Asymptotically-Optimal Multi-Query Path Planning for Moving A Convex Polygon in 2D

The classical shortest-path roadmaps, also known as reduced visibility graphs, provide a multi-query method for quickly 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 convex-shaped 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. RVG out-performs SOTA single-query sampling-based methods including BIT* and AIT* on both computation time and solution optimality fronts.