SQ-CBF: Signed Distance Functions for Numerically Stable Superquadric-Based Safety Filtering

Haocheng Zhao, Lukas Brunke, Oliver Lagerquist, SiQi Zhou, Angela P. Schoellig

Keywords: Robot Safety, Collision Avoidance, Teleoperation

Abstract: Safety filters based on control barrier functions~(CBFs) provide an effective mechanism for enforcing collision avoidance in robot manipulation, but their performance critically depends on the underlying geometric representation of the environment. This work presents a geometry-aware safety filter that models robot and environment geometries using expressive superquadrics (SQs). Our approach yields a numerically stable, real-time-capable CBF safety filter, SQ-CBF, by leveraging signed–distance functions and deriving a closed-form gradient expression. Simulation and real-world experiments show that our proposed SQ-CBF achieves stable collision avoidance while improving teleoperation efficiency in highly constrained or dynamic scenes.

Submission Number: 6