PathCover: A Fast Convex Decomposition along a Path via Randomized Iterative Space Partitioning (RISP) on Point Clouds

2026-08-06

AI Summary

This work addresses the computational bottleneck in real-time obstacle-free region generation for autonomous robot navigation by introducing PathCover, a framework that constructs continuous, overlapping, and collision-free convex polyhedral corridors directly from point cloud data along a reference path. Built upon a Random Iterative Space Partitioning (RISP) algorithm, PathCover enables efficient downstream model predictive control (MPC) and trajectory optimization. It achieves the first convex decomposition method with expected linear time complexity, guaranteeing finite-step termination and progressive path advancement to meet the real-time demands of LiDAR sensor rates. Experiments demonstrate that PathCover accelerates corridor construction by an order of magnitude over state-of-the-art methods on both synthetic and real LiDAR datasets while preserving comparable corridor volume, with validation in quadrotor simulations and physical quadruped robot deployments.

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.

Problem

• autonomous robot navigation
• obstacle-free corridor generation
• real-time computation
• point cloud processing
• trajectory planning

Innovation

• Randomized Iterative Space Partitioning
• Convex Decomposition
• Point Cloud Processing
• Real-time Corridor Generation
• Autonomous Navigation