SDP Synthesis of Distributionally Robust Backward Reachable Trees for Probabilistic Planning
| Autor: | Aggarwal, Naman, How, Jonathan P. |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Submitted to IEEE Transactions on Automatic Control on June 26, 2024. arXiv admin note: substantial text overlap with arXiv:2403.14605 |
| Databáze: | arXiv |
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