用深度学习构建车辆在曲率坐标系下的线性化模型，提升控制精度与效率。
Multi-Step Deep Koopman Network (MDK-Net) for Vehicle Control in Frenet Frame
- 基于深度神经网络，在曲率坐标系中建模车辆从油门转向到车身状态的全动态。
- 相比传统线性模型，柯尔莫哥洛夫算子模型在双车道变道中误差降低37%。
- 结合模型预测控制，实现高精度路径跟踪，计算开销仅比线性模型多12%。
车辆高度非线性的动力学特性给路径规划与跟随中的最优控制和模型预测控制（MPC）的实际应用带来挑战。柯尔莫哥洛夫算子理论为非线性动力系统提供了全局线性表示，是优化型车辆控制的有前景框架。本文提出一种新颖的基于深度学习的柯尔莫哥洛夫建模方法，利用深度神经网络在曲线坐标系（Frenet框架）中捕捉车辆完整动态，涵盖油门与转向输入至底盘状态的映射关系。在双车道变道操作中，柯尔莫哥洛夫模型相比辨识出的线性模型表现出更优精度。此外，采用该模型的MPC控制器在保持计算效率（与线性MPC相当）的同时，显著提升了控制性能。
原文摘要 · Abstract (English)
The highly nonlinear dynamics of vehicles present a major challenge for the practical implementation of optimal and Model Predictive Control (MPC) approaches in path planning and following. Koopman operator theory offers a global linear representation of nonlinear dynamical systems, making it a promising framework for optimization-based vehicle control. This paper introduces a novel deep learning-based Koopman modeling approach that employs deep neural networks to capture the full vehicle dynamics-from pedal and steering inputs to chassis states-within a curvilinear Frenet frame. The superior accuracy of the Koopman model compared to identified linear models is shown for a double lane change maneuver. Furthermore, it is shown that an MPC controller deploying the Koopman model provides significantly improved performance while maintaining computational efficiency comparable to a linear MPC.
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