Abstract:The problem of collision avoidance has increasingly become one of the research hotspots in related fields. Under the J2 perturbation environment, this paper discusses the problem of optimal collision avoidance maneuver design for low-thrust satellites and gives an efficient algorithm for the entire process of satellite collision avoidance and return maneuver. The calculation of the collision probability is carried out in the Earth-centered inertial (ECI) coordinate system, and the calculation of the optimal control of energy and fuel is carried out by constraining the collision probability. Different from the impulse maneuver, J2 perturbation is considered to observe its impact on the optimal control of low-thrust maneuver design. The efficiency of the indirect method to solve the fuel optimal collision avoidance problem is effectively improved by the method of co-state initial value normalization. The simulation results of energy and fuel optimal control with and without J2 perturbation are given and compared. The results show the effectiveness of this algorithm, and the fuel saving is 22.3% in this example.