用伯恩斯坦多项式实现更精准的机器人避障控制。
Geometry-Aware Control Barrier Functions for Collision Avoidance via Bernstein Polynomial Approximations
- 基于伯恩斯坦多项式构建几何感知的障碍物与机器人统一表示
- 通过最小距离统一定义屏障函数，提升避障安全性与实时性
- 适合复杂几何形状下的单/多机器人协同导航场景
安全导航常依赖于对机器人和障碍物形状的精确建模，但在不规则几何下难以实现。尽管控制屏障函数（CBFs）能高效保证安全集前向不变性，但常用的球体或超椭球等近似模型在非结构化场景中过于保守，或需大量局部基元，导致约束数量激增并影响实时性能。本文提出一种基于伯恩斯坦多项式符号距离场（BP-SDFs）的新几何感知控制屏障函数（CBF），统一表征障碍物与机器人，以统一最小距离定义屏障函数。得益于伯恩斯坦多项式的可微性，可轻松在闭环中施加控制约束。通过不同环境下的仿真验证，该方法在单机器人导航与异构多机器人避障中均有效保障了安全性。
原文摘要 · Abstract (English)
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.
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