Over the past decades, autonomous driving technologies have garnered significant attention. In the realm of autonomous driving systems, pinpointing an accurate dynamical model for motion control presents a formidable challenge, particularly due to the nonlinearity and inherent uncertainty associated with tire dynamics. In this paper, to address the challenges of designing efficient control strategies for vehicle nonlinear systems with an accurate tire force model, we propose a novel data-driven vehicle modelling approach that comprehensively encapsulates the characteristics of tire dynamics based on Koopman operator. The primary benefit of employing the Koopman operator lies in its ability to represent the nonlinear dynamics within a linear lifted feature space. In the proposed methodology, a neural network based tire force estimation method is considered to derive the precise behaviours of this force under various road conditions. The tire force is formulated as a part of the Koopman model in the lifted space, which is defined as the Koopman-f model. A data-based extended dynamic mode decomposition methodology is introduced to derive a finite-dimensional representation of the Koopman operator. Building upon the aforementioned Koopman-f model, a model predictive controller is developed for trajectory tracking control. Simulation results conducted within the CarSim environment demonstrate that our approach achieves superior identification and trajectory tracking performance with greater accuracy compared to traditional Koopman model-based methods.
Fang et al. (2025) studied this question.