We address the open problem of consensusbased formation control of nonholonomic multiagent vehicles with pre-imposed input constraints. That is the problem of stabilizing a group of second-order differential-drive nonholonomic robots, making them acquire a determined formation pattern around a non pre-specified point on the plane and a common non pre-specified orientation. This problem is also known as leaderless full consensus. Our controller is smooth and time-varying, and fully distributed. Its design is a natural modification of another controller proposed earlier, which relies on proportional feedback, damping injection, and a smooth time-varying term that injects persistency of excitation in the system to overcome the effects of nonholonomicity. It is assumed that the robots communicate over a network with an undirectedgraph topology.
This paper proposes a solution for the leader-follower consensus formation control problem of nonholonomic vehicles that exhibit input constraints. In this consensus problem, the position and the orientation of all the vehicles has to be regulated at a desired equilibrium, hence this pertains to a stabilization scenario. Therefore, in order to satisfy Brockett's theorem, the controller has to be designed to be either discontinuous or time-varying. The proposed scheme is a smooth bounded Proportional plus damping injection controller that incorporates a persistency of excitation term. A comparative simulation analysis with an unbounded control scheme is also provided.
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