Deep Koopman Operator-Informed Safety Command Governor for Autonomous Vehicles

Abstract: Modeling of nonlinear behaviors with physical-based models poses challenges. However, Koopman operator maps the original nonlinear system into an infinite-dimensional linear space to achieve global linearization of the nonlinear system through input and output data, which derives an absolute equivalent linear representation of the original state space. Due to the impossibility of implementing the infinite-dimensional Koopman operator, finite-dimensional kernel functions are selected as an approximation. Given its flexible structure and high accuracy, deep learning is initially employed to extract kernel functions from data and acquire a linear evolution dynamic of the autonomous vehicle in the lifted space. Additionally, the control barrier function (CBF) converts the state constraints to the constraints on the input to render safety property. Then, in terms of the lateral stability of the in-wheel motor driven vehicle, the CBF conditions are incorporated with the learned deep Koopman model. Because of the linear fashion of the deep Koopman model, the quadratic programming problem is formulated to generate the applied driving torque with minimal perturbation to the original driving torque as a safety command governor. In the end, to validate the fidelity of the deep Koopman model compared to other mainstream approaches and demonstrate the lateral improvement achieved by the proposed safety command governor, data collection and safety testing scenarios are conducted on a hardware-in-the-loop platform.