Path Planning in Unknown Environments Using Optimal Transport Theory

Abstract

This paper introduces a graph-based, potential-guided method for path planning problems in unknown environments, where obstacles are unknown until the robots are in close proximity to the obstacle locations. Inspired by optimal transport theory, the proposed method generates a graph connecting the initial and target configurations, and then finds a path over the graph using the available environmental information. The graph and path are updated iteratively when newly encountered obstacle information becomes available. The resulting method is a deterministic procedure proven to be complete, i.e., it is guaranteed to find a feasible path, when one exists, in a finite number of iterations. The method is scalable to high-dimensional problems. In addition, our method does not search the entire domain for the path, instead, the algorithm only explores a sub-region that can be described by the evolution of the Fokker-Planck equation. We demonstrate the performance of our algorithm via several numerical examples with different environments and dimensions, including high-dimensional cases.

Optimal Transport in Systems and Control

“…The overarching theme is ways to control uncertainty in state trajectories of dynamical systems and to specify objectives in terms of soft probabilistic terminal constraints; the pertinent emerging trend in control theory can thus be referred to as control of uncertainty. OMT has several other applications in systems and control that are not covered in this short survey, such as in inverse problems (73,74), filtering and estimation (75)(76)(77)(78)(79)(80), path planning (81), and swarm control (82).…”

Reactive Temporal Logic Planning for Multiple Robots in Unknown Environments

“…If the discovered obstacles intersect with their paths p j,t:Tj , for some j ∈ R next , then these robots j locally re-solve (6) using the updated map to design new paths. Note that existing reactive planning algorithms that can address reachability navigation problems in the presence of unknown obstacles can also be used to solve (6); see e.g., [23], [24], [26], [27], [29], [30], [46], [47].…”