Deep Neural Networks with Koopman Operators for Modeling and Control of Autonomous Vehicles

Abstract

Autonomous driving technologies have received notable attention in the past decades. In autonomous driving systems, identifying a precise dynamical model for motion control is nontrivial due to the strong nonlinearity and uncertainty in vehicle dynamics. Recent efforts have resorted to machine learning techniques for building vehicle dynamical models, but the generalization ability and interpretability of existing methods still need to be improved. In this paper, we propose a data-driven vehicle modeling approach based on deep neural networks with an interpretable Koopman operator. The main advantage of using the Koopman operator is to represent the nonlinear dynamics in a linear lifted feature space. In the proposed approach, a deep learning-based extended dynamic mode decomposition algorithm is presented to learn a finite-dimensional approximation of the Koopman operator. Furthermore, a data-driven model predictive controller with the learned Koopman model is designed for path tracking control of autonomous vehicles. Simulation results in a high-fidelity CarSim environment show that our approach exhibit a high modeling precision at a wide operating range and outperforms previously developed methods in terms of modeling performance. Path tracking tests of the autonomous vehicle are also performed in the CarSim environment and the results show the effectiveness of the proposed approach.

arXiv comment12 pages, 8 figures, 4 table, and 2 algorithms

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• Vehicular Applications of Koopman Operator Theory -- A Survey
• DDK: A Deep Koopman Approach for Dynamics Modeling and Trajectory Tracking of Autonomous Vehicles
• Self-tuning moving horizon estimation of nonlinear systems via physics-informed machine learning Koopman modeling
• Data-Driven Linear Koopman Embedding for Networked Systems: Model-Predictive Grid Control
• CKNet: A Convolutional Neural Network Based on Koopman Operator for Modeling Latent Dynamics from Pixels
• Mitigating Traffic Oscillations in Mixed Traffic Flow with Scalable Deep Koopman Predictive Control
• Multi-Step Deep Koopman Network (MDK-Net) for Vehicle Control in Frenet Frame
• Model predictive traction control system based on the Koopman operator
• Adaptive Deep Koopman Operator for Vehicle Dynamics Modeling: A Physics-Informed and Tire-Force-Driven Approach