Automatic bottom-following for underwater robotic vehicles

In this note we propose a solution for the automatic bottom-following problem for a low cost autonomous underwater vehicle. We consider the case that the seabed profile is not known in advance, and we show that it is possible to solve the bottom-following using only one echo sounder and without the need to measure the vertical velocity component (heave velocity). To this effect, we propose an output feedback controller that is obtained by first re-formulating the bottom-following into a trajectory tracking problem, then constructing a reference signal generator (the exo-system) using Fourier series theory, and finally solving the control design problem in the framework of nonlinear output regulation theory. An interesting feature of this approach is that the combination of the Fourier series with output regulation problem allows to bypass the need to compute explicitly the Fourier coefficients. To obtain an approximate solution of the resulting regulator equations we resort to pseudo-spectral methods. Stability analysis that takes explicitly into account the effects of the inner-loop autopilots, disturbances, and measurement noise is presented. Simulation results with real seabed data show the effectiveness of the proposed controller.