Equal-collision-probability-curve method for safe spacecraft close-range proximity maneuvers

An equal-collision-probability-curve (ECPC) method is developed in this paper to address the problem of safe spacecraft proximity maneuvers. Considering the uncertainties' influence, the ECPC, which represents the curve of equal-collision-probability-points in the space around the target spacecraft, is firstly established. It is optimal to maneuver along the gradient direction of the ECPC, which is the fastest change in the ECPC. To calculate this direction, a novel auxiliary function, which has the same gradient direction as the collision probability function, is proposed. Compared to traditional collision probability functions, the proposed function does not contain transcendental elements and hence the computational burden can be greatly decreased while maintaining the necessary accuracy. Then, the safe close-range proximity maneuver generated by ECPC method can be implemented along the estimated gradient direction. Analytical validation is performed to assess the use of such collision avoidance scheme for safety critical operations. Furthermore, an improved Linear Quadratic Regulator (LQR) is designed to track the reference trajectory and a Lyapunov-based analysis verifies the stability of the overall closed-loop system. Numerical simulations show that the novel ECPC method is more computationally efficient than traditional methods while maintaining the same accuracy. Moreover, the novel scheme can be easily validated to guarantee the safety of the mission.