用哈密顿-雅可比方法实时生成机器人应急路径，确保安全可达。
SCRAMPPI: Efficient Contingency Planning for Mobile Robot Navigation via Hamilton-Jacobi Reachability
- 基于哈密顿-雅可比可达性分析，在线计算安全集的后向可达值函数。
- 在对抗性逃逸任务中实现毫秒级实时规划，保证任意点都能返回安全区。
- 适合高风险场景下的移动机器人自主导航，如搜救、巡检等应用。
自主机器人通常以最小化代价完成预定行为，但对意外情况缺乏应对能力，需在出现异常时启用应急计划以避免任务失败。本文将此需求形式化为带安全约束的轨迹优化问题：从预定路径任一点出发，必须存在一条可行轨迹到达指定安全集。现有方法或放宽该硬约束，或采用昂贵的采样策略进行优化。本文提出将该问题建模为一个规避-可达问题，利用哈密顿-雅可比（HJ）可达性分析来验证应急路径的可行性。通过在线计算安全集的后向可达集值函数，并结合采样规划器MPPI进行基于重采样的滚动优化，既保证了硬约束满足，又显著提升了采样效率。最后，通过仿真与硬件实验，在对抗性逃逸任务中验证了算法在移动机器人上实现实时生成主路径与应急路径的能力。
原文摘要 · Abstract (English)
Autonomous robots commonly aim to complete a nominal behavior while minimizing a cost; this leaves them vulnerable to failure or unplanned scenarios, where a backup or contingency plan to a safe set is needed to avoid a total mission failure. This is formalized as a trajectory optimization problem over the nominal cost with a safety constraint: from any point along the nominal plan, a feasible trajectory to a designated safe set must exist. Previous methods either relax this hard constraint, or use an expensive sampling-based strategy to optimize for this constraint. Instead, we formalize this requirement as a reach-avoid problem and leverage Hamilton-Jacobi (HJ) reachability analysis to certify contingency feasibility. By computing the value function of our safe-set's backward reachable set online as the environment is revealed and integrating it with a sampling based planner (MPPI) via resampling based rollouts, we guarantee satisfaction of the hard constraint while greatly increasing sampling efficiency. Finally, we present simulated and hardware experiments demonstrating our algorithm generating nominal and contingency plans in real time on a mobile robot in an adversarial evasion task.
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