GSRM: Building Roadmaps for Query-Efficient and Near-Optimal Path Planning Using a Reaction Diffusion System

TL;DR

GSRM tackles the challenge of multi-query motion planning on 2D roadmaps by generating well-connected graphs with short, near-optimal paths and fast queries. It couples the Gray-Scott reaction-diffusion system with Delaunay triangulation to place roadmap vertices as evenly distributed spots and connect them via obstacle-free edges. Compared to SPARS2, ORM, PRM, and Gridmap, GSRM delivers shorter paths, higher success rates, and competitive online/query efficiency across diverse maps, with offline construction times that remain practical up to ~2000 vertices. The approach offers a scalable, grid-free roadmap construction paradigm that adapts to environmental structure and reduces path-length regret while maintaining robust connectivity. Future work includes extending the method to 3D settings and multi-agent scenarios with distance constraints, broadening practical applicability.

Abstract

Mobile robots frequently navigate on roadmaps, i.e., graphs where edges represent safe motions, in applications such as healthcare, hospitality, and warehouse automation. Often the environment is quasi-static, i.e., it is sufficient to construct a roadmap once and then use it for any future planning queries. Roadmaps are typically used with graph search algorithm to find feasible paths for the robots. Therefore, the roadmap should be well-connected, and graph searches should produce near-optimal solutions with short solution paths while simultaneously be computationally efficient to execute queries quickly. We propose a new method to construct roadmaps based on the Gray-Scott reaction diffusion system and Delaunay triangulation. Our approach, GSRM, produces roadmaps with evenly distributed vertices and edges that are well-connected even in environments with challenging narrow passages. Empirically, we compare to classical roadmaps generated by 8-connected grids, probabilistic roadmaps (PRM, SPARS2), and optimized roadmap graphs (ORM). Our results show that GSRM consistently produces superior roadmaps that are well-connected, have high query efficiency, and result in short solution paths.

Figures (8)

• Figure 1: Example roadmap with $290$ nodes and $957$ edges on the map Slam from \ref{['fig:gsrm-eval-map-slam']}. Blue dots are the vertices of the roadmap, black lines are the edges. The red line is an example path with a length of $0.479$. The roadmap was produced from the simulation of the Gray-Scott system shown in \ref{['fig:gsrm-example-last']}.
• Figure 2: Concentration of substance $U$ over time. The grid size is $l=300$. Black areas are obstacles, where the concentration is zero. The brighter the color, the higher the concentration of substance $U$. It is visible how the spotted pattern emerges.
• Figure 3: Maps used in evaluation. Gray and black areas are obstacles. White areas are free space.
• Figure 4: Examples of roadmaps generated by different algorithms in map Rooms. The red line is an example path. The paths for GSRM, SPARS2, and ORM share the same start and goal points, while the paths for PRM and Gridmap also share the same start and goal points. The last two examples use a different path query, because the query from the first examples are not successfully computable with them.
• Figure 5: Average path length regret of the shortest path between two random points in $\mathcal{C}_{\mathsf{free}}$ for different roadmap types. The shaded areas show the standard deviation across $100$ trials. GSRM provides the shortest paths in maps other than Plain.