Passage-traversing optimal path planning with sampling-based algorithms

TL;DR

This work introduces PTOPP, a novel path-planning paradigm that optimizes not just length but the traversed passages to maximize accessible free space along the path. It couples fast Gabriel-graph–based passage detection with Gabriel-cell decomposition to produce sparse, informative representations that enable efficient sampling-based planners (PRM$^*$, RRT$^*$, and variants) to optimize costs defined on passage traversals. The authors define several PTOPP categories (MPW-PTOPP, GPW-PTOPP, CPW-PTOPP) with carefully designed, compatible cost forms that guarantee monotonicity and order-preservation under path concatenation, ensuring asymptotic optimality. Experimental results in 2D and 3D spaces demonstrate significant improvements in achievable free space and competitive planning efficiency relative to baseline methods, validating PTOPP as a general and practical framework for accessible free-space optimization and beyond.

Abstract

This paper introduces a new paradigm of optimal path planning, i.e., passage-traversing optimal path planning (PTOPP), that optimizes paths' traversed passages for specified optimization objectives. In particular, PTOPP is utilized to find the path with optimal accessible free space along its entire length, which represents a basic requirement for paths in robotics. As passages are places where free space shrinks and becomes constrained, the core idea is to leverage the path's passage traversal status to characterize its accessible free space comprehensively. To this end, a novel passage detection and free space decomposition method using proximity graphs is proposed, enabling fast detection of sparse but informative passages and environment decompositions. Based on this preprocessing, optimal path planning with accessible free space objectives or constraints is formulated as PTOPP problems compatible with sampling-based optimal planners. Then, sampling-based algorithms for PTOPP, including their dependent primitive procedures, are developed leveraging partitioned environments for fast passage traversal check. All these methods are implemented and thoroughly tested for effectiveness and efficiency validation. Compared to existing approaches, such as clearance-based methods, PTOPP demonstrates significant advantages in configurability, solution optimality, and efficiency, addressing prior limitations and incapabilities. It is believed to provide an efficient and versatile solution to accessible free space optimization over conventional avenues and more generally, to a broad class of path planning problems that can be formulated as PTOPP.

Figures (20)

• Figure 1: Example of dense passage distributions (orange segments) using the pure visibility condition in a laboratory for drone swarm flight, e.g., mao2024optimal.
• Figure 2: Passage regions between obstacles. Blue dashed segments are convex hull sides of obstacles. Passages as obstacles' common projection shadow volume in the distance direction are in orange, which are not sensitive to obstacle size differences.
• Figure 3: Gabriel condition in passage detection exemplified with mobile robots. Due to intersections between $\mathcal{R}_{1,4}$ and $\mathcal{O}_3$, $\mathcal{O}_6$, $\mathcal{P}_{1-4}$ is not identified as a valid passage.
• Figure 4: Illustration of spatial passages in 3D space comprising only three obstacles. The passage between two tall obstacles has a valid height range starting at the lower obstacle.
• Figure 5: Due to obstacle sizes, the Gabriel graph constructed from obstacle centroids may miss some passages defined by (\ref{['Eqn: Amended Gabriel Condition']}). While $(\mathbf{c}_1, \mathbf{c}_8)$ is not an edge of $\mathcal{DG}(C_c)$ above, $\mathcal{P}_{1-8}$ is a valid passage above.