Dual-Equal-Collision-Probability-Curve method for spacecraft safe proximity maneuvers in presence of complex shape

In this paper, a Dual-Equal-Collision-Probability-Curve (DECPC) method is proposed for spacecraft close-range safe proximity considering complex shapes. The Equal-Collision-Probability-Curve (ECPC) method models the spacecraft as spheres and the complex shape of the main spacecraft deteriorates the safety performance of the space mission. In terms of this problem, the DECPC method is proposed to generate the collision avoidance maneuvers in the presence of complex shape. Furthermore, the geometrical shape of the main spacecraft is assumed to consist of one big main circle and some small gaps in this paper. Then, the big main circle generates the repulsive force and the gaps engenders the attractive force. Combing the repulsive force with the attractive force, the ultimate avoidance force is achieved. Subsequently, an improved Linear Quadratic Regular (ILQR) is designed to track the reference trajectory and the stability of the overall close-loop control system is proved by the Lyapunov-based method. Numerical simulations are performed in a close-range operation environment and verify the validity of the proposed DECPC avoidance method with the ILQR controller.