Lambert’s Problem with Multiple Constraints

Abstract

This paper proposes a new method to solve Lambert’s problem with multiple constraints, including the impulse-magnitude constraints, the trajectory-radius constraints, and the terminal-impact-angle constraint. First, the closed-form range of the chordal terminal velocity component for each constraint is derived. Then, the admissible intersection range for all constraints is obtained. Finally, the feasible solutions are solved in the admissible intersection range by using the terminal-velocity-based Lambert algorithm. The 180° case and the multiple-revolution case are also considered. The proposed method can be also extended to the Lambert algorithms with other independent variables. Compared with the typical method of first solving Lambert’s problem and then pruning the solutions that do not satisfy the constraints, the numerical examples show that the proposed method can reduce a lot of computational time.