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.

翻译：近似无碰撞空间是复杂环境中机器人规划的基础。由于凸几何表示（如多面体和椭球体）的结构特性可便捷地与凸优化结合，因此被广泛采用。基于迭代优化的膨胀方法能在杂乱环境中生成大体积多面体，但其效率会随障碍物集复杂度增加或传感器数据含噪声而下降。此类方法对初始化敏感，且通常依赖精确的几何模型。本文提出轻量级框架STAR-Filter，通过星形集构建作为快速滤波器，实现无碰撞空间中凸区域的生成。通过将障碍点识别为主动支撑约束，该方法在保持可行性和对传感器噪声鲁棒性的同时，显著减少了冗余计算。我们通过理论与数值分析，表征了不同复杂度环境下星形集及所提流水线的结构特性。仿真结果表明，所提框架在真实噪声与大尺度数据处理中，实现了最低计算耗时并降低了多面体生成的保守性。我们进一步验证了该框架在噪声环境下安全飞行走廊生成与敏捷四旋翼规划中的有效性。