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Optimizing AUV speed dynamics with a data-driven Koopman operator approach

Zhiliang Liu, Xin Zhao, Peng Cai, Bing Cong

TL;DR

This work tackles constrained speed control for autonomous underwater vehicles with nonlinear, multivariable dynamics by marrying data-driven Koopman operator theory with Model Predictive Control. By lifting nonlinear dynamics into a higher-dimensional space and identifying a finite-dimensional linear model via EDMD, the authors enable efficient, constraint-aware control that accounts for state, input, and incremental-input limits. The approach is implemented and validated through both MATLAB simulations and a ROS2-Gazebo platform, demonstrating accurate velocity prediction and robust reference tracking under actuator constraints. The results indicate that Koopman-based MPC can manage complex underwater dynamics while ensuring safe, practical operation, highlighting its potential for real-world AUV deployment and safer underwater exploration.

Abstract

Autonomous Underwater Vehicles (AUVs) play an essential role in modern ocean exploration, and their speed control systems are fundamental to their efficient operation. Like many other robotic systems, AUVs exhibit multivariable nonlinear dynamics and face various constraints, including state limitations, input constraints, and constraints on the increment input, making controller design challenging and requiring significant effort and time. This paper addresses these challenges by employing a data-driven Koopman operator theory combined with Model Predictive Control (MPC), which takes into account the aforementioned constraints. The proposed approach not only ensures the performance of the AUV under state and input limitations but also considers the variation in incremental input to prevent rapid and potentially damaging changes to the vehicle's operation. Additionally, we develop a platform based on ROS2 and Gazebo to validate the effectiveness of the proposed algorithms, providing new control strategies for underwater vehicles against the complex and dynamic nature of underwater environments.

Optimizing AUV speed dynamics with a data-driven Koopman operator approach

TL;DR

This work tackles constrained speed control for autonomous underwater vehicles with nonlinear, multivariable dynamics by marrying data-driven Koopman operator theory with Model Predictive Control. By lifting nonlinear dynamics into a higher-dimensional space and identifying a finite-dimensional linear model via EDMD, the authors enable efficient, constraint-aware control that accounts for state, input, and incremental-input limits. The approach is implemented and validated through both MATLAB simulations and a ROS2-Gazebo platform, demonstrating accurate velocity prediction and robust reference tracking under actuator constraints. The results indicate that Koopman-based MPC can manage complex underwater dynamics while ensuring safe, practical operation, highlighting its potential for real-world AUV deployment and safer underwater exploration.

Abstract

Autonomous Underwater Vehicles (AUVs) play an essential role in modern ocean exploration, and their speed control systems are fundamental to their efficient operation. Like many other robotic systems, AUVs exhibit multivariable nonlinear dynamics and face various constraints, including state limitations, input constraints, and constraints on the increment input, making controller design challenging and requiring significant effort and time. This paper addresses these challenges by employing a data-driven Koopman operator theory combined with Model Predictive Control (MPC), which takes into account the aforementioned constraints. The proposed approach not only ensures the performance of the AUV under state and input limitations but also considers the variation in incremental input to prevent rapid and potentially damaging changes to the vehicle's operation. Additionally, we develop a platform based on ROS2 and Gazebo to validate the effectiveness of the proposed algorithms, providing new control strategies for underwater vehicles against the complex and dynamic nature of underwater environments.

Paper Structure

This paper contains 18 sections, 26 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Problem formulation and preliminaries
  3. Velocity control model
  4. Koopman Operator Theory
  5. Dynamical System with Input
  6. Finding the estimated Koopman operator
  7. Koopman operator theory based MPC control
  8. MPC formulation
  9. Simulations and results
  10. Simulation in MATLAB
  11. Simulation in Gazebo
  12. Simulation platform
  13. Simulation Process
  14. Conclusion
  15. CRediT authorship contribution statement
  16. ...and 3 more sections

Figures (6)

  • Figure 1: Prediction comparison for different initial value
  • Figure 2: MPC control for the refering tracking
  • Figure 3: The input and input change rate signal
  • Figure 4: The simulated underwater vehicle and platform
  • Figure 5: The experiment process
  • ...and 1 more figures