Distributed Reinforcement Learning Containment Control for Multiple Nonholonomic Mobile Robots

Abstract

In this paper, the distributed optimal containment control problem for multiple nonholonomic mobile robots (NHMRs) differential game is studied via reinforcement learning. An approximation-based optimal control strategy is developed to ensure the optimal performance index and avoid the potential collision among agents. Firstly, the collision avoidance problem considered in this paper is addressed by exploiting a consensus-like interconnection on a directed graph and an error transformation function. Then, on the basis of the optimal backstepping technique, a single critic neural network is adopted to obtain the solution of the coupled Hamilton-Jacobi (HJ) equation, in which an improved learning mechanism is constructed to relax the requirement on initial control conditions. In addition, based on the Lyapunov stability theory, it is proved that all signals in the closed-loop optimal control are uniformly ultimately bounded. Finally, the proposed control protocol is applied to NHMRs system, which verifies that the solution of the coupled HJ equation solves the containment problem of differential game.