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

2026-04-29

AI Summary

In complex, noisy environments, traditional convex optimization methods are limited by their reliance on precise geometric models, sensitivity to initialization, and low computational efficiency. This work proposes STAR-Filter, a lightweight framework that, for the first time, leverages star-shaped sets to efficiently approximate collision-free convex free space. By identifying obstacle points as active support constraints, the method rapidly constructs a star-shaped set and generates an inflated convex polytope, substantially reducing redundant computation and conservatism. STAR-Filter enhances robustness to noise and computational efficiency while preserving safety guarantees, achieving the lowest runtime among competing approaches on real-world, large-scale noisy datasets. The framework has been successfully deployed for agile trajectory planning of quadrotor aerial vehicles.

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.

Problem

• free-space approximation
• convex representation
• sensor noise
• robot planning
• obstacle avoidance

Innovation

• starshaped set
• convex free-space approximation
• noise-robust planning
• efficient polytope generation
• Safe Flight Corridor