Serialized Red-Green-Gray: Quicker Heuristic Validation of Edges in Dynamic Roadmap Graphs

Abstract

Motion planning in dynamic environments, such as robotic warehouses, requires fast adaptation to frequent changes in obstacle poses. Traditional roadmap-based methods struggle in such settings, relying on inefficient reconstruction of a roadmap or expensive collision detection to update the existing roadmap. To address these challenges we introduce the Red-Green-Gray (RGG) framework, a method that builds on SPITE to quickly classify roadmap edges as invalid (red), valid (green), or uncertain (gray) using conservative geometric approximations. Serial RGG provides a high-performance variant leveraging batch serialization and vectorization to enable efficient GPU acceleration. Empirical results demonstrate that while RGG effectively reduces the number of unknown edges requiring full validation, SerRGG achieves a 2-9x speedup compared to the sequential implementation. This combination of geometric precision and computational speed makes SerRGG highly effective for time-critical robotic applications.

Figures (4)

• Figure 1: Examples of outer- and inner-approximations of swept volumes corresponding to roadmap edges. A manipulator link and a mobile robot are over-approximated by oriented bounding boxes (pink) and under-approximated by splines (dark blue). Obstacles are over-approximated by OBBs (gray) and under-approximated by oval shapes (light blue). In (a), $o_1$ yields a gray edge (invalid) and $o_2$ yields a green edge. In (b), $o_1$ yields a gray edge (valid) and $o_2$ yields a red edge.
• Figure 2: Gray objects denote static obstacles while light blue objects denote dynamic obstacles. (a) Initial roadmap validation with the obstacle in its starting position. (b) Over-approximations of the edges represented as OBBs in dark blue. (c) Under-approximations of the edges represented as splines in light blue.
• Figure 3: Light blue objects denote dynamic obstacles. (a) The edges corresponding to gray OBBs will be processed by SerRGG. (b) Red splines correspond to edges that are invalid, whereas gray splines are unknown (c) Final edge classification produced by SerRGG, where red edges are invalid, gray edges remain unknown, and green edges are valid.
• Figure 4: Gray objects denote static obstacles while light blue objects denote dynamic obstacles. (a) The region of the spatial grid affected by the obstacle's motion is highlighted in orange. (b) Roadmap edges associated with these grid cells are highlighted in orange and processed by SerRGG. (c) Final edge classification produced by SerRGG, where ref edges are invalid, gray edges remain unknown, and green edges are valid.