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Fast Motion Planning for Non-Holonomic Mobile Robots via a Rectangular Corridor Representation of Structured Environments

Alejandro Gonzalez-Garcia, Sebastiaan Wyns, Sonia De Santis, Jan Swevers, Wilm Decré

TL;DR

A deterministic free-space decomposition that creates a compact graph of overlapping rectangular corridors enables a significant reduction in the search space, without sacrificing path resolution, and is a highly efficient solution for large-scale navigation.

Abstract

We present a complete framework for fast motion planning of non-holonomic autonomous mobile robots in highly complex but structured environments. Conventional grid-based planners struggle with scalability, while many kinematically-feasible planners impose a significant computational burden due to their search space complexity. To overcome these limitations, our approach introduces a deterministic free-space decomposition that creates a compact graph of overlapping rectangular corridors. This method enables a significant reduction in the search space, without sacrificing path resolution. The framework then performs online motion planning by finding a sequence of rectangles and generating a near-time-optimal, kinematically-feasible trajectory using an analytical planner. The result is a highly efficient solution for large-scale navigation. We validate our framework through extensive simulations and on a physical robot. The implementation is publicly available as open-source software.

Fast Motion Planning for Non-Holonomic Mobile Robots via a Rectangular Corridor Representation of Structured Environments

TL;DR

A deterministic free-space decomposition that creates a compact graph of overlapping rectangular corridors enables a significant reduction in the search space, without sacrificing path resolution, and is a highly efficient solution for large-scale navigation.

Abstract

We present a complete framework for fast motion planning of non-holonomic autonomous mobile robots in highly complex but structured environments. Conventional grid-based planners struggle with scalability, while many kinematically-feasible planners impose a significant computational burden due to their search space complexity. To overcome these limitations, our approach introduces a deterministic free-space decomposition that creates a compact graph of overlapping rectangular corridors. This method enables a significant reduction in the search space, without sacrificing path resolution. The framework then performs online motion planning by finding a sequence of rectangles and generating a near-time-optimal, kinematically-feasible trajectory using an analytical planner. The result is a highly efficient solution for large-scale navigation. We validate our framework through extensive simulations and on a physical robot. The implementation is publicly available as open-source software.
Paper Structure (24 sections, 5 equations, 6 figures, 3 tables)

This paper contains 24 sections, 5 equations, 6 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Contributions
  3. Preliminaries
  4. Problem Formulation
  5. Architecture Overview
  6. Automatic Corridor Generation
  7. Design Objectives
  8. Algorithm
  9. Stage 1-2, Line Detection and Straightening
  10. Stage 3-4, Snap Point Extraction and Extension
  11. Stage 5-6, Face Identification and Corner Resolution
  12. Stage 7-8, Rectangle Generation and Obstacle Carving
  13. Stage 9, Corridor Connectivity Graph Construction
  14. Complexity Analysis
  15. Corridor-Based Motion Planning
  16. ...and 9 more sections

Figures (6)

  • Figure 1: Example illustrating the corridor-based motion planning framework: (a) input occupancy grid, (b) corridor decomposition, (c) planned corridor sequence (blue to red), and (d) generated analytical trajectory.
  • Figure 2: Automatic corridor generation pipeline example. (a) Floor plan as a binary image. (b) Detected line segments. (c) Straightened and shifted line segments. (d) Snap point extraction, blue dots mark full snap points, purple dots mark half snap points. (e) Closed rooms and continuous hallways after extending half snap points. (f) Pruned snap graph after obstacle removal. (g) Full snap extension, yellow dots mark the new double snap points. (h) Usage of snap points and faces to construct maximal axis-aligned rectangles. (i) Rectangle generation before obstacle carving. (j) Rectangles overlapping obstacles are split into fragments, resulting in the final coverage.
  • Figure 3: Representative Corridor Decompositions. (a) Small map (330x630 pixels) with 17 rectangles. (b)-(c) Large maps (1744x1624, 1738x2395 pixels) with 17 rectangles. (d) Large map (3444x1891 pixels) with 27 rectangles.
  • Figure 4: Motion Planning Benchmark. (Left) Computation Time vs Path Length. (Right) Average Computation Time vs Number of Corridors Traveled. Hybrid-A* failed to solve for some long paths.
  • Figure 5: Illustrative Motion Planning Comparison. This medium query has a path of 18m, traveling through 8 corridors. Compared to A* (31.14ms), Smac Hybrid-A* (467.78ms), and Smac State Lattice Planner (119.28ms), the proposed approach (23ms) achieves the fastest computation time while planning a kinematically feasible trajectory.
  • ...and 1 more figures

Theorems & Definitions (3)

  • Remark 1
  • Remark 2
  • Remark 3