Control of rigid formations for agents with passive nonlinear dynamics

This thesis concerns the decentralized formation shape control of a set of homogeneous agents in the plane whose actuation dynamics are nonlinear and passive. The formation shape is specified by a subset of interagent distances. The formation is modeled as an undirected graph, with vertices representing the agents. An edge exists between two vertices if the specification provides the distance between them. Enough distances are assumed to have been specified to make the underlying graph rigid. Each agent executes its control law by measuring its relative positions from its neighbor and by knowing its absolute velocity. The control law is the same as previously proposed for a network where the agents have linear time invariant (LTI) passive dynamics. Despite the nonlinearity we show local convergence of this same law. The stability proof is in fact simpler than given in the LTI case through a redefinition of the state space. The results are verified by simulations that show that the control law can indeed stabilize under wider ranges of dynamics than previously perceived.