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.

翻译：本文提出了一种新的最优路径规划范式，即通道穿越最优路径规划（PTOPP），该范式针对特定优化目标优化路径所穿越的通道。特别地，PTOPP用于寻找沿其全长具有最优可达自由空间的路径，这代表了机器人学中对路径的一项基本要求。由于通道是自由空间收缩并变得受限的区域，其核心思想是利用路径的通道穿越状态来全面表征其可达自由空间。为此，本文提出了一种基于邻近图的新型通道检测与自由空间分解方法，能够快速检测稀疏但信息丰富的通道并实现环境分解。基于此预处理，将具有可达自由空间目标或约束的最优路径规划表述为与基于采样的最优规划器兼容的PTOPP问题。随后，利用分区环境开发了用于PTOPP的基于采样算法及其依赖的基元过程，以实现快速的通道穿越检查。所有方法均经过实现，并进行了全面的有效性及效率验证。与现有方法（如基于间隙的方法）相比，PTOPP在可配置性、解的最优性和效率方面展现出显著优势，解决了先前的局限性与不足。该方法被认为为传统途径上的可达自由空间优化，以及更广泛地，为可表述为PTOPP的一大类路径规划问题，提供了一种高效且通用的解决方案。