R2: Optimal vector-based and any-angle 2D path planning with non-convex obstacles

A novel vector-based path planner, R2 (R in two dimensions), is introduced in this paper. R2 is optimal and online, returning any-angle paths by applying heuristic costs to vector-based searches. R2 delays line-of-sight checks to expand the most promising path that has the least detours from the start and goal points. As delayed checks can cause severe path cost underestimates, R2 infers the smallest known convex hull, the best hull, of obstacles while moving around them. To construct the best hull, phantom points are introduced, which are imaginary turning points lying on non-convex corners to guide future searches. Tracing rules are introduced to ensure that the estimated path cost from the best hull increases admissibly and monotonically between queues to the open-list. The distance between the start and goal points have little impact on R2's performance when compared to the number of line-of-sight checks that collide with obstacles. While having an exponential search time in the worst case with respect to the number of collided line-of-sight checks, R2 is much faster than state-of-the-art when the optimal path is expected to turn around few obstacles, especially on large maps with few disjoint and non-convex obstacles.