Leader-Following Graph-Based Distributed Formation Control

This paper presents the distributed formation control of a multi-agent system using graph theory with emphasis on consensus and cooperation issues. The focal point is to achieve and maintain a formation from any initial condition, with and without a leader that the entire formation must follow. Our analysis framework is based on tools from algebraic graph theory, matrix theory and control theory. We present a brief derivation of multi-agent consensus in continuous-time and the corresponding iterative form stated in discrete-time, because while the real scenario is continuous, the implementation that we simulate is discrete. Based on the discrete-time algorithm, we propose a solution to obtain and uphold consensus when there is a leader to command the entire network. Simulation results are presented, indicating the capabilities and limitations of the algorithms.