Adaptive Robust Control for Underactuated Bipedal Parallel Wheel-Legged Robots: A Nash Game-Based Constraint Following Approach

This article proposes a Nash game-optimized adaptive robust control framework for bipedal parallel wheel-legged robots. Specifically, the framework targets a balance between tracking accuracy and control effort under underactuation, constraint coupling, and substantial uncertainties. To address these challenges, a constraint following adaptive robust controller is adopted, while gain selection is posed as a two-player Nash game between performance and cost objectives. Consequently, the resulting equilibrium yields controller gains without heuristic tuning. Furthermore, Lyapunov analysis establishes uniform ultimate boundedness of the closed-loop trajectories under bounded disturbances and model errors. Finally, numerical simulations verify that the proposed approach achieves a superior balance, concurrently enhancing tracking accuracy while significantly reducing control effort compared to conventional methods.