  Motion control of underwater robotic vehicles is a demanding task with great
challenges imposed by external disturbances, model uncertainties and
constraints of the operating workspace. Thus, robust motion control is still an
open issue for the underwater robotics community. In that sense, this paper
addresses the tracking control problem or 3D trajectories for underactuated
underwater robotic vehicles operating in a constrained workspace including
obstacles. In particular, a robust Nonlinear Model Predictive Control (NMPC)
scheme is presented for the case of underactuated Autonomous Underwater
Vehicles (AUVs) (i.e., vehicles actuated only in surge, heave and yaw). The
purpose of the controller is to steer the underactuated AUV to a desired
trajectory with guaranteed input and state constraints within a partially known
and dynamic environment where the knowledge of the operating workspace is
constantly updated on-line via the vehicle's on-board sensors. In particular,
by considering a ball that covers the volume of the system, obstacle avoidance
with any of the detected obstacles is guaranteed, despite the model dynamic
uncertainties and the presence of external disturbances representing ocean
currents and waves. The proposed feedback control law consists of two parts: an
online law which is the result of a Finite Horizon Optimal Control Problem
(FHOCP) solved for the nominal dynamics; and a state feedback law which is
tuned off-line and guarantees that the real trajectories remain bound in a
hyper-tube centered along the nominal trajectories for all times. Finally, a
simulation study verifies the performance and efficiency of the proposed
approach.
