  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.
