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

arXiv:2602.11049v2 Announce Type: replace Abstract: Ensuring safe robot operation in cluttered and dynamic environments remains a fundamental challenge. While control barrier functions (CBFs) 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 (SQs) offer an expressive way to model complex shapes using a few primitives and are increasingly used for robot safety. To integrate this representation into CBF, 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 safety filtering. To address this issue, we formulate an SQ-based safety filter that uses signed distance functions (SDFs) as barrier candidates. Since analytical SDFs are unavailable for general SQs, we compute the distance using the efficient Gilbert-Johnson-Keerthi algorithm and derive its gradient in closed form. Extensive simulation and real-world experiments demonstrate consistent collision-free manipulation in cluttered 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.

Abstract:Ensuring safe robot operation in cluttered and dynamic environments remains a fundamental challenge. While control barrier functions (CBFs) 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 (SQs) offer an expressive way to model complex shapes using a few primitives and are increasingly used for robot safety. To integrate this representation into CBF, 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 safety filtering. To address this issue, we formulate an SQ-based safety filter that uses signed distance functions (SDFs) as barrier candidates. Since analytical SDFs are unavailable for general SQs, we compute the distance using the efficient Gilbert-Johnson-Keerthi algorithm and derive its gradient in closed form. Extensive simulation and real-world experiments demonstrate consistent collision-free manipulation in cluttered 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.

Robotics (cs.RO)

arXiv:2602.11049 [cs.RO]

(or arXiv:2602.11049v2 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2602.11049 Focus to learn more arXiv-issued DOI via DataCite

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

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