用高斯过程构建安全边界，让机器人自动避障。
Gaussian Process Implicit Surfaces as Control Barrier Functions for Safe Robot Navigation
- 用高斯过程隐式表示安全区域，从传感器数据中学习
- 后验方差提供可量化的安全裕度，避免碰撞
- 适合需要动态避障的机械臂和无人机场景
水平集方法是现代安全控制技术（如控制屏障函数）的基础，同时也用于通过距离场隐式表示几何形状。受这两个范式的启发，我们提出一个统一框架：将隐式表面本身作为控制屏障函数。利用高斯过程隐式表面（GPIS）表示安全边界，通过传感器测量获得的安全样本对高斯过程进行条件化。后验均值定义了安全表面（安全信念），后验方差提供了鲁棒的安全裕度。尽管高斯过程具备不确定性估计和解析可处理性等优点，但其计算复杂度随数据量呈立方增长。为此，我们提出一种稀疏解法，称为稀疏高斯屏障函数。据我们所知，此前尚未有研究明确使用GPIS来构造CBF。我们在两种场景下验证该方法：在模拟环境中，7自由度机械臂围绕斯坦福兔子模型避障；在真实环境中，四旋翼无人机在3D空间中绕实体椅子飞行。实验表明，无论是否采用稀疏化，高斯屏障函数均能实现安全交互与无碰撞轨迹执行，而这些轨迹若不加约束将与物体相交。
原文摘要 · Abstract (English)
Level set methods underpin modern safety techniques such as control barrier functions (CBFs), while also serving as implicit surface representations for geometric shapes via distance fields. Inspired by these two paradigms, we propose a unified framework where the implicit surface itself acts as a CBF. We leverage Gaussian process (GP) implicit surface (GPIS) to represent the safety boundaries, using safety samples which are derived from sensor measurements to condition the GP. The GP posterior mean defines the implicit safety surface (safety belief), while the posterior variance provides a robust safety margin. Although GPs have favorable properties such as uncertainty estimation and analytical tractability, they scale cubically with data. To alleviate this issue, we develop a sparse solution called sparse Gaussian CBFs. To the best of our knowledge, GPIS have not been explicitly used to synthesize CBFs. We validate the approach on collision avoidance tasks in two settings: a simulated 7-DOF manipulator operating around the Stanford bunny, and a quadrotor navigating in 3D around a physical chair. In both cases, Gaussian CBFs (with and without sparsity) enable safe interaction and collision-free execution of trajectories that would otherwise intersect the objects.
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