Bidirectional Sampling-Based Motion Planning Without Two-Point Boundary Value Solution

Sharan Nayak, Michael W. Otte

Abstract: Bidirectional path and motion planning approaches decrease planning time, on average, compared to their unidirectional counterparts. In single-query feasible motion planning, using bidirectional search to find a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">continuous</i> motion plan requires an edge connection between the forward search tree and the reverse search tree. Such a tree–tree connection requires solving a two-point boundary value problem (BVP). However, obtaining a closed-form two-point BVP solution can be difficult or impossible for many systems. While numerical methods can provide a reasonable solution in many cases, they are often computationally expensive, numerically unstable, or sensitive (to an initial guess) for the purposes of single-query sampling-based motion planning. To overcome this challenge, we present a novel bidirectional search strategy that does not require solving the two-point BVP. Instead of connecting the forward and reverse trees directly, the reverse tree’s cost information is used as a guiding heuristic for forward search. This enables the forward search to quickly grow down the reverse tree—converging to a fully feasible solution <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">without</i> a direct tree–tree connection and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">without</i> the solution to a two-point BVP. In this article, we propose two algorithms that use this strategy for single-query feasible motion planning for various dynamical systems, performing experiments in both simulation and hardware testbeds. We find that these algorithms perform better than or comparable to the existing state-of-the-art methods with respect to quickly finding an initial feasible solution.