Homotopic Path Set Planning for Robot Manipulation and Navigation

TL;DR

This work tackles the challenge of planning spatial path sets for multiple agents in cluttered environments under homotopy constraints. It introduces an extended visibility-based passage detection to yield sparse passages and a passage-aware single-path planner with a tunable cost $f(\sigma) = Len(\sigma) - k_P f_P(\sigma)$, enabling flexible trade-offs between path length and available free space. Path sets are generated efficiently via a pivot-path transfer framework, including pivot planning, repositioning, and coordinated deformable transfer, ensuring strong homotopic-like coordination among all agents. The approach is validated through extensive simulations and real-world-like experiments in deformable-object manipulation and swarm navigation, demonstrating reduced computation, feasible coordination, and practical applicability in dense environments.

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.

Figures (19)

• Figure 1: Block diagram illustrating the overall workflow and main modules in the proposed path set planning pipeline. Blocks in the bottom row are the key components of corresponding modules.
• Figure 2: For simplicity, segments connecting obstacle side centers represent passages formed by two obstacles here. All passages pass the visibility check, but only black ones are useful in free space determination.
• Figure 3: $(\mathcal{E}_1, \mathcal{E}_4)$ will pass the original visibility check, but cannot pass the extended variant because both $\mathcal{E}_3$ and $\mathcal{E}_6$ intersect $\mathcal{R}_{1,3}$.
• Figure 4: In the left 2D case, DO point path 1 and 2 are not homotopic and thus infeasible. In the right 3D case, though path 1 and 2 are not strong path homotopic-like, the shown DO pose is feasible.
• Figure 5: In the shown passage, $\sigma_2$ is the pivot path. $\sigma_{t, 1}, \sigma_{t, 3}$ are transferred from $\sigma_2$ and both collide with obstacles. To tackle this, $\sigma_2$ is repositioned first. $\sigma_{t, 1}, \sigma_{t, 3}$ are then locally deformed.