Optimal collision-free Cartesian trajectory planning for a free-floating space robot with nonzero linear and angular momentum

Abstract

An unmanned chaser satellite equipped with a robotic manipulator can be employed for active debris removal and in-orbit servicing missions. It is often assumed that the control system of the chaser satellite is switched off during the capture operation performed with the manipulator. However, due to the limited accuracy of the chaser control system, which relies on thrusters for the approach phase, achieving zero relative velocity of the chaser with respect to the target satellite may not be possible. Moreover, in the tangent capture scenario, the chaser satellite is intentionally accelerated to a specific linear velocity before initiating the capture operation. This paper presents an optimal trajectory planning method applicable to a manipulator mounted on a free-floating satellite with nonzero initial velocity and nonzero but constant linear and angular momentum. The trajectory of the manipulator end-effector is parameterized in the Cartesian space using an 8th-order polynomial. The trajectory planning task is formulated as a constrained nonlinear optimization problem and solved using an interior-point algorithm. Constraints include joint position limits and collision avoidance with spherical obstacles. Two objective functions are considered: minimizing the trajectory length and minimizing the attitude changes of the chaser satellite. The proposed approach is validated through numerical simulations conducted using parameters from a prototype of the 7-DoF WMS 1 Lemur space manipulator. Trajectories obtained with the proposed approach are compared to two nonoptimal trajectories: a straight-line trajectory and a collision-free trajectory obtained with the artificial potential field method.