通过优化超平面方向，实现更宽松的安全控制，提升动态系统避障性能。
Least Restrictive Hyperplane Control Barrier Functions
- 用可优化的超平面替代固定距离函数，构建更灵活的安全约束
- 在加速约束下对双积分系统测试，逼近障碍物时仍保持安全
- 适合高速运动、复杂障碍场景下的机器人控制应用
控制屏障函数（CBFs）能为动态系统提供可证明的安全保障。然而，对于计算资源有限、高阶动力学或靠近复杂形状障碍物的系统，寻找有效的CBF往往十分困难。常见方法是使用纯距离依赖的CBF。本文研究超平面型控制屏障函数（H-CBF），其中超平面将智能体与障碍物分离。首先指出，传统的距离基CBF是特定情况下的H-CBF——即超平面为障碍物的支撑超平面，且垂直于智能体与障碍物间的连线。随后，我们通过优化支撑超平面的方向，寻找最小限制的超平面CBF，从而在保证安全的前提下，允许更接近期望控制的动作，尤其在高速接近复杂障碍物时表现更优。实验在具有加速度约束的双积分系统上进行，该系统需穿越任意形状的静态和移动障碍物群，验证了方法的有效性。
原文摘要 · Abstract (English)
Control Barrier Functions (CBFs) can provide provable safety guarantees for dynamic systems. However, finding a valid CBF for a system of interest is often non-trivial, especially for systems having low computational resources, higher-order dynamics, and moving close to obstacles of complex shape. A common solution to this problem is to use a purely distance-based CBF. In this paper, we study Hyperplane CBFs (H-CBFs), where a hyperplane separates the agent from the obstacle. First, we note that the common distance-based CBF is a special case of an H-CBF where the hyperplane is a supporting hyperplane of the obstacle that is orthogonal to a line between the agent and the obstacle. Then we show that a less conservative CBF can be found by optimising over the orientation of the supporting hyperplane, in order to find the Least Restrictive Hyperplane CBF. This enables us to maintain the safety guarantees while allowing controls that are closer to the desired ones, especially when moving fast and passing close to obstacles. We illustrate the approach on a double integrator dynamical system with acceleration constraints, moving through a group of arbitrarily shaped static and moving obstacles.
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