Gaussian Belief Trees for Chance Constrained Asymptotically Optimal Motion Planning

TL;DR

This paper introduces belief-$\mathcal{A}$, a framework extending sampling-based motion planning algorithms to belief space for linear systems, ensuring probabilistic safety and asymptotic optimality.

Contribution

It generalizes deterministic sampling-based planners to handle uncertainty in belief space while maintaining probabilistic guarantees and optimality.

Findings

Effective in finding safe, low-cost paths in simulation.

Applicable to both holonomic and non-holonomic systems.

Preserves probabilistic completeness and asymptotic optimality.

Abstract

In this paper, we address the problem of sampling-based motion planning under motion and measurement uncertainty with probabilistic guarantees. We generalize traditional sampling-based tree-based motion planning algorithms for deterministic systems and propose belief-$\mathcal{A}$, a framework that extends any kinodynamical tree-based planner to the belief space for linear (or linearizable) systems. We introduce appropriate sampling techniques and distance metrics for the belief space that preserve the probabilistic completeness and asymptotic optimality properties of the underlying planner. We demonstrate the efficacy of our approach for finding safe low-cost paths efficiently and asymptotically optimally in simulation, for both holonomic and non-holonomic systems.