Formation Control for a Multi-agent System

Cooperative control of multi-agent systems is an active research area both in control theory and vehicles. Problems such as flocking, consensus, coverage and pattern formation are some of the important problems that have been studied over the past few years. Lin zhiyun proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node([1-3]). Bazoula and Maaref designed an PLC controller for separation and bearing control.. Guo Yi designed a cooperative control scheme in the framework of Lyapunov theorem for general linear dynamic systems([4-5]). Maria and Ali proposed a decentralized cooperative controller for a group of mobile agents based on the navigation function formalism([6-8]). But, there is an important problem that needs to be solved: many current systems can't be still a formation when someone agent is damaged. In this paper, we will present an effective method to solve this problem. We suppose that each agent knows the positions and velocities of its neighbors which are in a ball range of it, and the agent can only communicate with its neighbors. This is important to determine which agents need to be reorganized when someone agent is damaged. We present a decentralized formation control algorithm with topology reorganization. In this algorithm, a collective potential function is presented to form a formation in a local minimum, and a repulsive potential function is presented to avoid obstacles. A special parameter C-2i is designed to determine when to start the topology reorganization and when to finish. Under this control, agents that adjoin to the damage agent will connect to each other to reorganize a new topology. A theorem about keeping connectivity is given, and Lyapunov stability theorem is applied to prove stability of the dynamic system. Some simulation results will demonstrate that this algorithm is effective to tree topology.