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

Shortest-path roadmaps, also known as reduced visibility graphs, provide 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 multiquery sampling-based methods on both computation time and solution optimality fronts. Source code and supplementary materials are available at https://github.com/arc-1/rvg.