Bidirectional Sampling Based Search Without Two Point Boundary Value Solution

TL;DR

This paper introduces a novel bidirectional motion planning approach that avoids solving complex two-point boundary value problems by using the reverse tree's cost information as a heuristic, leading to faster feasible path discovery.

Contribution

The authors propose two new algorithms, GBRRT and GABRRT, which improve bidirectional motion planning by eliminating the need for two-point BVP solutions, demonstrated through simulations and hardware experiments.

Findings

Algorithms perform on par or better than existing methods.

Faster convergence to feasible solutions without solving BVP.

Effective across multiple dynamical systems and real-world hardware.

Abstract

Bidirectional 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 continuous motion plan requires an edge connection between the forward and reverse search trees. Such a tree-tree connection requires solving a two-point Boundary Value Problem (BVP). However, a two-point BVP solution can be difficult or impossible to calculate for many systems. 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 the forward search. This enables the forward search to quickly converge to a feasible solution without solving the two-point BVP. We propose two new algorithms (GBRRT and GABRRT) that use this strategy and run multiple software simulations using multiple dynamical systems and real-world hardware experiments to show that our algorithms perform on-par or better than existing state-of-the-art methods in quickly finding an initial feasible solution.