SPITE: Simple Polyhedral Intersection Techniques for modified Environments

TL;DR

SPITE addresses the challenge of motion planning in environments with discrete obstacle changes by converting a configuration-space roadmap into a dynamic data structure that uses 3D swept-volume approximations (cigars) and a hierarchical Cigar Tree to rapidly identify and revalidate affected nodes and edges. By discretizing configuration-space sweeps along roadmap edges and storing cigars in an AABB-like tree, SPITE achieves 10–40% faster update times and up to 60% faster motion-planning queries in modified environments, while reducing preprocessing time from hours to minutes. The approach is evaluated against a grid-based dynamic-roadmap method, LazyPRM, and RRT across mobile-robot and 5DOF manipulator scenarios, demonstrating its practical benefits for multi-query planning. The work notably reduces the computational burden of reusing roadmaps under workspace changes, enabling more responsive planning in settings like warehouses and human-robot collaboration, with future enhancements including oriented bounding boxes and lazy planning heuristics.

Abstract

Motion planning in modified environments is a challenging task, as it compounds the innate difficulty of the motion planning problem with a changing environment. This renders some algorithmic methods such as probabilistic roadmaps less viable, as nodes and edges may become invalid as a result of these changes. In this paper, we present a method of transforming any configuration space graph, such as a roadmap, to a dynamic data structure capable of updating the validity of its nodes and edges in response to discrete changes in obstacle positions. We use methods from computational geometry to compute 3D swept volume approximations of configuration space points and curves to achieve 10-40 percent faster updates and up to 60 percent faster motion planning queries than previous algorithms while requiring a significantly shorter pre-processing phase, requiring minutes instead of hours needed by the competing method to achieve somewhat similar update times.

Figures (5)

• Figure 1: An image of the 5DOF UR5e robot used in physical experiments to test the validity of paths produced in simulation. Shelf environments are likely to be modified as stored items are added, removed, or placed in new locations.
• Figure 2: A modified environment $E=\left\{B, \{o_1, o_2\}\right\}$ with an overlaid roadmap for a small robot with two translational DOFs and one rotational DOF. The valid and invalid nodes of the graph are depicted as configurations with black and white centered points respectively, and valid and invalid edges are depicted as full and dashed segments respectively. The obstacle $o_2$ moves from its first position seen in \ref{['fig:obstacle:move:before']} to a new one seen in \ref{['fig:obstacle:move:after']}, an event that changes the validity of several nodes and edges.
• Figure 3: In (a) we illustrate a set of configurations of a mobile manipulator with 2 translational DOFs and 3 angular joints composing an edge in some roadmap, and in (b) we see the point cloud and the cigar corresponding to the 3rd link of the robot. In (c) and (d) a similar process can be seen for a simple 3DOF planar robot.
• Figure 4: Different orientations of similar line segment obstacles (in blue) and their corresponding axis-aligned bounding boxes.
• Figure 5: An illustration of the environment used for the experiments described in Section \ref{['sec:motion:planning:experiments']}. Two configurations of the translational cube robot are seen in red. In every Iteration of the experiment each of the blue obstacles changed its position with probability $1/2$. Note that the bounding box is not illustrated for the sake of clarity.