Approximate optimal and scalable control for collision-free formation of uncertain nonholonomic robots

This paper studies the formation tracking problem for nonholonomic multirobot systems under model uncertainties. A new local variable is designed to transform the collision-free formation control objective into an optimization problem through integrating several filtered signals into tracking errors. The optimal control policies for nominal kinematic model are learned by approximate dynamic programming (ADP) technique using a simplified critic-only neural network (NN) based algorithm, which scales well since the computational complexity is independent with the number of robots and obstacles. Then, to handle the effects from robots’ uncertainties, the ADP control policies are redesigned by adding a two time-scale based compensator. It is shown that under proper conditions, the NN weights’ estimation errors are uniformly ultimately bounded, while the robust formation tracking and collision avoidance can be achieved. Numerical simulations finally illustrate the effectiveness of the proposed controller.