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Asymptotically Optimal Sampling-Based Path Planning Using Bidirectional Guidance Heuristic

Yi Wang, Bingxian Mu

TL;DR

BIGIT* introduces a bidirectional, asymptotically optimal sampling-based motion planner that combines a meet-in-the-middle strategy with a lazy edge-checking scheme and uniform-cost search on an implicit random geometric graph (RGG). A novel bidirectional guidance heuristic is learned from a preliminary bidirectional search, which tightly constrains the informed search region and directs a second bidirectional search to a valid path, achieving faster initial solutions and quicker convergence to optimality. The algorithm employs a MM-based variant with a new stopping condition, lazy-MM in the first batch, and sparse collision checks, along with Dijkstra-based heuristic refinement to ensure admissibility. Theoretical guarantees include admissibility, asymptotic optimality, and probabilistic completeness, while experiments on abstract $\mathbb{R}^{16}$ problems and a campus drone task demonstrate superior performance compared with EIT* and AIT*. This work advances high-dimensional, informed, sampling-based planning by integrating bidirectional guidance with lazy evaluation and batch-based refinement to accelerate optimal convergence in practical robotics scenarios.

Abstract

This paper introduces Bidirectional Guidance Informed Trees (BIGIT*),~a new asymptotically optimal sampling-based motion planning algorithm. Capitalizing on the strengths of \emph{meet-in-the-middle} property in bidirectional heuristic search with a new lazy strategy, and uniform-cost search, BIGIT* constructs an implicitly bidirectional preliminary motion tree on an implicit random geometric graph (RGG). This efficiently tightens the informed search region, serving as an admissible and accurate bidirectional guidance heuristic. This heuristic is subsequently utilized to guide a bidirectional heuristic search in finding a valid path on the given RGG. Experiments show that BIGIT* outperforms the existing informed sampling-based motion planners both in faster finding an initial solution and converging to the optimum on simulated abstract problems in $\mathbb{R}^{16}$. Practical drone flight path planning tasks across a campus also verify our results.

Asymptotically Optimal Sampling-Based Path Planning Using Bidirectional Guidance Heuristic

TL;DR

BIGIT* introduces a bidirectional, asymptotically optimal sampling-based motion planner that combines a meet-in-the-middle strategy with a lazy edge-checking scheme and uniform-cost search on an implicit random geometric graph (RGG). A novel bidirectional guidance heuristic is learned from a preliminary bidirectional search, which tightly constrains the informed search region and directs a second bidirectional search to a valid path, achieving faster initial solutions and quicker convergence to optimality. The algorithm employs a MM-based variant with a new stopping condition, lazy-MM in the first batch, and sparse collision checks, along with Dijkstra-based heuristic refinement to ensure admissibility. Theoretical guarantees include admissibility, asymptotic optimality, and probabilistic completeness, while experiments on abstract problems and a campus drone task demonstrate superior performance compared with EIT* and AIT*. This work advances high-dimensional, informed, sampling-based planning by integrating bidirectional guidance with lazy evaluation and batch-based refinement to accelerate optimal convergence in practical robotics scenarios.

Abstract

This paper introduces Bidirectional Guidance Informed Trees (BIGIT*),~a new asymptotically optimal sampling-based motion planning algorithm. Capitalizing on the strengths of \emph{meet-in-the-middle} property in bidirectional heuristic search with a new lazy strategy, and uniform-cost search, BIGIT* constructs an implicitly bidirectional preliminary motion tree on an implicit random geometric graph (RGG). This efficiently tightens the informed search region, serving as an admissible and accurate bidirectional guidance heuristic. This heuristic is subsequently utilized to guide a bidirectional heuristic search in finding a valid path on the given RGG. Experiments show that BIGIT* outperforms the existing informed sampling-based motion planners both in faster finding an initial solution and converging to the optimum on simulated abstract problems in . Practical drone flight path planning tasks across a campus also verify our results.

Paper Structure

This paper contains 14 sections, 2 theorems, 1 equation, 3 figures, 3 algorithms.

Table of Contents

  1. INTRODUCTION
  2. BACKGROUND
  3. Potential Disadvantages of ABOPs
  4. Bidirectional Guidance Informed Trees
  5. Notation
  6. Neighbors' Connection
  7. MM-Variant
  8. Lazy-MM in First Batch Sampling
  9. Finding A Valid Path
  10. Analysis
  11. Experimental Results
  12. Planning for Abstract Problems
  13. Planning on A Campus Map
  14. Conclusions and Future Work

Key Result

Theorem 1

BIGIT* provides an admissible heuristic on a given RGG.

Figures (3)

  • Figure 1: Demonstrating the Bidirectional Guidance Informed Trees ( BIGIT*). (A) Constructing a preliminary bidirectional motion tree via a bidirectional heuristic search with a new lazy strategy. (B) Acquiring estimated bounds for updating heuristic. (C) Updating heuristic with the estimated bounds from (B) using uniform-cost search. (D) Use a bidirectional search with the bidirectional guidance heuristic to find a valid path.
  • Figure 2: Experimental environments: abstract problems in (a) and (b); real-world scenarios in (c).
  • Figure 3: Comparative performance of BIGIT* and EIT* across different domains in terms of median solution cost and success rate over time, with 95$\%$ confidence interval in each plot. $\mathrel{}$ and $\mathrel{}$ denote BIGIT* and EIT*, respectively.

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof