Dual-quaternion-based modeling and control for motion tracking of a tumbling target

Abstract

This paper investigates the problem of controlling a chasing spacecraft (chaser) to track and rendezvous with an uncontrolled target. Based on the actual situation, the torque-free motion of an axisymmetric prolate rigid body is employed to represent the short-term attitude motion of the tumbling target. By taking advantage of the dual quaternion's compact and efficient description of the general rigid motion, the coupled and integrated model of the 6-degree-of-freedom (6-DOF) relative motion between the chaser and the tumbling target is derived in the chaser's body fixed frame after taking full consideration of coordinate transformation. Based on the logarithm of dual quaternion, a sliding mode control (SMC) law based on the exponential reaching law and the continuous relay function is brought forward to address the problem of synchronization control of the 6-DOF relative motion. Simulation results illustrate the effectiveness of the proposed method.