# Bidirectional Sampling Based Search Without Two Point Boundary Value Solution

arXiv: https://arxiv.org/abs/2010.14692 · HTML: https://mlsanity.com/paper/2010.14692/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2020.

## Built on by (most cited first, 1 of 1)

- [BiC-MPPI: Goal-Pursuing, Sampling-Based Bidirectional Rollout Clustering Path Integral for Trajectory Optimization](https://mlsanity.com/paper/2410.06493/) (2024)

## Abstract (arXiv)

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.