Tube-based robust model predictive control for robot manipulators with integral sliding mode residual error bounds

To address the problem of safe trajectory tracking for robotic manipulators subject to model uncertainties, external disturbances, and constraints on both states and torques, this paper proposes a robust tube-based model predictive control (TMPC) method that accounts for residual errors within the integral sliding mode boundary layer. The method employs inverse dynamics feedback linearization to transform the manipulator dynamics into a linear double-integrator system with matched disturbances, combining an outer-loop TMPC with an inner-loop integral sliding mode compensator to achieve constrained trajectory tracking and disturbance rejection. To account for the nonzero residual error induced by the saturation function introduced to mitigate chattering in practical sliding mode control, this paper establishes an explicit mapping between the boundary layer thickness and the residual error tube using Lyapunov analysis, and derives analytical expressions for the outer envelopes of the error tube components. Furthermore, based on the derived error bounds, the state and actual torque constraints are robustly tightened to formulate a nominal optimization problem that satisfies the original constraints. By designing a terminal feedback law, a terminal cost, and an ellipsoidal terminal set, the recursive feasibility, closed-loop constraint satisfaction, and practical stability of the actual system are proven. Experimental results on a 6-DOF robotic manipulator demonstrate that the proposed method effectively compensates for uncertainties and handles sliding mode boundary layer residual errors, achieving high-precision robust trajectory tracking while ensuring adherence to state and torque constraints.