用哈密顿-雅可比方法实现卫星避障，确保在最坏情况下仍能安全规避碰撞。
Hamilton--Jacobi Reachability for Spacecraft Collision Avoidance
- 构建零和微分博弈模型，将干扰视为未知意图的有界对抗项。
- 计算后向可达集，标识出无论如何都无法避免碰撞的危险状态区。
- 结合监督式混合控制逻辑，为卫星提供可数学证明的安全避让时机。
本文提出一种基于哈密顿-雅可比（HJ）可达性的双星避碰框架，适用于同轨道平面内的两颗卫星，其相对运动采用径向-切向-法向（RTN）坐标系中的平面希尔-克洛赫西-威尔斯（HCW）动力学建模。目标状态空间定义为满足美国联邦通信委员会（FCC）轨道标准的最小间距要求下的不安全相对构型。航天器间的交互被建模为零和微分博弈，其中玩家1为可控卫星，玩家2为具有未知意图的有界对抗扰动。本文给出HJ公式，并计算后向可达集，表征在最坏扰动下无法避免碰撞的相对状态集合；而该集合外的状态则存在可保证无碰撞的轨迹。这些可达集与监督式混合控制逻辑集成，用于判断何时必须启动规避机动，从而实现可扩展的数学化安全保证。
原文摘要 · Abstract (English)
This article presents a Hamilton--Jacobi (HJ) reachability framework for a two--satellite collision avoidance problem operating in the same circular orbit, where relative motion is modeled in the radial--tangential--normal (RTN) frame using planar Hill--Clohessy--Wiltshire (HCW) dynamics. We define the target state space as unsafe relative configurations in the orbit plane corresponding to minimum separation requirements consistent with Federal Communications Commission (FCC) orbital standards. The interaction between spacecraft is formulated as a zero--sum differential game, where Player 1 is the controlled satellite and Player 2 is modeled as a bounded adversarial disturbance with unknown intent. We present the HJ formulation and compute backward reachable sets that characterize relative states from which collision cannot be avoided under worst-case disturbances, while states outside this set admit provably collision-free trajectories. These reachable sets are integrated with supervisory hybrid control logic to determine when evasive maneuvers must be initiated, enabling mathematically grounded safety guarantees for scalability.
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