  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.
