Coordination of multiagents interacting under independent position and velocity topologies

We consider the coordination control for multiagent systems in a very general framework where the position and velocity interactions among agents are modeled by independent graphs. Different algorithms are proposed and analyzed for different settings, including the case without leaders and the case with a virtual leader under fixed position and velocity interaction topologies, as well as the case with a group velocity reference signal under switching velocity interaction. It is finally shown that the proposed algorithms are feasible in achieving the desired coordination behavior provided the interaction topologies satisfy the weakest possible connectivity conditions. Such conditions relate only to the structure of the interactions among agents while irrelevant to their magnitudes and thus are easy to verify. Rigorous convergence analysis is preformed based on a combined use of tools from algebraic graph theory, matrix analysis as well as the Lyapunov stability theory.