Multi-Step Deep Koopman Network (MDK-Net) for Vehicle Control in Frenet Frame

The highly nonlinear dynamics of vehicles present a major challenge for the practical implementation of optimal and Model Predictive Control (MPC) approaches in path planning and following. Koopman operator theory offers a global linear representation of nonlinear dynamical systems, making it a promising framework for optimization-based vehicle control. This paper introduces a novel deep learning-based Koopman modeling approach that employs deep neural networks to capture the full vehicle dynamics-from pedal and steering inputs to chassis states-within a curvilinear Frenet frame. The superior accuracy of the Koopman model compared to identified linear models is shown for a double lane change maneuver. Furthermore, it is shown that an MPC controller deploying the Koopman model provides significantly improved performance while maintaining computational efficiency comparable to a linear MPC.

@article{abtahi2025_2503.03002,
  title={ Multi-Step Deep Koopman Network (MDK-Net) for Vehicle Control in Frenet Frame },
  author={ Mohammad Abtahi and Mahdis Rabbani and Armin Abdolmohammadi and Shima Nazari },
  journal={arXiv preprint arXiv:2503.03002},
  year={ 2025 }
}