Approximating collision-free space is fundamental to robot planning in complex environments. Convex geometric representations, such as polytopes and ellipsoids, are widely employed due to their structural properties, which can be easily integrated with convex optimization. Iterative optimization-based inflation methods can generate large volume polytopes in cluttered environments, but their efficiency degrades as the obstacle set becomes more complex or when sensor data are noisy. These methods are also sensitive to initialization and often rely on accurate geometric models. In this paper, we propose the STAR-Filter, a lightweight framework that employs starshaped set construction as a fast filter for convex region generation in collision-free space. By identifying obstacle points as active supporting constraints, the proposed method significantly reduces redundant computation while preserving feasibility and robustness to sensor noise. We provide theoretical and numerical analyses that characterize the structural properties of the starshaped set and proposed pipeline in environments of varying complexity. Simulation results show that the proposed framework achieves the lowest computation time and reduces conservativeness in polytope generation for real-world noisy and large-scale data. We demonstrate the effectiveness of the framework for Safe Flight Corridor (SFC) generation and agile quadrotor planning in noisy environments.
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.
Autonomous robot navigation requires rapid construction of obstacle-points-separated convex regions for trajectory planning. When obstacles are represented as point clouds from LiDAR or depth cameras, these regions must be constructed directly from finite obstacle samples while providing suitable constraints for downstream optimization. However, existing corridor-generation methods often struggle to meet real-time, sensor-rate computational requirements. To address this bottleneck, we introduce RISP, a randomized algorithm that constructs convex polytopes from finite point-cloud data, and PathCover, which chains these polytopes along a reference path to form an overlapping corridor. We prove finite termination, sequential intersection, and complete path coverage with respect to the supplied finite point set. Under a probabilistic elimination condition, the sampling-and-elimination stage of RISP has expected O(n) time and unconditional worst-case O(n^2) time. Extensive benchmarks on synthetic and real-world LiDAR datasets demonstrate an order-of-magnitude speedup over state-of-the-art methods in both corridor generation as well as trajectory optimization, while closed-loop quadrotor simulation and a physical quadruped traversal demonstrate integration with downstream motion planners. These results establish corridor separation from the supplied point-cloud representation and practical implementation feasibility. Source code of the entire pipeline is available at https://github.com/kunalnk123690/PathCover.
Kunal S. Narkhede, Abhijeet M. Kulkarni, Guoquan Huang +1
Obstacle avoidance is essential for safe navigation and motion planning. Recent radiance field reconstruction methods enable object detection and modeling with high fidelity, but remain too memory- and compute-intensive for on-board perception-based path planning. To address these limitations, we propose PolyMerge to convert a large, photorealistic 3D Gaussian Splatting (3DGS) model of a scene into a lightweight representation of convex polytopes whose union provably over-approximates all obstacles in the original 3DGS model. PolyMerge tunes the polytope count to trade off conservativeness and compute cost, and integrates with control barrier functions (CBFs) to plan collision-free paths. We showcase PolyMerge in simulation and hardware experiments on a Crazyflie drone, which uses PolyMerge to compute and follow safe trajectories in real time under severe onboard compute constraints, outperforming baselines in speed while guaranteeing safety. For our code and videos, visit https://athlon76.github.io/PolyMerge-website/.
Jihoon Hong, Chih-Yuan Chiu, Sara Fridovich-Keil +1