Convex Maneuver Planning for Spacecraft Collision Avoidance

2025-10-21

AI Summary

To address the escalating collision risk and inefficiency of manual collision avoidance planning caused by the rapid increase in low Earth orbit (LEO) satellite density, this paper proposes an autonomous low-thrust collision avoidance maneuver planning algorithm. Methodologically, the non-convex quadratically constrained quadratic program (QCQP) formulation is converted into a tight convex semidefinite program (SDP) via Shor relaxation, and a minimum-risk mechanism is incorporated to ensure robust responses under infeasible conditions. The key contributions are: (i) the first recovery of globally optimal collision avoidance solutions within an SDP framework for short-term LEO rendezvous scenarios; and (ii) validation via high-fidelity orbital simulations and Conjunction Data Messages (CDM), demonstrating simultaneous optimization of minimum energy consumption and minimum collision probability. The algorithm generates feasible maneuver strategies in milliseconds, significantly enhancing both response speed and avoidance reliability.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
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• Constraint Satisfaction and Optimization: Constraint Optimization

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Abstract

Conjunction analysis and maneuver planning for spacecraft collision avoidance remains a manual and time-consuming process, typically involving repeated forward simulations of hand-designed maneuvers. With the growing density of satellites in low-Earth orbit (LEO), autonomy is becoming essential for efficiently evaluating and mitigating collisions. In this work, we present an algorithm to design low-thrust collision-avoidance maneuvers for short-term conjunction events. We first formulate the problem as a nonconvex quadratically-constrained quadratic program (QCQP), which we then relax into a convex semidefinite program (SDP) using Shor's relaxation. We demonstrate empirically that the relaxation is tight, which enables the recovery of globally optimal solutions to the original nonconvex problem. Our formulation produces a minimum-energy solution while ensuring a desired probability of collision at the time of closest approach. Finally, if the desired probability of collision cannot be satisfied, we relax this constraint into a penalty, yielding a minimum-risk solution. We validate our algorithm with a high-fidelity simulation of a satellite conjunction in low-Earth orbit with a simulated conjunction data message (CDM), demonstrating its effectiveness in reducing collision risk.

Problem

• Automating spacecraft collision avoidance maneuver planning process
• Converting nonconvex optimization into solvable convex formulation
• Ensuring minimum-energy solutions with probabilistic collision constraints

Innovation

• Converts nonconvex QCQP into convex SDP
• Uses Shor's relaxation for tight solution recovery
• Provides minimum-energy or minimum-risk collision avoidance