![]() ![]() Furthermore, it is demonstrated how this methodology can be utilized to forecast highway network conditions. By obtaining a decomposition of data sets collected by the Federal Highway Administration and the California Department of Transportation, we are able to reconstruct observed data, distinguish any growing or decaying patterns, and obtain a hierarchy of previously identified and never before identified spatiotemporal patterns. Here we demonstrate how the Koopman mode decomposition can offer a model-free, data-driven approach for analyzing and forecasting traffic dynamics. All the while, the ever-increasing demands on transportation systems has left traffic agencies in dire need of a robust method for analyzing and forecasting traffic. Therefore, it is difficult to develop a mathematical or artificial intelligence model that describes the time evolution of traffic systems. ![]() The unpredictable elements involved in a vehicular traffic system, like human interaction and weather, lead to a very complicated, high-dimensional, nonlinear dynamical system. Finally, we design a linear MPC with Deep EDMD (DE-MPC) for realizing reference tracking and test the controller in the CarSim environment. Also, the proposed approach outperforms the EDMD method, the multi-layer perception (MLP) method, and the Extreme Learning Machines-based EDMD (ELM-EDMD) method in terms of modeling performance. Simulation results in a high-fidelity CarSim environment are reported, which show the capability of the Deep EDMD approach in multi-step prediction of vehicle dynamics at a wide operating range. Different from other machine learning-based approaches, deep neural networks play the role of learning feature representations for EDMD in the framework of the Koopman operator. As the core contribution, we propose a deep learning-based extended dynamic mode decomposition (Deep EDMD) algorithm to learn a finite approximation of the Koopman operator. The approach results in a global model that integrates the dynamics in both longitudinal and lateral directions. The main idea is to use the Koopman operator for representing the nonlinear dynamics in a linear lifted feature space. In this paper, we propose a deep learning framework relying on an interpretable Koopman operator to build a data-driven predictor of the vehicle dynamics. Many efforts have resorted to machine learning techniques for building data-driven models, but it may suffer from interpretability and result in a complex nonlinear representation. However, it is nontrivial for identifying a global model of vehicle dynamics due to the existence of strong non-linearity and uncertainty. In autonomous driving systems, \textcolor information of vehicle dynamics is required in most cases for designing of motion planning and control algorithms. 'uav_collision_ge_exp.Autonomous vehicles and driving technologies have received notable attention in the past decades.'uav_collision_avoidance.m' executes a simple experiment where 2 UAVs avoid collision with each other.'uav_learning.m' generates training data and learns a model.These files are (all can be run separately by utilizing learned models that are stored in the repository): The 3 remaining scripts are concerned with learning an approximate Koopman operator for an UAV and simulating 2 different experiments utilizing the learned model. 'robotarium_collision_obstacle_avoidance.m' executes a simulated experiment at the Robotarium where 5 agents avoid collision with each other and a fixed obstacle.'robotarium_collision_avoidance.m' executes a simulated experiment at the Robotarium where 5 agents avoid collision with each other.'robotarium_obstacle_avoidance.m' executes a simulated experiment at the Robotarium where a single agent avoids a fixed obstacle.'dubin_learning.m' generates training data and learns a model.The first 4 scripts are concerned with learning an approximate Koopman operator for a Dubin's car model and then using the learned model to run experiments in the Georgia Tech Robotarium. This repository contains 7 main scripts that run different parts of experiments demonstrating the Koopman CBF framework. Code for collision avoidance experiments with CBFs synthesized using learned Koopman operators. ![]()
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