SUMMARYWe propose a novel formal approach to robust motion planning (MP) in dynamic environments based on reachability analysis. While traditional MP methods usually fail to provide formal robust safety and performance guarantees, our approach provably ensures safe task achievement in time-varying and adversarial environments under parametric uncertainty. We leverage recent results on Hamilton–Jacobi (HJ) reachability and differential games in order to compute offline guaranteed motion plans that are compatible with the sampled-data (SD) paradigm. Also, we synthesize online provably robust safety-preserving and target-reaching feedback controls. Unlike earlier applications of reachability analysis to MP, our methodology handles arbitrary time-varying constraints, adversarial agents such as pursuing obstacles or evading targets, and takes into account the robot’s configuration. Furthermore, we use HJ projections in order to reduce significantly the computational burden without trading off safety guarantees. The validity of this approach is demonstrated through the case study of a robot arm subject to measurement errors, which is tasked with safely reaching a goal in a known time-varying workspace while avoiding capture by an unpredictable pursuer. Finally, the performance of the approach and research perspectives are discussed.

中文翻译：

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基于采样数据 Hamilton-Jacobi 可达性的动态环境中的鲁棒运动规划

摘要我们提出了一种基于可达性分析的动态环境中鲁棒运动规划（MP）的新形式方法。虽然传统的 MP 方法通常无法提供正式的稳健安全和性能保证，但我们的方法可证明确保在参数不确定性的时变和对抗环境中安全地完成任务。我们利用最近关于 Hamilton-Jacobi (HJ) 可达性和差分博弈的结果来计算与采样数据 (SD) 范式兼容的离线保证运动计划。此外，我们综合了在线可证明稳健的安全保护和达到目标的反馈控制。与早期对 MP 的可达性分析应用不同，我们的方法处理任意时变约束、对抗性代理，例如追逐障碍物或逃避目标，并考虑到机器人的配置。此外，我们使用 HJ 投影来显着减少计算负担而不牺牲安全保证。这种方法的有效性通过对受测量误差影响的机器人手臂的案例研究得到证明，该机器人手臂的任务是在已知的时变工作空间中安全地达到目标，同时避免被不可预知的追捕者捕获。最后，讨论了该方法的性能和研究前景。它的任务是在已知的时变工作空间中安全地达到目标，同时避免被不可预知的追捕者捕获。最后，讨论了该方法的性能和研究前景。它的任务是在已知的时变工作空间中安全地达到目标，同时避免被不可预知的追捕者捕获。最后，讨论了该方法的性能和研究前景。