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GNN-DIP: Neural Corridor Selection for Decomposition-Based Motion Planning

Peng Xie, Yanlinag Huang, Wenyuan Wu, Amr Alanwar

Abstract

Motion planning through narrow passages remains a core challenge: sampling-based planners rarely place samples inside these narrow but critical regions, and even when samples land inside a passage, the straight-line connections between them run close to obstacle boundaries and are frequently rejected by collision checking. Decomposition-based planners resolve both issues by partitioning free space into convex cells -- every passage is captured exactly as a cell boundary, and any path within a cell is collision-free by construction. However, the number of candidate corridors through the cell graph grows combinatorially with environment complexity, creating a bottleneck in corridor selection. We present GNN-DIP, a framework that addresses this by integrating a Graph Neural Network (GNN) with a two-phase Decomposition-Informed Planner (DIP). The GNN predicts portal scores on the cell adjacency graph to bias corridor search toward near-optimal regions while preserving completeness. In 2D, Constrained Delaunay Triangulation (CDT) with the Funnel algorithm yields exact shortest paths within corridors; in 3D, Slab convex decomposition with portal-face sampling provides near-optimal path evaluation. Benchmarks on 2D narrow-passage scenarios, 3D bottleneck environments with up to 246 obstacles, and dynamic 2D settings show that GNN-DIP achieves 99--100% success rates with 2--280 times speedup over sampling-based baselines.

GNN-DIP: Neural Corridor Selection for Decomposition-Based Motion Planning

Abstract

Motion planning through narrow passages remains a core challenge: sampling-based planners rarely place samples inside these narrow but critical regions, and even when samples land inside a passage, the straight-line connections between them run close to obstacle boundaries and are frequently rejected by collision checking. Decomposition-based planners resolve both issues by partitioning free space into convex cells -- every passage is captured exactly as a cell boundary, and any path within a cell is collision-free by construction. However, the number of candidate corridors through the cell graph grows combinatorially with environment complexity, creating a bottleneck in corridor selection. We present GNN-DIP, a framework that addresses this by integrating a Graph Neural Network (GNN) with a two-phase Decomposition-Informed Planner (DIP). The GNN predicts portal scores on the cell adjacency graph to bias corridor search toward near-optimal regions while preserving completeness. In 2D, Constrained Delaunay Triangulation (CDT) with the Funnel algorithm yields exact shortest paths within corridors; in 3D, Slab convex decomposition with portal-face sampling provides near-optimal path evaluation. Benchmarks on 2D narrow-passage scenarios, 3D bottleneck environments with up to 246 obstacles, and dynamic 2D settings show that GNN-DIP achieves 99--100% success rates with 2--280 times speedup over sampling-based baselines.
Paper Structure (37 sections, 3 theorems, 7 equations, 5 figures, 4 tables, 1 algorithm)

This paper contains 37 sections, 3 theorems, 7 equations, 5 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries and Related Work
  3. Decomposition-Based Motion Planning
  4. Learning and GNNs for Motion Planning
  5. Problem Formulation
  6. GNN Portal Scoring
  7. Graph Representation and Feature Engineering
  8. Node Features ($d_n = 11$ in 2D) and Edge Features ($d_e = 9$ in 2D)
  9. GNN Architecture
  10. Training
  11. Label Generation
  12. Focal Loss
  13. Optimization
  14. Decomposition-Informed Planner
  15. GNN-Guided Edge Weight Integration
  16. ...and 22 more sections

Key Result

Proposition 1

The weight eq:gnn_weight is strictly positive and continuous; it recovers the centroid-distance baseline when $\hat{s}_{ij} = 0$ (graceful degradation); and higher scores yield lower weights, concentrating the $k$-shortest search on predicted near-optimal portals.

Figures (5)

  • Figure 1: GNN-DIP pipeline on a labyrinth with polygon obstacles. (a) Planning problem with start ($\star$) and goal ($\circ$). (b) CDT decomposes the free space into 385 triangular cells. (c) The GNN selects a corridor of 73 cells (light blue), and the Funnel algorithm computes the initial path (green) in parallel across corridor candidates. (d) Phase 2 refines the solution within a shrinking informed ellipsoid (orange dashed $\to$ red solid).
  • Figure 2: PDT convergence plots: success rate (top) and median cost (bottom) vs. time. Top row: 2D very hard scenarios (100 runs, 2 s). Bottom row: 3D bottleneck scenarios (50 runs, 20 s) and Dense BN Office ($\sim$600 cells); $\mathcal{G}$-DIP converges 2$\times$ faster than DIP on the dense variant.
  • Figure 3: Dynamic 2D benchmark summary across 10 scenarios. (a) Average path cost: GNN-DIP achieves lower cost on all scenarios, especially multi-room (6--8% reduction). (b) Average solve time: GNN-DIP solves in 1.8--44 ms vs. OMPL's 500 ms budget (50--280$\times$ speedup). (c) Success rate: GNN-DIP achieves 99% vs. OMPL's 40% after collision post-validation.
  • Figure 4: CBF behavior within CDT cells. (a) Typical cell: path traverses the convex interior far from the wall, $h(q) \gg 0$, CBF inactive. (b) Narrow cell near a bottleneck: path forced close to wall, $h \approx r$, CBF activates to enforce clearance.
  • Figure 5: CBF-guarded passage tube. Safe swept volume (green) clipped to free space; tube constricts at the narrow door where the robot maintains wall clearance.

Theorems & Definitions (10)

  • Definition 1: Motion Planning Problem
  • Definition 2: Free-Space Decomposition
  • Definition 3: Cell Adjacency Graph
  • Definition 4: Corridor
  • Proposition 1: Properties of GNN Edge Weights
  • Definition 5: Informed Ellipsoid
  • Theorem 1: Completeness of DIP
  • proof : Proof sketch
  • Theorem 2: Convergence of DIP
  • proof : Proof sketch