构建分布鲁棒的反向可达树，实现高效多查询概率规划。
SDP Synthesis of Distributionally Robust Backward Reachable Trees for Probabilistic Planning
- 用模糊集代替分布图谱，单条边覆盖一族分布的控制策略。
- 反向计算最大模糊集，所需路网规模仅为现有方法的几分之一。
- 适用于带随机扰动的动态系统多目标规划，适合机器人路径规划场景。
本文提出最大椭球反向可达树（MAXELLIPSOID BRT），一种针对存在随机运动不确定性与控制输入约束的动态系统进行多查询规划的方法。不同于现有基于分布路网的规划方法，本文构建的是分布模糊集的路网，使得每条边可同时为一类分布提供可行控制序列，从而实现高效多查询规划。具体而言，通过构造最大尺寸的模糊集反向可达树及对应的分布鲁棒边控制器，以逆向方式从目标状态开始计算这些分布集合。利用凸半定松弛求解新颖的非线性规划问题，实现高效计算。实验表明，该方法在反向计算分布集合时，所需路网规模仅为当前最优方法的极小部分。同时，本文还对前期工作中的最大覆盖技术给出了形式化证明。
原文摘要 · Abstract (English)
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.
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