A three-dimensional hydrodynamic and control model to simulate tethered underwater robot system is proposed. The fluid motion around the moving robot main body with running control ducted propellers is governed by Navier-Stokes equations, and multiple sliding mesh technique is applied to solve the governing equations. The governing equation of umbilical cable connected to the robot is based on the Ablow and Schechter method. The six-degrees-of-freedom equations of motion for underwater vehicle simulations proposed by Gertler and Hargen are adopted to estimate the hydrodynamic performance of the underwater robot. In the model, the feed-forward control algorithm is applied to adjust the length of the umbilical cable according to the robot trajectory control target, the incremental PID control algorithm is adopt to regulate the rotating speeds of the ducted propellers producing appropriate thrusts for the robot control. With the proposed hydrodynamic and control model, hydrodynamic behaviors of the robot under definite trajectory control manipulations are observed numerically.
The numerical results of robot trajectory control simulations indicate that the feed-forward control algorithm for adjusting the length of the umbilical cable, and the incremental PID control algorithm for regulating the rotating speeds of the propellers are feasible and effective, the adjusting the length of the umbilical cable with feed-forward control technique is largely responsible for the vertical trajectory control to the robot, while regulating the rotating speeds of the propellers by the PID control algorithm play a leading role in the horizontal trajectory manipulation, the deviation between the designated trajectory and the control one at each time step is acceptable.