Residual Koopman Model Predictive Control for Enhanced Vehicle Dynamics with Small On-Track Data Input

2025-07-24

AI Summary

To address the trade-off between model accuracy and computational efficiency in vehicle trajectory tracking—where conventional controllers (e.g., Pure Pursuit and MPC) struggle—this paper proposes a Residual Koopman Model Predictive Control (RKMPC) framework. RKMPC builds upon a physics-informed kinematic model, employs linear MPC (LMPC) for primary control generation, and augments it with a neural network that learns the residual of the Koopman operator to enable high-fidelity, low-data-dependent dynamic compensation. Innovatively, it adopts a bilinear MPC architecture, preserving model interpretability while enhancing real-time performance and robustness. Experimental results demonstrate that, compared to LMPC, RKMPC reduces lateral tracking error by 11.7–22.1%, heading error by 8.9–15.8%, and improves front-wheel steering stability by up to 27.6%. Moreover, it achieves these gains using only 20% of the training data required by standard Koopman MPC.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Planning with Language Models
• Machine Learning: Mixture of Experts (MoE)

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

In vehicle trajectory tracking tasks, the simplest approach is the Pure Pursuit (PP) Control. However, this single-point preview tracking strategy fails to consider vehicle model constraints, compromising driving safety. Model Predictive Control (MPC) as a widely adopted control method, optimizes control actions by incorporating mechanistic models and physical constraints. While its control performance critically depends on the accuracy of vehicle modeling. Traditional vehicle modeling approaches face inherent trade-offs between capturing nonlinear dynamics and maintaining computational efficiency, often resulting in reduced control performance. To address these challenges, this paper proposes Residual Koopman Model Predictive Control (RKMPC) framework. This method uses two linear MPC architecture to calculate control inputs: a Linear Model Predictive Control (LMPC) computes the baseline control input based on the vehicle kinematic model, and a neural network-based RKMPC calculates the compensation input. The final control command is obtained by adding these two components. This design preserves the reliability and interpretability of traditional mechanistic model while achieving performance optimization through residual modeling. This method has been validated on the Carsim-Matlab joint simulation platform and a physical 1:10 scale F1TENTH racing car. Experimental results show that RKMPC requires only 20% of the training data needed by traditional Koopman Model Predictive Control (KMPC) while delivering superior tracking performance. Compared to traditional LMPC, RKMPC reduces lateral error by 11.7%-22.1%, decreases heading error by 8.9%-15.8%, and improves front-wheel steering stability by up to 27.6%. The implementation code is available at: https://github.com/ZJU-DDRX/Residual Koopman.

Problem

• Enhances vehicle dynamics with minimal on-track data input
• Improves trajectory tracking accuracy over traditional MPC methods
• Balances computational efficiency and nonlinear dynamics modeling

Innovation

• Combines linear MPC with neural network compensation
• Uses residual modeling for performance optimization
• Requires minimal training data for superior tracking