Gaussian Control Barrier Functions: Non-Parametric Paradigm to Safety
Gaussian Control Barrier Functions: Non-Parametric Paradigm to Safety
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DOI：
10.1109/access.2022.3206372
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发表时间：
2022-03
期刊：
影响因子：
3.9
通讯作者：
Mouhyemen Khan;Tatsuya Ibuki;Abhijit Chatterjee
中科院分区：
文献类型：
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作者：
Mouhyemen Khan;Tatsuya Ibuki;Abhijit Chatterjee
受控制屏障函数(CBF)在解决安全性问题上的成功以及数据驱动功能建模技术的兴起的启发，我们提出了一种基于高斯过程(GP)的CBF在线综合的非参数方法。如果一个动力系统的状态的一个子集保持在规定的集合内，也称为安全集合，则该动力系统被定义为安全的。CBF通过先验地设计候选函数来实现安全性。然而，设计这样的函数可能是具有挑战性的。考虑在需要确定安全和可航行区域的灾难恢复场景中设计CBF。这里的安全决策边界是未知的，不能先验地设计。此外，CBF采用了参数设计方法，在实践中无法处理对外管局设置的任意更改。在我们的方法中，我们与安全样本合作，通过假设这些样本上的灵活GP先验来在线构建CBF，并将我们的公式称为高斯CBF。GPS具有良好的分析处理能力和稳健的不确定性估计能力。这允许实现具有高安全性保证的后验，同时还可以解析地计算相关的偏导数以实现安全控制。此外，高斯CBF可以根据采样数据任意改变安全集，从而允许非凸安全集。我们在四旋翼上进行了实验验证，展示了1)任意安全集的安全控制，2)在线安全集合成的碰撞避免，3)并置高斯CBF和存在噪声状态下的CBF。实验视频链接为：https://youtu.be/HX6uokvCiGk.
Inspired by the success of control barrier functions (CBFs) in addressing safety, and the rise of data-driven techniques for modeling functions, we propose a non-parametric approach for online synthesis of CBFs using Gaussian Processes (GPs). A dynamical system is defined to be safe if a subset of its states remains within the prescribed set, also called the safe set. CBFs achieve safety by designing a candidate function a priori. However, designing such a function can be challenging. Consider designing a CBF in a disaster recovery scenario where safe and navigable regions need to be determined. The decision boundary for safety here is unknown and cannot be designed a priori. Moreover, CBFs employ a parametric design approach and cannot handle arbitrary changes to the safe set in practice. In our approach, we work with safety samples to construct the CBF online by assuming a flexible GP prior on these samples, and term our formulation as a Gaussian CBF. GPs have favorable properties such as analytical tractability and robust uncertainty estimation. This allows realizing the posterior with high safety guarantees while also computing associated partial derivatives analytically for safe control. Moreover, Gaussian CBFs can change the safe set arbitrarily based on sampled data, thus allowing non-convex safe sets. We validated experimentally on a quadrotor by demonstrating safe control for 1) arbitrary safe sets, 2) collision avoidance with online safe set synthesis, 3) and juxtaposed Gaussian CBFs with CBFs in the presence of noisy states. The experiment video link is: https://youtu.be/HX6uokvCiGk.