Geometric path following with ocean current estimation for ASVs and AUVs

A control strategy for path following of linear paths for under-actuated autonomous surface vessels (ASVs) and autonomous underwater vehicles (AUVs) is presented. We consider the case in which an unknown ocean current is affecting the system. We adopt a Luenberger observer to estimate the current. The desired orientation of the vehicles is assigned using a rotation matrix, and this is defined using the estimated vector of the ocean current and a vector containing the cross track error. Since the desired orientation is given in the form of a rotation matrix, an attitude error function defined on the SO(2) group is used in order to define an orientation error. The desired surge velocity is defined based on the ocean current estimate in order to counteract the current and keep a desired along-path velocity (speed over ground). Based on a mathematical model describing both the kinematics and dynamics of the vehicles, and using cascaded systems theory, almost semi-global asymptotic stability (almost-SGAS) is proven. Simulation results are included that validate the theoretical result.