Abstract: This paper addresses path set planning that yields important applications in robot manipulation and navigation such as path generation for deformable object keypoints and swarms. A path set refers to the collection of finite agent paths to represent the overall spatial path of a group of keypoints or a swarm, whose collective properties meet spatial and topological constraints. As opposed to planning a single path, simultaneously planning multiple paths with constraints poses nontrivial challenges in complex environments. This paper presents a systematic planning pipeline for homotopic path sets, a widely applicable path set class in robotics. An extended visibility check condition is first proposed to attain a sparse passage distribution amidst dense obstacles. Passage-aware optimal path planning compatible with sampling-based planners is then designed for single path planning with adjustable costs. Large accessible free space for path set accommodation can be achieved by the planned path while having a sufficiently short path length. After specifying the homotopic properties of path sets, path set generation based on deformable path transfer is proposed in an efficient centralized manner. The effectiveness of these methods is validated by extensive simulated and experimental results.
