面向概率规划的分布鲁棒后向可达树的SDP综合
SDP Synthesis of Distributionally Robust Backward Reachable Trees for Probabilistic Planning
AI总结：
针对随机运动不确定性下的动态系统多查询规划问题，提出基于凸半定松弛的MAXELLIPSOID BRT算法，构建分布模糊集后向可达树，以更小的路图规模实现高效分布鲁棒规划。
摘要：
本文提出了最大椭球后向可达树（MAXELLIPSOID BRT），这是一种用于动态系统规划的多查询算法，适用于存在随机运动不确定性且控制输入受约束的场景。与现有构建分布路图的概率规划方法不同，本文提出的方法引入了一个构建分布模糊集路图的框架，使得所提路图中的每条边能同时为一族分布提供可行控制序列，从而实现高效的多查询规划。具体而言，我们构建了包含最大规模模糊集的后向可达树，以及对应的分布鲁棒边控制器。实验表明，从目标出发以反向方式计算这些分布集，可实现高效规划，且所需路图规模仅为当前最优方法的一小部分。这些最大模糊集和边的计算，是通过对一个新型非线性规划进行凸半定松弛实现的。我们还正式证明了一个关于我们前期工作中所提技术的最大覆盖范围定理。
英文摘要：
The paper presents Maximal Ellipsoid Backward Reachable Trees MAXELLIPSOID BRT, which is a multi-query algorithm for planning of dynamic systems under stochastic motion uncertainty and constraints on the control input. In contrast to existing probabilistic planning methods that grow a roadmap of distributions, our proposed method introduces a framework to construct a roadmap of ambiguity sets of distributions such that each edge in our proposed roadmap provides a feasible control sequence for a family of distributions at once leading to efficient multi-query planning. Specifically, we construct a backward reachable tree of maximal size ambiguity sets and the corresponding distributionally robust edge controllers. Experiments show that the computation of these sets of distributions, in a backwards fashion from the goal, leads to efficient planning at a fraction of the size of the roadmap required for state-of-the-art methods. The computation of these maximal ambiguity sets and edges is carried out via a convex semidefinite relaxation to a novel nonlinear program. We also formally prove a theorem on maximum coverage for a technique proposed in our prior work.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
