically in directed dynamic networks is studied. A new rule, N-nearest neighbors rule, is proposed for multi-agent coordination. Based on N-nearest neighbors rule, a class of distributed controllers is applied for multi-agent networks to reach consensus asymptotically. Secondly, based on simplified Vicsek's model, coordinated collective motion of groups of autonomous mobile robots is studied. A qualitative analysis for the collective dynamics of multiple autonomous robots with directed interconnected topology using nearest neighbor rules is given. A necessary and sufficient graphical condition is proposed to guarantee that the headings of all robots converge to the same heading. The graph having a globally reachable node plays a crucial role in convergence analysis. Furthermore, we show that the globally reachable node having no neighbors serves as a group leader as a special case.A nonlinear model for multi-robot formations is studied. A nonlinear sliding mode controller is proposed to coordinate a group of nonholonomic mobile robots such that a desired formation can be achieved. We prove theoretically that under certain reasonable assumptions the formation is asymptotically stable even with bounded disturbances; that is, the proposed sliding mode controller can asymptotically stabilize the errors in relative distance, relative bearing and heading direction, respectively.