OM-Koop: Online Memorable Koopman Operator Learning for Marine Robots Steering Dynamics

The steering dynamics of marine robots play a pivotal role in achieving precise maneuvering. However, complex and unpredictable ocean disturbances pose challenges for rapid online learning of accurate dynamics. This paper presents the Online Memory Koopman Learning (OM-Koop) framework, a hybrid model that combines physical priors, online data and stability preserving mechanisms to solve the nonlinear dynamic capture challenge and dynamically adapt to the marine environment. Firstly, we construct the Koopman operator-based uncertainty model online using the state error of the steering model and sliding window methods. The model can effectively capture the nonlinear features that are not represented in the predefined steering model. To ensure stability, the eigenvalues of the Koopman operator are constrained during online learning, guaranteeing Lyapunov stability. Secondly, in order to improve the efficiency of online learning, the Long Short-Term Memory (LSTM) neural network is involved in the construction process of the Koopman operator, which enhances the model’s memory capability. Finally, through field experiments using Autonomous Surface Vehicles (ASVs) and Autonomous Underwater Vehicles (AUVs) in field environments, comparative analyses with other learning strategies show that OM-Koop has excellent adaptability and robustness while guaranteeing Lyapunov stability. Note to Practitioners—The motivation of this article is that the steering dynamic behavior of marine robots is highly affected by unpredictable ocean environments, which poses great challenges in achieving precise manipulation in practical applications. In this paper, we propose the OM-Koop framework to address these challenges by integrating physical priors, online data learning, and stability preserving mechanisms. Theoretical analyses show that the proposed framework ensures Lyapunov stability while dynamically adapting to nonlinear disturbing forces imposed by the environment. Field experiments on AUV and ASV validate the robustness and adaptability of the framework, demonstrating its potential for practical deployment in dynamic marine environments. And the proposed framework has prospects for practical applications in other robotic systems.