The trajectory of tethered underwater robot is usually controlled by actuating the rotating speeds of control propellers attached to the robot and/or adjusting the length of umbilical cable. When the trajectory control problem of a tethered underwater robot is studied, it is necessary to couple the main body of underwater robot, umbilical cable and control propellers together forming an integrated hydrodynamic model so that the robot is in a comprehensive dynamic equilibrium condition, suitable control algorithms are then jointed into the hydrodynamic model constructing a hydrodynamic and control model for the tethered underwater robot system. Only in this way the hydrodynamic and control nature of a tethered underwater robot during different kinds of control manipulations can be numerically revealed objectively.
In this paper, a hydrodynamic and control model to simulate the trajectory following control of a tethered underwater robot system is proposed, and the hydrodynamic performances of the robot and the umbilical cable are observed. To achieve this goal, three-dimensional hydrodynamic model of tethered underwater robot system is first introduced, feed-forward control technique for adjusting the length of umbilical cable and incremental PID algorithm for regulating the rotating speeds of propellers are then incorporated into the hydrodynamic model forming the hydrodynamic and control model. Based on the established hydrodynamic and control mode, relationships between the thrusts from the propellers and the rotating speeds of the propellers, and those among the trajectory following of the underwater robot and the control actions of adjusting the length of umbilical cable and governing the rotating speeds of the propellers are analyzed, and also the hydrodynamic performances of the tethered underwater robot system under the control manipulation are observed. In the research, the amplitude limit filtering method is applied in solving the governing equations of the umbilical cable, this technique is applied to avoid the chattering effect in the cable tension computation, so that a successive and stable computation process is maintained. The main factors affecting the singular nature of coefficient matrices during the numerical solutions of the proposed model are also investigated in the paper.