Adaptive Dynamic Programming-Based Finite-Time Optimal Backstepping Force/Position Control of Reconfigurable Robot Manipulators via Pareto Optimal

To address the force/position control challenges in transitioning from free-space motion to tasks involving environmental contact, this paper proposes an Adaptive Dynamic Programming (ADP)-based finite-time optimal backstepping force/position control method for Reconfigurable Robot Manipulators (RRMs), which ensures rapid convergence of state errors under external constraints while maintaining system stability. By integrating robust control, the proposed method enhances both convergence speed and robustness against uncertainties. Furthermore, the parameters related to robustness are optimized using a cooperative game-theoretic approach based on Pareto optimality. A Lyapunov-based analysis demonstrates the closed-loop system’s Semi-Global Practical Finite-time Stability (SGPFS). Experimental validation confirms the effectiveness of the proposed control method. Note to Practitioners—In applications such as space operations, deep-sea exploration, and disaster rescue, RRMs must smoothly transition from free-space movement to tasks involving physical contact with external environments. Traditional force/position control methods often struggle to maintain stability and achieve rapid convergence under these conditions. This paper introduces a control strategy that combines ADP with backstepping to achieve finite-time optimal control. The proposed approach ensures stability, fast convergence, and robustness to uncertainties, addressing practical needs for energy efficiency and reliable force/position tracking. Moreover, the method optimizes control parameters through a cooperative game-theoretic framework based on Pareto optimality, balancing control effort and the convergence domain size. Experimental results confirm the practical effectiveness of the proposed strategy in complex environments.