Gaussian Belief Trees for Chance Constrained Asymptotically Optimal Motion Planning
This work addresses motion planning with probabilistic guarantees for robotics, but it is incremental as it generalizes existing deterministic methods to belief space.
The paper tackles motion planning under uncertainty by extending sampling-based tree planners to belief space for linearizable systems, preserving probabilistic completeness and asymptotic optimality. It demonstrates efficient, safe path finding in simulations for holonomic and non-holonomic systems.
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.