SDP Synthesis of Distributionally Robust Backward Reachable Trees for Probabilistic Planning

Naman Aggarwal, Jonathan P. How

Abstract: In this article, we present Maximal Ellipsoid Backward Reachable Trees MAXELLIPSOID BRT, which is a multiquery 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 multiquery 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 backward 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 on probabilistic planning (Aggarwal et al., 2024).

External IDs:dblp:journals/tac/AggarwalH25