Physics-informed Deep Mixture-of-Koopmans Vehicle Dynamics Model with Dual-branch Encoder for Distributed Electric-drive Trucks

Advanced autonomous driving systems require accurate vehicle dynamics modeling. However, identifying a precise dynamics model remains challenging due to strong nonlinearities and the coupled longitudinal and lateral dynamic characteristics. Previous research has employed physics-based analytical models or neural networks to construct vehicle dynamics representations. Nevertheless, these approaches often struggle to simultaneously achieve satisfactory performance in terms of system identification efficiency, modeling accuracy, and compatibility with linear control strategies. In this paper, we propose a fully data-driven dynamics modeling method tailored for complex distributed electric-drive trucks (DETs), leveraging Koopman operator theory to represent highly nonlinear dynamics in a lifted linear embedding space. To achieve high-precision modeling, we first propose a novel dual-branch encoder which encodes dynamic states and provides a powerful basis for the proposed Koopman-based methods entitled KODE. A physics-informed supervision mechanism, grounded in the geometric consistency of temporal vehicle motion, is incorporated into the training process to facilitate effective learning of both the encoder and the Koopman operator. Furthermore, to accommodate the diverse driving patterns of DETs, we extend the vanilla Koopman operator to a mixture-of-Koopman operator framework, enhancing modeling capability. Simulations conducted in a high-fidelity TruckSim environment and real-world experiments demonstrate that the proposed approach achieves state-of-the-art performance in long-term dynamics state estimation.

Residual Learning towards High-fidelity Vehicle Dynamics Modeling with Transformer

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.