STAR-Filter: Efficient Convex Free-Space Approximation via Starshaped Set Filtering in Noisy Environments

TL;DR

The paper introduces STAR-Filter, a fast and robust convex free-space approximation method using starshaped sets, improving efficiency and noise robustness in robot planning amidst complex, noisy environments.

Contribution

It presents a novel starshaped set filtering approach that reduces computation and enhances robustness in convex free-space approximation for robot planning.

Findings

Achieves lowest computation time compared to existing methods.

Reduces conservativeness in polytope generation.

Effective for quadrotor planning in noisy environments.

Abstract

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.