This study presents a novel framework for precise force control of fin-actuated underwater robots by integrating a deep neural network (DNN)-based surrogate model with reinforcement learning (RL). To address the complex interactions with the underwater environment and the high experimental costs, a DNN surrogate model acts as a simulator for enabling efficient training for the RL agent. Additionally, grid-switching control is applied to select optimized models for specific force reference ranges, improving control accuracy and stability. Experimental results show that the RL agent, trained in the surrogate simulation, generates complex thrust motions and achieves precise control of a real soft fin actuator. This approach provides an efficient control solution for fin-actuated robots in challenging underwater environments.

Deep-learning inverse techniques have attracted significant attention in recent years. Among them, the neural adjoint (NA) method, which employs a neural network surrogate simulator, has demonstrated impressive performance in the design tasks of artificial electromagnetic materials (AEM). However, the impact of the surrogate simulators' accuracy on the solutions in the NA method remains uncertain. Furthermore, achieving sufficient optimization becomes challenging in this method when the surrogate simulator is large, and computational resources are limited. Additionally, the behavior under constraints has not been studied, despite its importance from the engineering perspective. In this study, we investigated the impact of surrogate simulators' accuracy on the solutions and discovered that the more accurate the surrogate simulator is, the better the solutions become. We then developed an extension of the NA method, named Neural Lagrangian (NeuLag) method, capable of efficiently optimizing a sufficient number of solution candidates. We then demonstrated that the NeuLag method can find optimal solutions even when handling sufficient candidates is difficult due to the use of a large and accurate surrogate simulator. The resimulation errors of the NeuLag method were approximately 1/50 compared to previous methods for three AEM tasks. Finally, we performed optimization under constraint using NA and NeuLag, and confirmed their potential in optimization with soft or hard constraints. We believe our method holds potential in areas that require large and accurate surrogate simulators.