New guidance law solves spacecraft pursuit-evasion speed constraints

A new paper from researchers Yahli Drucker and Vitaly Shaferman tackles a critical challenge in orbital mechanics: pursuit-evasion scenarios where a low-thrust spacecraft must intercept a target while enforcing a specific terminal relative speed. The problem is formulated as a linear-quadratic zero-sum differential game with soft constraints on terminal position and velocity, plus running costs on control effort. The key innovation is a method that uses cost weighting to achieve any desired terminal speed, without needing hard constraints. The authors derive an analytical closed-loop optimal guidance law that forms a saddle-point solution, meaning neither player can unilaterally improve their outcome. They also perform a conjugate point analysis to verify optimality, including the rarely studied case of a negative-definite velocity weighting matrix at high terminal speeds.

Simulation results validate the guidance law's performance across various target maneuvers. Compared to a state-of-the-art optimal-control-based guidance law, the new method consistently satisfies speed constraints while offering a substantial advantage when the target is optimally evading. This work has direct implications for autonomous satellite operations, space debris removal, and orbital security. By enabling precise control of terminal approach speed with minimal fuel consumption, it could improve the efficiency and safety of close-proximity maneuvers in space. The 22-page paper (with 9 figures) has been submitted for journal publication and is available on arXiv.