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

2026-02-11

AI Summary

This work addresses the failure of safety filtering in complex dynamic environments when using superquadric-based control barrier functions, which often arises from ill-conditioned gradients of implicit functions. To overcome this limitation, the authors propose a novel safety filtering framework that, for the first time, incorporates signed distance functions as barrier candidates in place of conventional implicit representations for superquadrics. The approach leverages the Gilbert–Johnson–Keerthi (GJK) algorithm to efficiently compute inter-object distances and employs stochastic smoothing to estimate gradients in a numerically stable manner. This enables real-time, robust obstacle avoidance even under challenging conditions such as complex geometries, sensor noise, and dynamic disturbances. Extensive simulations and real-world experiments demonstrate that the method effectively mitigates gradient ill-conditioning and significantly enhances both system safety and teleoperation efficiency.

Technology Category

• Natural Language Processing: Safety and Robustness
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• superquadrics
• control barrier functions
• signed distance functions
• safety filtering
• gradient ill-conditioning

Innovation

• Signed Distance Function
• Superquadric
• Control Barrier Function
• Randomized Smoothing
• GJK Algorithm