Fast Trajectory Planning for Approaching Disabled Satellites Based on Moving Frame

Approaching disabled satellites is crucial for missions such as space debris removal and on-orbit servicing. However, the conventional numerical trajectory planning method is time-consuming, making it unsuitable for urgent situations. In this article, an analytical fast trajectory planning method for approaching disabled satellites is proposed. First, an approach moving frame is designed and established to reduce the complexity of the scene. Subsequently, acceleration and angular acceleration are utilized instead of control force and torque while implementing the bang-coast-bang control mode. This allows the differential equations to be solved while maintaining solution optimality. Simulations are presented to validate the effectiveness of the proposed method, demonstrating a significant reduction in planning time cost while maintaining optimality.