Trajectory Tracking Nonlinear Controller for Underactuated Underwater Vehicles Based on Velocity Transformation

Abstract

This paper proposes an algorithm that performs the task of tracking the desired trajectory for underactuated marine vehicles (primarily underwater) that move horizontally. The control scheme, which takes into account model inaccuracies and external disturbances, was designed using the quantities obtained after the transformation of the dynamic equations of motion resulting from the decomposition of the inertia matrix. This, in turn, led to the equation of dynamics with a diagonal inertia matrix. A specific feature of the offered controller is its dual role. It not only allows tracking the desired trajectory, but at the same time, makes it possible to estimate the impact of dynamic couplings when the vehicle is in motion. Such an approach to the tracking task is important at the initial design stage when the choice of the control algorithm has not yet been decided and experimental tests have not been performed. This is feasible because the new variables after the velocity transformation include not only vehicle parameters, but also actual velocities and forces. Therefore, it is also possible to track the original variables. The theoretical results were followed up with simulation tests conducted on a model with three degrees of freedom for two underwater vehicles.

Keywords

• underactuated marine vehicle in horizontal motion
• trajectory tracking
• backstepping
• integral sliding mode control
• robustness
• velocity transformation