Approximate optimal and safe coordination of nonlinear second-order multirobot systems with model uncertainties

This paper investigates the approximate optimal coordination for nonlinear uncertain second-order multi-robot systems with guaranteed safety (collision avoidance) Through constructing novel local error signals, the collision-free control objective is formulated into an coordination optimization problem for nominal multi-robot systems. Based on approximate dynamic programming technique, the optimal value functions and control policies are learned by simplified critic-only neural networks (NNs). Then, the approximated optimal controllers are redesigned using adaptive law to handle the effects of robots' uncertain dynamics. It is shown that the NN weights estimation errors are uniformly ultimately bounded under proper conditions, and safe coordination of multiple robots can be achieved regardless of model uncertainties. Numerical simulations finally illustrate the effectiveness of the proposed controller.