SQ-CBF: スーパークワドリックの安全フィルタリングのための符号付き距離関数による数値的安定化
SQ-CBF: Signed Distance Functions for Numerically Stable Superquadric-Based Safety Filtering
スーパークワドリックの陰関数を直接使うと勾配が不安定になる問題を指摘し、符号付き距離関数をバリア候補として用いる安全フィルタリング手法を提案した。
詳しい要約
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著者: Haocheng Zhao, Lukas Brunke, Oliver Lagerquist, Siqi Zhou, Angela P. Schoellig
分類: cs.RO
原文アブストラクト
Ensuring safe robot operation in cluttered and dynamic environments remains a fundamental challenge. While control barrier functions provide an effective framework for real-time safety filtering, their performance critically depends on the underlying geometric representation, which is often simplified, leading to either overly conservative behavior or insufficient collision coverage. Superquadrics offer an expressive way to model complex shapes using a few primitives and are increasingly used for robot safety. To integrate this representation into collision avoidance, most existing approaches directly use their implicit functions as barrier candidates. However, we identify a critical but overlooked issue in this practice: the gradients of the implicit SQ function can become severely ill-conditioned, potentially rendering the optimization infeasible and undermining reliable real-time safety filtering. To address this issue, we formulate an SQ-based safety filtering framework that uses signed distance functions as barrier candidates. Since analytical SDFs are unavailable for general SQs, we compute distances using the efficient Gilbert-Johnson-Keerthi algorithm and obtain gradients via randomized smoothing. Extensive simulation and real-world experiments demonstrate consistent collision-free manipulation in cluttered and unstructured scenes, showing robustness to challenging geometries, sensing noise, and dynamic disturbances, while improving task efficiency in teleoperation tasks. These results highlight a pathway toward safety filters that remain precise and reliable under the geometric complexity of real-world environments.
