Geometry-Aware Control Barrier Functions for Collision Avoidance via Bernstein Polynomial Approximations
This work provides a less conservative and more efficient collision avoidance method for robots with irregular geometries, which is beneficial for real-time navigation in unstructured environments.
This paper addresses collision avoidance for robots with irregular geometries by introducing a novel geometry-aware Control Barrier Function (CBF) based on Bernstein-Polynomial Signed Distance Fields (BP-SDFs). This approach provides a unified representation for robots and obstacles, enabling a unified minimum distance representation for the barrier function and facilitating closed-loop control through the differentiability of Bernstein polynomials. The method's efficiency and performance in guaranteeing safety were validated in simulations for single-robot and heterogeneous multi-robot collision avoidance.
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.