Time-Optimal Collision Avoidance Via a Greedy Polynomial Backward Sweep

2026-05-31

AI Summary

This work addresses the challenge of determining the latest feasible maneuver initiation time for low-thrust spacecraft to avoid on-orbit collisions. The authors propose a Greedy Time-Optimal (GTO) backward-scan method that starts from the nominal closest approach epoch and iteratively propagates maneuvers backward in time. At each step, the thrust direction is selected to locally minimize a collision risk metric, while differential algebra techniques enable efficient online updates of the closest approach time and state sensitivities. By integrating a greedy strategy with polynomial-based backward scanning for the first time, the approach achieves near-optimal performance while meeting onboard real-time computational constraints. Numerical experiments demonstrate that the method maintains high accuracy across large-scale conjunction scenarios, incurs only minor suboptimality relative to optimal control benchmarks, and offers the computational efficiency required for onboard deployment.

Abstract

Spacecraft collision avoidance for low-thrust satellites often requires determining not only how to maneuver, but also how late a maneuver can begin while still ensuring safety. This paper presents a greedy time-optimal (GTO) backward-sweep method to find the latest maneuver initiation time. The method starts from the nominal time of closest approach and iteratively propagates the maneuver backward in time, selecting at each step the thrust direction that locally minimizes the chosen danger metric. Differential algebra is used to efficiently propagate state sensitivities and update the time of closest approach online. The method is tested on a large dataset of conjunctions, using both miss distance and probability of collision as safety metrics. The approach achieves accurate results and only a small loss of optimality relative to an optimal-control benchmark, while retaining runtimes suitable for on-board implementation.

Problem

• collision avoidance
• time-optimal
• low-thrust satellites
• maneuver initiation time
• spacecraft safety

Innovation

• greedy time-optimal
• backward sweep
• collision avoidance
• differential algebra
• low-thrust spacecraft