Bounding the Distance to Unsafe Sets With Convex Optimization
Bounding the Distance to Unsafe Sets With Convex Optimization
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DOI：
10.1109/tac.2023.3285862
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发表时间：
2021-10
影响因子：
6.8
通讯作者：
Jared Miller;M. Sznaier
中科院分区：
文献类型：
--
作者：
Jared Miller;M. Sznaier
本文提出了一种算法来约束动力系统的轨迹上的点与不安全集合上的点之间的最小距离。先前关于验证轨迹安全性的工作包括障碍和密度方法，这些方法在距离方面不提供接近不安全轨迹的余地。距离估计问题放松到蒙格-康托洛维奇型最优运输问题的基础上，现有的占用测量方法的峰值估计。可以为多面体范数距离开发专门的程序（例如，L1和Lincoln）以及对于形状沿沿着轨迹行进的情形（例如，刚体运动）。当距离目标可分离时，距离估计问题将是相关稀疏的。
This work proposes an algorithm to bind the minimum distance between points on trajectories of a dynamical system and points on an unsafe set. Prior work on certifying safety of trajectories includes barrier and density methods, which do not provide a margin of proximity to the unsafe set in terms of distance. The distance estimation problem is relaxed to a Monge–Kantorovich-type optimal transport problem based on existing occupation-measure methods of peak estimation. Specialized programs may be developed for polyhedral norm distances (e.g., L1 and Linfinity) and for scenarios where a shape is traveling along trajectories (e.g., rigid body motion). The distance estimation problem will be correlatively sparse when the distance objective is separable.