Tube-Based Geometric Model Predictive Tracking Control for Robot Manipulators in Task Space With Disturbances

This paper proposes a novel tube-based geometric model predictive control (GMPC) framework on Lie groups for robust and real-time trajectory tracking control of robot manipulators under uncertainties. The proposed method directly computes joint torques from task-space error dynamics, eliminating inverse kinematics and ensuring efficient torque-level control. To guarantee constraint satisfaction and robustness, the tube-based GMPC is formulated to constrain the actual system trajectory within a bounded tube surrounding the nominal path, ensuring both feasibility and input-to-state stability. A disturbance observer is employed to estimate external disturbances, while a weighted whole-body controller is integrated to enhance disturbance rejection and increase the control frequency. The effectiveness of the proposed algorithm is validated through numerical simulation and experimental studies using an industrial robot manipulator. The comparative results demonstrate the stability and robustness of the proposed scheme in manipulator trajectory tracking control.