Geometry of Radial Basis Neural Networks for Safety Biased Approximation of Unsafe Regions
Geometry of Radial Basis Neural Networks for Safety Biased Approximation of Unsafe Regions
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DOI：
10.23919/acc55779.2023.10156278
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发表时间：
2022-10
期刊：
影响因子：
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通讯作者：
Ahmad Abuaish;Mohit Srinivasan;P. Vela
中科院分区：
文献类型：
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作者：
Ahmad Abuaish;Mohit Srinivasan;P. Vela
基于障碍函数的不等式约束是一种手段，以加强控制系统的安全规格。当与凸优化程序结合使用时，它们提供了一种计算效率高的方法来加强一般类控制仿射系统的安全性。采用这种方法时的主要假设之一是障碍函数本身的先验知识，即，安全设置的知识。在导航通过未知的环境中，局部安全集随时间而演变，这样的知识是不存在的。这篇手稿的重点是基于安全和不安全的样本测量来合成表征安全集的归零屏障函数，例如，从导航应用中的感知数据。先前的工作制定了一个监督机器学习算法，其解决方案保证了具有特定水平集属性的零障碍函数的构建。然而，它没有探索用于合成过程的神经网络设计的几何形状。这篇手稿描述了用于归零障碍函数合成的神经网络的具体几何形状，并展示了网络如何提供必要的表示将状态空间分裂为安全和不安全区域。
Barrier function-based inequality constraints are a means to enforce safety specifications for control systems. When used in conjunction with a convex optimization program, they provide a computationally efficient method to enforce safety for the general class of control-affine systems. One of the main assumptions when taking this approach is the a priori knowledge of the barrier function itself, i.e., knowledge of the safe set. In the context of navigation through unknown environments where the locally safe set evolves with time, such knowledge does not exist. This manuscript focuses on the synthesis of a zeroing barrier function characterizing the safe set based on safe and unsafe sample measurements, e.g., from perception data in navigation applications. Prior work formulated a supervised machine learning algorithm whose solution guaranteed the construction of a zeroing barrier function with specific level-set properties. However, it did not explore the geometry of the neural network design used for the synthesis process. This manuscript describes the specific geometry of the neural network used for zeroing barrier function synthesis, and shows how the network provides the necessary representation for splitting the state space into safe and unsafe regions.