Homotopy-Aware Corridor Generation without Predefined Reference Paths
Authors: Haoze Dong, Minghan Li, Meng Guo, Zhongkui Li
Abstract
Generating safe corridors is essential for collision-free robotic motion planning, yet most existing methods rely on predefined reference paths, which bias corridor geometry and implicitly limit the homotopy classes that can be explored. We propose a reference-path-free corridor generation framework on graphs of convex sets (GCS) that constructs corridors directly as sequences of convex sets, allowing corridor structure to emerge from the free-space representation rather than from a guiding path. To reason about similarity among corridors, we extend visibility-based deformation from paths to convex-set sequences, enabling the fusion of topologically redundant corridors while preserving distinct alternatives. To overcome the limited adaptability of existing GCS methods based on static global decompositions, we further develop an adaptive multi-scale GCS, in which a sampling-based fine-scale graph supports localized updates and a visibility-based coarse-scale graph enables compact global exploration. The two levels maintain topological consistency, allowing incremental updates without full graph reconstruction under environmental uncertainty. Numerical experiments characterize GCS construction, corridor generation, homotopy-aware exploration, and local updates, showing efficient graph construction, stable trajectory-level performance, and shorter-duration homotopy-aware trajectories than existing baselines. Hardware experiments on ground and aerial robots, including deployment with onboard localization, further validate the framework under translated and previously unknown obstacles.
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.
Kunal S. Narkhede, Abhijeet M. Kulkarni, Guoquan Huang +1
Convex free regions provide a structured and optimization-friendly representation of collision-free space for robot navigation in unknown and cluttered environments. However, existing methods typically enlarge local collision-free regions mainly according to surrounding obstacle geometry. In cluttered environments, such strategies may fail to generate regions that both accommodate robot geometry and preserve traversable extension along candidate motion directions, thereby limiting downstream traversal, especially in narrow passages. Even when such a region is available, safe motion generation remains challenging, because safety checking at discretized trajectory samples does not guarantee continuously collision-free motion when robot geometry is modeled explicitly. To address these issues, we propose a navigation framework that jointly incorporates candidate motion directions and robot geometry into convex free-region generation, and achieves continuously collision-free motion through continuous-safe trajectory generation. Within each region, the framework performs geometry-aware target pose selection and trajectory generation, together with Lipschitz-based continuous safety certification and local refinement. The resulting free regions and candidate motions are maintained in a region-based graph to support incremental planning. Quantitative results in cluttered 2D navigation scenarios show that the proposed method generates free regions better aligned with downstream traversal and enables reliable collision-free navigation, while additional 3D and real-world experiments on a quadrupedal robot and a UAV demonstrate the extensibility and practical applicability of the framework. The open-source project can be found at https://github.com/ZhichengSong6/FRGraph.
Spatiotemporal motion planning, especially in multi-robot settings, requires robots to reason about collision-free regions that change over time, which is challenging in continuous spaces when feasible regions are transient and geometrically constrained. We present an algorithmic framework based on graphs of space-time convex sets (ST-GCSs), where collision-free regions are represented as convex sets in space-time and trajectories correspond to paths on the graph together with continuous motions within the selected sets. We formulate time-optimal planning on ST-GCSs as a graph-search problem over path-indexed states and develop a best-first search solver that evaluates partial paths via continuous trajectory optimization, guided by admissible heuristics and dominance checks. We further present an Exact Convex Decomposition (ECD) scheme to reserve trajectory occupancies in space-time, enabling unified handling of dynamic obstacles and multi-robot interactions. For multi-robot motion planning, we integrate ST-GCS planning and ECD into prioritized planning methods and introduce a windowed coordination scheme to improve efficiency. Extensive experiments on single-robot and multi-robot problems demonstrate substantial speedups over various planners while maintaining high solution quality, particularly in environments with narrow and transient feasible regions. Large-scale demonstrations further show that the proposed multi-robot motion planner can solve instances with up to 100 robots within only a few minutes. Project homepage: https://sites.google.com/view/stgcs