Task-Constrained Trajectory Planning of Free-Floating Space-Robotic Systems Using Convex Optimization

This paper addresses the trajectory-planning problem for a free-floating space-robotic system for which there are no actuations on the base spacecraft. The mission considered is that the end effector is subject to task compliance constraints and the whole system is kinematically redundant such that it can incorporate various objects such as collision avoidance. Based on the conservation of the system moment, trajectory planning is formulated as a convex quadratic programming problem in the joint space. The attitude disturbance on the base spacecraft due to the dynamic coupling between the manipulator and the base is shown to be a convex function of the design variables and is incorporated in the objective function to be minimized. Physical constraints including obstacle avoidance and the bounds on the joint angles, joint velocities, and joint accelerations are directly included in the developed framework. The proposed quadratic programming formulation allows for rapid generation of optimal trajectories, which brings robustness to the planning. Numerical simulations for a 10-degree-of-freedom space manipulator validate the efficacy of the proposed approach and demonstrate the method's potential for real-time applications.