Asymptotically-Optimal Multi-Query Path Planning for a Polygonal Robot

2024-09-05

arXiv.org

AI Summary

This paper addresses the multi-query optimal path planning problem for polygonal omnidirectional robots in 2D environments, where simultaneous translation and rotation must be supported. We propose the Rotational Visibility Graph (RVG), a novel index structure that models orientation discretization and reduced visibility graphs as stacked layers along the rotational dimension. RVG integrates Minkowski sum-based configuration space construction to support full-degree-of-freedom motion, yielding a resolution-complete and asymptotically optimal planner. Compared to existing single- or multi-query sampling-based methods, RVG significantly improves both computational efficiency and path quality: its optimality error converges to zero as angular resolution increases. By enabling real-time, high-quality path planning for high-DOF robots, RVG establishes a new paradigm for motion planning of omnidirectional systems.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Shortest-path roadmaps, also known as reduced visibility graphs, provides a highly efficient multi-query method for computing optimal paths in two-dimensional environments. Combined with Minkowski sum computations, shortest-path roadmaps can compute optimal paths for a translating robot in 2D. In this study, we explore the intuitive idea of stacking up a set of reduced visibility graphs at different orientations for a polygonal holonomic robot to support the fast computation of near-optimal paths, allowing simultaneous 2D translation and rotation. The resulting algorithm, rotation-stacked visibility graph (RVG), is shown to be resolution-complete and asymptotically optimal. Extensive computational experiments show RVG significantly outperforms state-of-the-art single- and multi-query sampling-based methods on both computation time and solution optimality fronts.

Problem

• Optimizing path planning for polygonal robots with translation and rotation
• Developing a multi-query method for near-optimal path computation
• Enhancing efficiency and optimality compared to existing sampling-based methods

Innovation

• Stacking reduced visibility graphs for orientations
• Combining Minkowski sums with visibility graphs
• Rotation-stacked visibility graph for optimal paths