Distributed Optimal Containment Control of Wheeled Mobile Robots via Adaptive Dynamic Programming

In this article, the distributed optimal containment (DOC) control of wheeled mobile robots (WMRs) is investigated via adaptive dynamic programming. To begin with, a novel performance index function which contains containment errors and their derivatives is designed for each following WMR without requiring the discount factor, which simplifies the controller design process and enhances the practicality of the control method. Subsequently, the DOC control of WMRs is formulated as a differential graphical game whose Nash equilibrium can be formed by using the optimal responses of all following WMRs. Moreover, a critic-only structure is built to obtain an approximate DOC control law, which provides a solution for the coupled Hamilton–Jacobi–Bellman equation of each following WMR. Stability analysis demonstrates that the containment error of each following WMR is uniformly ultimately bounded. Finally, a group of WMRs are utilized to verify the effectiveness of the present DOC control scheme.