DDK: A Deep Koopman Approach for Dynamics Modeling and Trajectory Tracking of Autonomous Vehicles

Autonomous driving has attracted lots of attention in recent years. An accurate vehicle dynamics is important for autonomous driving techniques, e.g. trajectory prediction, motion planning, and control of trajectory tracking. Although previous works have made some results, the strong nonlinearity, precision, and interpretability of dynamics for autonomous vehicles are open problems worth being studied. In this paper, the approach based on the Koopman operator named deep direct Koopman (DDK) is proposed to identify the model of the autonomous vehicle and the identified model is a linear time-invariant (LTI) version, which is convenient for motion planning and controller design. In the approach, the Koopman eigenvalues and system matrix are considered as trainable tensors with the original states of the autonomous vehicle being concatenated to a part of the Koopman eigenfunctions so that a physically interpretable subsystem can be extracted from the identified latent dynamics. Subsequently, the process of the identification model is trained under the proposed method based on the dataset which consists of about 60km of data collected with a real electric SUV while the effectiveness of the identified model is validated. Meanwhile, a high-fidelity vehicle dynamics is identified in CarSim with DDK, and then, a linear model predictive control (MPC) called DDK-MPC integrating DDK is designed to validate the performance for the control of trajectory tracking. Simulation results illustrate that the model of the nonlinear vehicle dynamics can be identified effectively via the proposed method and that excellent tracking performance can be obtained with the identified model under DDK-MPC.