Residual Learning towards High-fidelity Vehicle Dynamics Modeling with Transformer

Abstract: The vehicle dynamics model serves as a vital component of autonomous driving systems, as it describes the temporal changes in vehicle state. In a long period, researchers have made significant endeavors to accurately model vehicle dynamics. Traditional physics-based methods employ mathematical formulae to model vehicle dynamics, but they are unable to adequately describe complex vehicle systems due to the simplifications they entail. Recent advancements in deep learning-based methods have addressed this limitation by directly regressing vehicle dynamics. However, the performance and generalization capabilities still require further enhancement. In this letter, we address these problems by proposing a vehicle dynamics correction system that leverages deep neural networks to correct the state residuals of a physical model instead of directly estimating the states. This system greatly reduces the difficulty of network learning and thus improves the estimation accuracy of vehicle dynamics. Furthermore, we have developed a novel Transformer-based dynamics residual correction network, DyTR. This network implicitly represents state residuals as high-dimensional queries, and iteratively updates the estimated residuals by interacting with dynamics state features. The experiments in simulations demonstrate the proposed system works much better than physics model, and our proposed DyTR model achieves the best performances on dynamics state residual correction task, reducing the state prediction errors of a simple 3 DoF vehicle model by an average of 92.3% and 59.9% in two dataset, respectively.

• The paper proposes DyTR, a Transformer-based residual correction approach that significantly reduces prediction errors by up to 92.3% compared to baseline models.
• The method combines deep learning with physics-based models by using historical vehicle states and control signals to accurately forecast dynamics.
• Experimental results show that DyTR robustly generalizes across diverse driving conditions and vehicle configurations for reliable long-term predictions.

Introduction

The paper "Residual Learning towards High-fidelity Vehicle Dynamics Modeling with Transformer" (2502.11800) focuses on improving vehicle dynamics modeling, a critical aspect for autonomous driving (AD) technologies. Traditional physics-based models often fall short in capturing complex vehicular dynamics due to inherent simplifications. Although deep learning (DL) models can improve these estimations, they struggle with generalization and prediction accuracy in long-term scenarios. This work proposes a novel residual correction system utilizing a Transformer-based architecture, termed DyTR, that refines estimates made by physics-based models, resulting in significant improvements in prediction accuracy.

Methodology

Problem Formulation

Vehicle dynamics modeling aims to predict future states of vehicles accurately. The conventional approach involves physics-based models like the 3 DoF and 14 DoF models, which often lack precision due to simplifications. The paper introduces a novel Dynamic Residual Correction (DRC) framework which employs a deep neural network (DNN) to adjust the estimations of a base physical model rather than directly predicting the dynamics itself.

In particular, the base model calculates future states, which are then corrected by predicting residuals using historical data and vehicle configurations. The relationship between real and predicted dynamics is formalized as:

$\delta = s - \hat{s}$

where $s$ is the real state and $\hat{s}$ is the estimated state by the base model.

Data Generation

Due to the lack of extensive vehicle dynamics datasets, the authors used a co-simulation approach involving MATLAB and CarSim to generate real and estimated vehicle states across different scenarios. This dataset serves to train and evaluate the proposed DRC framework.

Figure 1: The diagram of data generation pipeline through co-simulation by MATLAB and CarSim.

DyTR Network Structure

The DyTR model enhances the Transformer architecture by incorporating a dynamics residual query system. This involves encoding a sequence of historical vehicle dynamics and control signals, which the Transformer processes to refine the estimated state:

Figure 2: The network structure of our proposed Transformer-based DRC model, DyTR. The model takes historical T-step states, T-step control signals, vehicle configurations, and estimated future states by the base model as input, and estimates the residuals of dynamics states.

• Feature Extraction: The model extracts dynamics features from control signals and estimated states, projecting them into high-dimensional spaces.
• Temporal Fusion: Temporal Transformer Encoder integrates these features while maintaining their temporal order.
• Residual Estimation: A Transformer Decoder iteratively updates a high-dimensional dynamics residual query, allowing the system to predict residuals with higher accuracy.

Experimental Results

The experiments extensively validate DyTR against both simple physical models and conventional DNN-based methods:

• Accuracy: DyTR significantly outperforms baseline models, reducing errors by up to 92.3% and 59.9% on different datasets. The 3 DoF and 14 DoF models typically depicted substantial errors in long-term predictions which DyTR effectively minimizes.
• Generalization: DyTR shows robust generalization across different driving conditions and vehicle configurations, which is a marked improvement over other hybrid models.

  Figure 3: A case of the state correction performance by DyTR on the val1 split.

Ablation Studies

Ablation studies highlight the importance of key parameters and architectural choices:

• Temporal Length: Optimal performance observed at a temporal length of 15, balancing information capture and model complexity.
• Transformer Layers: A depth of 2 layers in the Transformer modules was found to provide the best trade-off between accuracy and computational efficiency.
• Residual Query Design: Incorporating both the base model's predictions and vehicle configurations enhances the model's adaptability to varying conditions.

Conclusion

This research introduces a transformative approach to vehicle dynamics modeling through the DyTR network. By effectively utilizing a Transformer-based framework within a DRC scheme, this model provides high-fidelity state predictions essential for advanced AD functionalities. Future directions could explore further optimizations in network architectures and expand to real-world vehicular datasets to ensure seamless transitions from simulated environments to practical applications.