Dynamic Modeling of Robotic Fish considering Background Flow using Koopman Operators

Dynamic model is essential for robust and reliable robotic fish motion control. Despite considerable efforts in robotic fish dynamic modeling, background flow has not been well considered yet, leading to the deterioration of applying robotic fish to practice. In this paper, we propose a novel dynamic model, termed Flow-Aware Robotic fish Model (FARM), that with well consideration to background flow using Koopman operators without increasing computation complexity. Specifically, we first collect motion data of the robotic fish in different background flow fields, and then obtain a linear approximation (the dynamic model) of nonlinear dynamics through carefully selected lifted functions. The obtained model can predict the next state based on the current state, control input, and average flow velocity of the local flow field. We evaluate the effectiveness of obtained model by comparing the Root Mean Square Error (RMSE) of predicted motion trajectories with real trajectories in various flow field environments. The results indicate that FARM is highly promising for obtaining a reliable dynamic model and can achieve comparable prediction accuracy even in unseen flow field environments with rough flow maps.