Deep Bilinear Koopman Model for Real-Time Vehicle Control in Frenet Frame

2025-07-16

AI Summary

To address the challenges of nonlinear, strongly coupled dynamics modeling and real-time control for autonomous vehicles in the Frenet coordinate system, this paper proposes a deep bilinear Koopman model. The method employs a deep neural network to jointly learn the Koopman operator and its low-dimensional invariant subspace, while enforcing a convexity-preserving bilinear structure for input-state interactions. A multi-step prediction loss and a cumulative error regulation (CER) module are introduced to significantly improve long-horizon prediction accuracy and closed-loop tracking robustness. The resulting model enables embedded real-time model predictive control (MPC). Hardware-in-the-loop validation on the dSPACE SCALEXIO platform demonstrates a 32.7% reduction in trajectory tracking error compared to baseline controllers, confirming the model’s unified capability in high-fidelity dynamics representation, efficient prediction, and practical deployment.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Model-Based Reasoning
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

Abstract

Accurate modeling and control of autonomous vehicles remain a fundamental challenge due to the nonlinear and coupled nature of vehicle dynamics. While Koopman operator theory offers a framework for deploying powerful linear control techniques, learning a finite-dimensional invariant subspace for high-fidelity modeling continues to be an open problem. This paper presents a deep Koopman approach for modeling and control of vehicle dynamics within the curvilinear Frenet frame. The proposed framework uses a deep neural network architecture to simultaneously learn the Koopman operator and its associated invariant subspace from the data. Input-state bilinear interactions are captured by the algorithm while preserving convexity, which makes it suitable for real-time model predictive control (MPC) application. A multi-step prediction loss is utilized during training to ensure long-horizon prediction capability. To further enhance real-time trajectory tracking performance, the model is integrated with a cumulative error regulator (CER) module, which compensates for model mismatch by mitigating accumulated prediction errors. Closed-loop performance is evaluated through hardware-in-the-loop (HIL) experiments using a CarSim RT model as the target plant, with real-time validation conducted on a dSPACE SCALEXIO system. The proposed controller achieved significant reductions in tracking error relative to baseline controllers, confirming its suitability for real-time implementation in embedded autonomous vehicle systems.

Problem

• Model nonlinear vehicle dynamics in Frenet frame
• Learn Koopman operator for real-time control
• Enhance trajectory tracking with error compensation

Innovation

• Deep neural network learns Koopman operator
• Bilinear interactions preserve convexity for MPC
• CER module compensates for model mismatch