Investigations on the Hybrid Tracking Control of an Underactuated Autonomous Underwater Robot

Abstract

The problem of trajectory tracking control of an underactuated autonomous underwater robot (AUR) in a three-dimensional (3-D) space is investigated in this paper. The control of an underactuated robot is different from fully actuated robots in many aspects. In particular, these robot systems do not satisfy Brockett's necessary condition for feedback stabilization and no continuous time-invariant state feedback control law exists that makes a specified equilibrium of the closed-loop system asymptotically stable. The uncertainty of hydrodynamic parameters, along with the coupled, nonlinear dynamics of the underwater robot, also makes the navigation and tracking control a difficult task. The proposed hybrid control law is developed by combining sliding mode control (SMC) and classical proportional–integral–derivative (PID) control methods to reduce the tracking errors arising out of disturbances, as well as variations in vehicle parameters like buoyancy. Here, a trajectory planner computes the body-fixed linear and angular velocities, as well as vehicle orientations corresponding to a given 3-D inertial trajectory, which yields a feasible 6-d.o.f. trajectory. This trajectory is used to compute the control signals for the three available controllable inputs by the hybrid controller. A supervisory controller is used to switch between the SMC and PID control as per a predefined switching law. The switching function parameters are optimized using Taguchi design techniques. The effectiveness and performance of the proposed controller is investigated by comparing numerically with classical SMC and traditional linear control systems in the presence of disturbances. Numerical simulations using the full set of nonlinear equations of motion show that the controller does quite well in dealing with the plant nonlinearity and parameter uncertainties for trajectory tracking. The proposed controller response shows less tracking error without the usually present control chattering. Some practical features of this control law are also discussed.