Quick Heuristic Validation of Edges in Dynamic Roadmap Graphs

TL;DR

This work tackles updating robot motion planning roadmaps in dynamic environments by introducing the Red-Green-Gray (RGG) paradigm, an extension of SPITE that uses outer- and inner-approximations to rapidly classify edges and nodes as valid, invalid, or unknown. It leverages oriented bounding boxes for outer approximations and splines with spheres for inner approximations, stored in AABB trees to enable fast lazy collision checks and selective revalidation. The authors show that RGG improves edge validity labeling accuracy while sustaining update runtimes comparable to grid-based dynamic roadmaps, outperforming a baseline method in identifying invalid edges. The approach promises faster, more reliable multi-query planning under moving obstacles and can be extended toward real-time, GPU-accelerated implementations with further hierarchical and approximation refinements.

Abstract

In this paper we tackle the problem of adjusting roadmap graphs for robot motion planning to non-static environments. We introduce the "Red-Green-Gray" paradigm, a modification of the SPITE method, capable of classifying the validity status of nodes and edges using cheap heuristic checks, allowing fast semi-lazy roadmap updates. Given a roadmap, we use simple computational geometry methods to approximate the swept volumes of robots and perform lazy collision checks, and label a subset of the edges as invalid (red), valid (green), or unknown (gray). We present preliminary experimental results comparing our method to the well-established technique of Leven and Hutchinson, and showing increased accuracy as well as the ability to correctly label edges as invalid while maintaining comparable update runtimes.

Figures (7)

• Figure 1: An illustration of a roadmap for a 2D translational disk robot in a 2D environment. The edges, shown as sequences of robot configuration along line segments, may become invalid as obstacles change their positions. When the obstacle, labeled $o$, moves from its first position, shown in Figure \ref{['fig:dynamic:roadmap:before']}, to another position, shown in Figure \ref{['fig:dynamic:roadmap:after']}, two edges become invalid (red).
• Figure 2: Two examples of outer- and inner-approximations of a swept volume created by motion of a robot (corresponding to a roadmap edge). One link of the manipulator and the entire mobile robot are over-approximated by an oriented bounding box (pink) and under-approximated by two splines (yellow), and obstacles are over-approximated by an AABB (gray) and under-approximated by an oval shape (light blue). In Figure \ref{['fig:rgg:example:manip']}$o_1$ gives rise to a gray edge (edge is invalid), and $o_2$ gives rise to a green edge. In Figure \ref{['fig:rgg:example:mobile']}$o_1$ gives rise to a gray edge (edge is valid), and $o_2$ gives rise to a red edge.
• Figure 3: The output of Algorithm \ref{['alg:sphere:generation']} on an input tetrahedron $P$, $k=4$, and $j=4$.
• Figure 4: Illustration of the definitions used for Algorithm \ref{['alg:shortcutting']} for finding shortcuts in splines. One spline contains a bad segment (red), and the other only good segments (green).
• Figure 5: An illustration of an experiment described in Section \ref{['sec:experiment']}. Configurations of the simulated 6DOF manipulator forming an edge in the workspace. The depicted edge is invalid due to the orientation of the rectangular prism obstacle.