Global Directional Control of a Slender Autonomous Underwater Vehicle

C ONVENTIONAL streamlined autonomous underwater vehicles (AUVs) are underactuated by design. Typically, they include a propulsor and torque actuators, such as control planes. In this Note, it is assumed that the 6 degrees of freedom vehicle is actuated in 4 degrees of freedom: surge, roll, pitch, and yaw. The control objective is to globally asymptotically stabilize longitudinalaxis translation of the vehicle in a desired inertial direction. A provably convergent, global directional controller could enhance the operation of agile vehicles in dynamic environments, such as rivers, tidal basins, or other coastal areas. Energy-based tools are appealing for designing such controllers because they provide natural candidate Lyapunov functions for stability analysis. As an example, a passivity-based technique known as interconnection and damping assignment was used to stabilize the unstable dynamics of a slender, underactuatedAUV in [1]. The paper assumed an idealized (inviscid) dynamic model and did not consider the attitude kinematics. A nonlinear directional controller was developed in [2] using potential energy shaping, although that model also omitted viscous effects. This Note treats the directional stabilization problem for a vehicle model which requires minimal assumptions about the viscous effects. The result therefore allows a broad range of viscous force and moment models. Directional stabilization for AUVs may be considered a natural, intermediate step between waypoint navigation and general, threedimensional path following, as described in [3], for example. Several approaches have been proposed to address three-dimensional path following for underactuated, 6 degrees of freedom AUVs. These approaches include adaptive feedback [4], switching theory [5], and backstepping [3,6]. Here, we consider the more fundamental problem of directional stabilization for a slender, underactuated AUV and we approach the problem from an energy perspective. The stabilization result, which is adapted from [7], is based on themethod of feedback passivation described in [8]. In this approach, a given system is transformed into a feedback interconnection of two passive subsystems. It follows from passive system theory that the interconnection is passive and therefore that the system is stable. Asymptotic stability may be shown through further analysis, with suitably defined feedback dissipation included, if necessary. As is the case in this Note, exploiting intrinsic properties such as passivity often allows one to derive control algorithms which are globally effective and which work with the natural dynamics rather than dominate or supplant them.