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

2026-05-28

AI Summary

This work proposes a geometry-aware control barrier function (CBF) based on a Bernstein polynomial signed distance field (BP-SDF) to address the limitations of traditional safe navigation methods, which are often either overly conservative or computationally expensive when handling irregular geometric shapes. The approach leverages Bernstein polynomials for the first time to construct a differentiable, compact, and geometrically accurate signed distance field that uniformly represents both robot and obstacle geometries. By exploiting the differentiable minimum distance derived from this field, the method yields low-dimensional, closed-loop safety constraints. Experimental results demonstrate that the proposed framework efficiently ensures collision avoidance in both single-robot and heterogeneous multi-robot scenarios while maintaining strong real-time performance.

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) either are 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.

Problem

• Collision Avoidance
• Irregular Geometries
• Control Barrier Functions
• Signed Distance Fields
• Robot Navigation

Innovation

• Control Barrier Functions
• Bernstein Polynomials
• Signed Distance Fields
• Collision Avoidance
• Geometry-Aware Navigation