State-Extended MPC for Trajectory Tracking and Optimal Obstacle Avoidance in Multi-Point Suspension Systems

Ground-based three-dimensional motion testing of space manipulators typically relies on active suspension-based gravity compensation systems. The design of such systems faces two fundamental challenges: first, how multiple suspension winch units can precisely track the dynamic trajectories of the corresponding suspension interfaces on the manipulator; and second, how to achieve optimal collision avoidance among the suspension mechanisms themselves during the tracking process. To address these challenges, this paper presents a multi-point suspension system endowed with kinematic redundancy for the trajectory tracking task, thereby ensuring precise tracking of the manipulator’s complex three-dimensional motions. The key innovation of this work lies in formulating the internal collision avoidance constraints as safety distance functions and integrating them into the system states. These are then combined with the trajectory-tracking states to construct a unified state-extended system model that exhibits typical underactuated characteristics. For this model, and under the concurrent influence of external disturbances from both the manipulator’s motion and the proximity to collision boundaries, a dedicated Model Predictive Controller (MPC) is designed. The results demonstrate that the proposed controller can generate an optimal coordinated collision-avoidance motion plan for the suspension winch units while maintaining precise trajectory tracking, thereby effectively solving the coordinated motion-planning problem for such complex underactuated systems. The proposed MPC achieves maximum tracking errors of 0.64 mm (X) and 0.13 mm (Z)—substantially lower than the 1.3 mm and 1.9 mm results listed in the comparative scheme—while delivering optimal collision avoidance, which is only suboptimally realized in the baseline.