Trajectory tracking control of two-joint underwater manipulator in ocean-wave environment

In this study, a dynamic model of a two-joint manipulator used in underwater robots considering the influence of ocean waves was derived based on the Lagrange principle and Newton–Euler method. The Morison equation was employed to calculate the inertial force and water resistance of ocean waves acting on the manipulator. The ocean force terms in the new model vary with time, which makes trajectory tracking control more complicated than in models used in land and still-water environments. The ideal trajectory of the manipulator was tracked using proportional-derivative (PD) control and sliding mode control (SMC). The PD control proved weak in trajectory tracking, whereas the sliding mode control could quickly and accurately track the ideal trajectory. Three reaching laws were compared, and variable exponential reaching law 2 was the most suitable for trajectory tracking. To test the sliding mode control ability, an experiment was conducted in an ocean-wave environment with varying ocean wave heights, wave frequencies, and water depths. In addition, variations in input torque were observed. It was also found that the input torque required in an ocean-wave environment was higher than that required in land and still-water environments.