PathCover: A Fast Convex Decomposition along a Path via Randomized Iterative Space Partitioning (RISP) on Point Clouds
arXiv:2608.05586v1 Announce Type: new Abstract: Autonomous robot navigation requires the rapid generation of obstacle-free regions for trajectory planning. However, existing corridor generators struggle to meet real-time, sensor-rate computational constraints. To resolve this bottleneck, we introduce PathCover, a framework driven by RISP; a novel randomized algorithm that constructs convex polytopes directly from raw point cloud data in expected linear time under a mild probabilistic elimination condition. PathCover generates sequences of overlapping, obstacle-free polytopes that safely constrain downstream MPC and trajectory optimization. We mathematically guarantee that the algorithm terminates in finite steps while ensuring continuous progress along any obstacle-free reference path. Extensive benchmarks on synthetic and real-world LiDAR datasets demonstrate an order-of-magnitude speedup over state-of-the-art methods while maintaining comparable corridor volumes. The complete pipeline is validated via high-fidelity quadrotor simulations and physical deployment on a quadrupedal robot navigating constrained environments using live LiDAR perception.
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[Submitted on 6 Aug 2026]
Title:PathCover: A Fast Convex Decomposition along a Path via Randomized Iterative Space Partitioning (RISP) on Point Clouds
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Abstract:Autonomous robot navigation requires the rapid generation of obstacle-free regions for trajectory planning. However, existing corridor generators struggle to meet real-time, sensor-rate computational constraints. To resolve this bottleneck, we introduce PathCover, a framework driven by RISP; a novel randomized algorithm that constructs convex polytopes directly from raw point cloud data in expected linear time under a mild probabilistic elimination condition. PathCover generates sequences of overlapping, obstacle-free polytopes that safely constrain downstream MPC and trajectory optimization. We mathematically guarantee that the algorithm terminates in finite steps while ensuring continuous progress along any obstacle-free reference path. Extensive benchmarks on synthetic and real-world LiDAR datasets demonstrate an order-of-magnitude speedup over state-of-the-art methods while maintaining comparable corridor volumes. The complete pipeline is validated via high-fidelity quadrotor simulations and physical deployment on a quadrupedal robot navigating constrained environments using live LiDAR perception.
Comments: 13 pages, 5 figures
Subjects:
Robotics (cs.RO)
Cite as: arXiv:2608.05586 [cs.RO]
(or arXiv:2608.05586v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2608.05586
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Kunal Sanjay Narkhede [view email] [v1] Thu, 6 Aug 2026 04:17:13 UTC (4,770 KB)
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