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

Jinyu Miao, Pu Zhang, Rujun Yan, Yifei He, Bowei Zhang, Zheng Fu, Ke Wang, Qi Song, Kun Jiang, Mengmeng Yang, Diange Yang

Abstract

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.

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

Abstract

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.
Paper Structure (22 sections, 28 equations, 7 figures, 8 tables)

This paper contains 22 sections, 28 equations, 7 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Physics-based Vehicle Dynamics Model
  4. Learning-based Vehicle Dynamics Model
  5. Koopman-based Vehicle Dynamics Model
  6. Methodology
  7. Problem Statement
  8. Preliminaries: Koopman Operator for Forced Systems
  9. KODE: Deep Koopman with Dual Branch Encoder
  10. Physics-informed Learning for Deep Koopman
  11. Mixture-of-Koopmans for Varying Driving Patterns
  12. Vehicle State Data Collection by Simulation
  13. Sim-to-Real Vehicle Adaptation
  14. Experiments
  15. Experimental Settings
  16. ...and 7 more sections

Figures (7)

  • Figure 1: A diagram of (a) physics-based dynamics model, (b) learning-based dynamics model, and (c) the proposed Koopman-based dynamics model KODE using a dual-branch encoder and MoK operator, respectively.
  • Figure 2: An overview of the proposed method. The dynamics states are encoded to dynamics embeddings through a dual-branch encoder. Specific Koopman operator is selected by given driving pattern. Then, the dynamics embeddings are linearly evolved and decoded to future dynamics states.
  • Figure 3: A diagram of feature interaction by Transformer encoder and feature aggregation by Transformer decoder, respectively.
  • Figure 4: A diagram of geometric consistency of the temporal vehicle motion.
  • Figure 5: A diagram of five driving patterns in this work.
  • ...and 2 more figures