Geometry-Aware Control Barrier Functions for Collision Avoidance via Bernstein Polynomial Approximations

Abstract:Safe navigation often relies on well-defined conditions based on the shape of robots and obstacles, and can be challenging when they have irregular geometries. While Control Barrier Functions (CBFs) offer an efficient mechanism to enforce safe set forward invariance, common shape surrogates (e.g., spheres or super-ellipsoids) are either overly conservative in unstructured scenes or require many local primitives, which inflates constraint counts and degrades real-time performance. In this paper, we introduce a novel geometry-aware Control Barrier Function (CBF) based on Bernstein-Polynomial Signed Distance Fields (BP-SDFs). It provides a unified way to represent the obstacles and robots, so as to represent the barrier function with a unified minimum distance. Benefiting from the differentiability of the Bernstein polynomials, one can easily enforce the control constraints in a closed loop. We validate the method's efficiency and performance to guarantee safety in single-robot navigation and heterogeneous multi-robot collision avoidance via simulations under different environments.

Accepted by 2026 IEEE International Conference on Robotics and Automation (ICRA 2026). Project page: this https URL

Robotics (cs.RO); Systems and Control (eess.SY)

arXiv:2605.30696 [cs.RO]

(or arXiv:2605.30696v2 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2605.30696 Focus to learn more arXiv-issued DOI via DataCite

2026 IEEE International Conference on Robotics and Automation (ICRA), pp. 10449-10456

https://doi.org/10.1109/ICRA57385.2026.11696181 Focus to learn more DOI(s) linking to related resources

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