Efficient Probabilistic Planning with Maximum-Coverage Distributionally Robust Backward Reachable Trees

2025-10-06

AI Summary

This paper addresses multi-query motion planning for linear Gaussian systems under uncertainty, proposing a distributionally robust belief-space planning method that guarantees, with high probability, reaching a target region defined as the Minkowski sum of an Euclidean ball (or ellipsoid) and a ball. The method introduces spherical ambiguity sets to model uncertainty and constructs a distributionally robust backward reachable tree with maximal coverage. Its key contributions are: (1) a novel integration of distributionally robust optimization, Gaussian fuzzy set modeling, belief-space planning, and parameterized ellipsoidal Minkowski sums; and (2) rigorous theoretical proof—under mild conditions—that the method achieves superior coverage performance over existing approaches, attaining theoretical optimality in the noise-free case. Simulation results demonstrate that the proposed algorithm significantly improves path success rate and robustness across diverse noise scenarios, consistently outperforming state-of-the-art methods.

Technology Category

• Planning, Routing, and Scheduling: Planning under Uncertainty
• Intelligent Robots: Motion and Path Planning
• Multiagent Systems: Multiagent Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Security and Privacy: Large-scale security measurements

Abstract

This paper presents a new multi-query motion planning algorithm for linear Gaussian systems with the goal of reaching a Euclidean ball with high probability. We develop a new formulation for ball-shaped ambiguity sets of Gaussian distributions and leverage it to develop a distributionally robust belief roadmap construction algorithm. This algorithm synthe- sizes robust controllers which are certified to be safe for maximal size ball-shaped ambiguity sets of Gaussian distributions. Our algorithm achieves better coverage than the maximal coverage algorithm for planning over Gaussian distributions [1], and we identify mild conditions under which our algorithm achieves strictly better coverage. For the special case of no process noise or state constraints, we formally prove that our algorithm achieves maximal coverage. In addition, we present a second multi-query motion planning algorithm for linear Gaussian systems with the goal of reaching a region parameterized by the Minkowski sum of an ellipsoid and a Euclidean ball with high probability. This algorithm plans over ellipsoidal sets of maximal size ball-shaped ambiguity sets of Gaussian distributions, and provably achieves equal or better coverage than the best-known algorithm for planning over ellipsoidal ambiguity sets of Gaussian distributions [2]. We demonstrate the efficacy of both methods in a wide range of conditions via extensive simulation experiments.

Problem

• Develops robust motion planning for linear Gaussian systems
• Achieves certified safety for maximal ambiguity set coverage
• Enables high-probability reachability of Euclidean ball targets

Innovation

• Distributionally robust belief roadmap for motion planning
• Synthesizes robust controllers for Gaussian ambiguity sets
• Maximal coverage planning for ellipsoidal and ball targets