# Position Tracking Control of 4-DOF Underwater Robot Leg Using Deep Learning
## 1 Introduction  
In recent years, research and development of legged robots has made remarkable progress, demonstrating outstanding motion control performance even in complex environments with irregular terrain and various obstacles [1, 2, 3, 4, 5]. Some have even performed advanced motion control capabilities in challenging activities, such as parkour [6]. However, these developments have been primarily limited to field environments, with relatively slow progress observed in the development of Underwater Legged Robots (ULRs). Until now, most underwater robots have been designed as submarine-shaped Remotely Operated Vehicles (ROVs), commonly moving through water using propellers [7, 8, 9]. In many cases, underwater tasks are carried out on surfaces such as the seafloor. However, the bodies of submarine-shaped ROVs, floating in the fluid can be pushed and experience oscillations when encountering underwater currents, leading to a decrease in control performance. Moreover, they require high energy consumption to maintain the position and posture of the body. To address these limitations, there is a growing focus on the development of ULRs, designed to enhance static stability by making direct contact with the surfaces [10, 11]. Figure 1 illustrates the scenario concept of radial-type quadruped ULR under development. The robot attaches to the lower surface of the ship, walks on it, and removes entangled fishing nets from the propeller. This study specifically focused on the leg position control of this type of ULR. In dynamic walking control, achieving faster control of the robot's joints is crucial. However, in the case of underwater movement, the surrounding fluid directly affects the robot's motion. Buoyancy makes the robot float, while drag and added mass act like sandbags tethered to the robot. Furthermore, the robot's movement in the intended direction for control is impeded by the effects of lift and vortex. While these hydrodynamic effects are relatively simple to calculate in a static state, performing complex motion controls such as walking poses significant challenges due to their non-linearity and complexity. However, considering these factors is essential to enhance the motion control performance of ULRs [12]. In general, robot position tracking control involves adjusting the torque output of the joints. However, if the control methods designed for robots operating in the air are applied underwater without modification, the control performance, such as position accuracy, will be reduced due to the reasons mentioned above. In the case of a PD controller, a commonly used feedback control method, higher control gains are necessary to counteract the influence of the fluid and ensure higher position accuracy. However, this results in increased torque output in each joint, reducing compliance with disturbances. On the other hand, Computed Torque Control (CTC), a representative model-based control technique, typically utilizes the Newton-Euler method as a basis to reflect the dynamic characteristics of the robot and facilitate efficient calculation and control. However, in the process, the equation of motion must be exactly calculated, and the computation of the hydrodynamic effects during motion control is very challenging. In summary, the existing control methods designed for air environments are not suitable for application in underwater contexts. In this study, we propose the hybrid control method that combines a deep learning neural network, based on experimental data, with a task-space PD controller and evaluate its tracking performance. Dynamic characteristics are acquired through deep learning to simplify compensation for the effects of fluid during the position-tracking control of a quadruped walking robot. This process eliminates the need to individually calculate the fluid's dynamic characteristics, thereby reducing the computational complexity.