Data-Driven Modeling of Automated Vehicles: Koopman Operator Approach and Its Application

Abstract

This paper presents a data-driven modeling method with the Koopman operator for automated vehicles. The lateral motion of a vehicle can be calculated using a linear motion model; however, owing to the complex interactions between the tires and road, a vehicle's lateral dynamics may have underlying nonlinear behaviors. Hence, it is necessary to model the full vehicle dynamics effectively as a linear framework. To this end, we adopt the Koopman operator to express the vehicle's nonlinear dynamics as a linear structure. The Koopman operator exists in the infinite-dimensional space, so we apply the extended dynamic mode decomposition approach to approximate the Koopman operator as a finite-dimensional operator. We used the CarSim simulator to calculate the complex vehicle motion, which has 27 degrees of freedom. The experimental results with the simulator show that the vehicle model based on the Koopman operator has a 0.07% model fitting error for a given dataset.