Adaptive Hand Position for Underactuated Underwater Vehicles

The hand position is a virtual point on a vehicle, located at a specific distance in front of its center of mass. This concept is a simple yet effective method that can be used for the stabilization and control of a wide range of systems, including nonholonomic vehicles (e.g., differential drive robots) and underactuated vehicles (e.g., certain types of autonomous surface and underwater vehicles). In previous works on underactuated vehicles, the hand position was fixed (i.e., constant). In this article, we introduce the concept of an adaptive (time-varying) hand position to underactuated underwater vehicles and demonstrate its effectiveness on the 3-D trajectory-tracking problem. To do so, we first define the transformation from the vehicle's coordinate system to the hand position coordinates. Then, we use the adaptive hand position concept to design a trajectory-tracking controller with saturations. We use Lyapunov methods to prove that the controller renders the system uniformly globally asymptotically stable. The theoretical results are verified in numerical simulations.