Optimal dynamic formation control of multi-agent systems in constrained environments

We address the optimal dynamic formation problem in mobile leader-follower networks where an optimal formation is generated to maximize a given objective function while continuously preserving connectivity. We show that in a convex mission space, the connectivity constraints can be satisfied by any feasible solution to a mixed integer nonlinear optimization problem (MINLP). For the class of optimal formation problems where the objective is to maximize coverage, we show that the optimal formation is a tree which can be efficiently constructed without solving a MINLP. In a mission space constrained by obstacles, we separate the formation process into intervals with no obstacles detected and intervals where one or more obstacles are detected. In the latter case, we propose a minimum-effort reconfiguration approach for the formation which still optimizes the objective function while avoiding the obstacles and ensuring connectivity. We include simulation results illustrating this dynamic formation process.