A geometric virtual structure approach to decentralized formation control

We present a unified approach to decentralized formation control of a network of agents, where the agents are modeled in the framework of geometric mechanics. The approach naturally accommodates underactuation, second-order agent dynamics, and nonholonomic constraints. Overall formation objectives are specified for a virtual structure (VS), while individual agent objectives are defined relative to the VS. We restate the formation control problem as a coupled set of local two-body problems. We construct a decentralized formation controller assuming independent solution of the local problems, plus asymptotic consensus of the VS states. A constructive solution of the local problem completes the controller design. The method is illustrated on simulations of two planar systems-a waypoint tracking and formation reconfiguration problem, and a target intercept problem using proportional navigation. To our knowledge, these problems have not been previously solved in the control literature.