用物理信息神经网络解决控制屏障函数相对阶不稳问题
Addressing Relative Degree Issues in Control Barrier Function Synthesis with Physics-Informed Neural Networks
- 将控制屏障函数合成转化为边值问题求解
- 确保系统各状态区域相对阶恒定，避免控制失效
- 在无人机实验中验证了安全约束的有效性
在机器人领域，基于控制屏障函数（CBF）的安全滤波器常用于强制执行状态约束。当CBF的相对阶在状态空间中变化时，可能在安全集内出现控制输入无约束的区域。若作为安全滤波器实现，这可能导致靠近安全边界时产生抖振，最终威胁系统安全。为此，本文提出一种新方法：将CBF合成建模为一组边值问题的求解，并利用物理信息神经网络（PINNs）求解。该方法确保所合成的CBF在整个可允许状态集合中保持恒定相对度，从而防止控制无约束情形。我们在仿真中展示该方法，并通过真实四旋翼飞行器实验进一步验证其有效性，证明其能有效维持期望的系统安全特性。
原文摘要 · Abstract (English)
In robotics, control barrier function (CBF)-based safety filters are commonly used to enforce state constraints. A critical challenge arises when the relative degree of the CBF varies across the state space. This variability can create regions within the safe set where the control input becomes unconstrained. When implemented as a safety filter, this may result in chattering near the safety boundary and ultimately compromise system safety. To address this issue, we propose a novel approach for CBF synthesis by formulating it as solving a set of boundary value problems. The solutions to the boundary value problems are determined using physics-informed neural networks (PINNs). Our approach ensures that the synthesized CBFs maintain a constant relative degree across the set of admissible states, thereby preventing unconstrained control scenarios. We illustrate the approach in simulation and further verify it through real-world quadrotor experiments, demonstrating its effectiveness in preserving desired system safety properties.
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