发表机构
Nanyang Technological University（南洋理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对航天器近距离操作的追击-逃逸博弈，提出基于支撑函数的逃逸证书与安全策略，提供精确单侧保证，并利用投影外梯度法快速求解，适用于圆轨道与椭圆轨道。
AI 中文摘要
检查或维护非合作航天器是一个双人博弈：目标可以施加推力以破坏检查者的计划。Hamilton-Jacobi-Isaacs可达性分析能够精确求解此类博弈，但其计算成本随状态维度呈指数增长，而基于学习的控制器虽可扩展却无法提供任何保证。凸优化公式通常是常用的规避途径，通常被构造为凸-凹鞍点问题。然而，这种框架在终端距离轨道博弈中失效：在加入控制代价正则化后，支付函数对两个控制输入均为凸函数，因此纯开环鞍点不一定存在。取而代之，我们通过支撑函数从博弈双方的终端可达集中推导出两个精确的单侧保证：一个逃逸证书，证明目标能够维持一个保证的安全距离；以及一个安全策略，限制检查者所能强制的脱靶量。两者共同界定了交战过程，且不假设玩家理性。在超过两百次扰动试验中，逃逸证书无误地将捕获与逃逸区分开来。一种投影外梯度方法在大约25毫秒内提供策略对，并通过最佳响应间隙进行就地验证。该构造通过Yamanaka-Ankersen动力学不变地适用于椭圆参考轨道，其中轨道相位使脱靶量变化近两倍，这一结果由非线性开普勒传播复现。在滚动时域博弈中，检查者在十个代表性交战中于半数情况下实现捕获。仅测角导航误差、禁入区、多追击者以及闭环博弈均作为扩展内容加以处理。
英文摘要
Inspecting or servicing a non-cooperative spacecraft is a two-player game: the target can thrust to defeat the inspector's plan. Hamilton-Jacobi-Isaacs reachability answers such games exactly but its cost grows exponentially with state dimension, while learning-based controllers scale yet certify nothing. Convex formulations are the usual escape, typically cast as convex-concave saddle-point problems. That framing fails in the terminal-distance orbital game: with effort regularization, the payoff is convex in both controls, so no pure open-loop saddle point need exist. In its place we derive two exact one-sided guarantees read from the players' terminal reachable sets via support functions: an escape certificate proving the target can hold a guaranteed standoff, and a security strategy bounding the miss distance the inspector can force. Together they bracket the engagement without assuming player rationality, and over two hundred perturbed trials the escape certificate separated capture from escape without error. A projected extragradient method supplies a strategy pair in about 25 ms, certified in place by best-response gaps. The construction carries unchanged to elliptical reference orbits via Yamanaka-Ankersen dynamics, where the orbital phase moves miss distance by nearly a factor of two, reproduced by nonlinear Keplerian propagation. Under receding-horizon play the inspector captures in half of ten representative engagements. Angles-only navigation error, keep-out zones, multiple pursuers, and closed-loop play are treated as extensions.
Comments38 pages, 10 figures, 19 tables (9 in appendices); accepted at Aerospace Science and Technology, 11 September 2026; ID: AESCTE-D-26-03480R1
