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.

翻译：航天器防撞的交会分析与机动规划目前仍是一个人工操作且耗时费力的过程，通常涉及对人工设计机动方案进行反复的前向仿真。随着低地球轨道卫星密度的日益增长，自主化对于高效评估和规避碰撞变得至关重要。本研究提出一种针对短期交会事件设计低推力防撞机动方案的算法。我们首先将该问题表述为一个非凸二次约束二次规划问题，随后利用肖尔松弛将其转化为凸半定规划问题。我们通过实验证明该松弛是紧致的，从而能够恢复原始非凸问题的全局最优解。我们的模型在确保最近接近点处达到期望碰撞概率的同时，生成能量最优解。最后，若无法满足期望碰撞概率要求，我们将该约束松弛为惩罚项，从而得到风险最优解。我们通过低地球轨道卫星交会的高保真仿真及模拟交会数据消息验证了本算法的有效性，证明了其在降低碰撞风险方面的优越性能。