Abstract: The separation of coal and gangue plays a pivotal role in enhancing coal quality, reducing transportation costs, and mitigating environmental pollution, thereby facilitating the efficient and clean utilization of coal resources and promoting sustainable mine development. To address the challenges of high labor intensity and low efficiency inherent in traditional manual gangue sorting, a rigid-flexible hybrid-driven parallel gangue sorting robot consisting of a rigid drive rod and four cables is proposed. However, the dynamic impacts arising from the pick-and-place operation of the gangues, uncertainties in dynamic parameters, and external disturbances inevitably have an important influence on the tracking accuracy and stability of the gripper of the robot, potentially leading to the failure of the pick-and-place operation of the target gangues. As a result, the dynamics and robust model predictive control for the proposed rigid-flexible hybrid-driven parallel gangue sorting robot are investigated. First, a systematic scheme for the proposed rigid-flexible hybrid-driven parallel gangue sorting robot is presented, including an analysis of the degrees of freedom and the establishment of its kinematic model. Second, taking into account the parameter perturbations in the robot’s model and external disturbances during the pick-and-place operation of the target gangues, the dynamic model of the robot is developed with the Newton-Euler method. Third, a robust model predictive control method incorporating tension constraints is proposed for the presented rigid-flexible hybrid-driven parallel gangue sorting robot, which optimizes the real-time collaborative allocation of the driving forces of the four cables and the rigid drive rod. This method dynamically counteracts impacts and external disturbances during of the pick-and-place of the gangues, enabling high-precision trajectory tracking control for the gripper of the robot. Finally, some simulations are performed for the proposed rigid-flexible hybrid-driven parallel gangue sorting robot using a spatial helical trajectory and a four-segment sorting trajectory. And the results demonstrate that the maximum trajectory deviation of the gripper is limited to 3.7×10⁻³ m, the attitude angle error stabilizes at 3.2×10⁻³ rad, and cable tensions consistently satisfy the driving force constraints. These findings verify the effectiveness of the proposed control strategy in reliable pick-and-place operation of the gangues under complex operational conditions.