Back-stepping Recursive Decentralized Finite-time Trajectory Tracking Control for Space Parallel Robots with a Bricard Mechanism

A space parallel robot with a Bricard mechanism (SPRBM) is an mechanism for space debris removal. In contrast to traditional serial manipulators, the SPRBM can capture targets of arbitrary shapes, provided the target's envelope falls within the capture range of the SPRBM's net port, with no stringent requirements on the capture point's location. Additionally, owing to the properties of parallel mechanisms, the SPRBM can capture targets possessing greater motion energy than traditional serial manipulators. However, the SPRBM has complicated dynamics, posing significant challenges for dynamic modeling and trajectory tracking control. In this study, we introduce a back-stepping recursive decentralized finite-time control scheme for the trajectory tracking control of the SPRBM. First, the equation of motion for the SPRBM was derived using a recursive algorithm. Then, the back-stepping recursive decentralized finite-time control was formulated, assuming that communication between the decentralized controllers was feasible. The communicated information comprised the relative motion states at the joints, the geometry and mass parameters, and the control torques. Finally, numerical experiments were conducted to validate the effectiveness of the proposed control scheme.