Control of an Underactuated Underwater Vehicle in 3D Space under Field-of-View Constraints

Exponential Set-Point Stabilization of Underactuated Vehicles Moving in Three-Dimensional Space

“…Theorem 1: Let denote the configuration of an underactuated vehicle whose kinematics are formulated in (3). Let be the exponential coordinates of the configuration g. Construct two rotation matrices and as in ( 16) and (17), and let and represent the exponential coordinates of and , respectively. Design the following control law for the underactuated vehicle…”

“…For instance, a continuous timevarying feedback is presented in [16] based on the properties of homogeneous system as well as the averaging and Lyapunov techniques, and the controller can locally exponentially stabilize an underactuated vehicle system. In [17], the authors present a methodology called switched seesaw control for the stabilization of underactuated vehicles, in which input-to-state practical stability is obtained under the provided conditions. The authors in [18] investigate the control of underactuated vehicles using dipolar reference vector fields combined with viability theory, where the proposed controller guarantees the convergence in a neighborhood of the desired configuration.…”

“…From (18), the angular velocity ω has a discontinuous form, which corresponds to the Brockett's theorem. The discontinuity of ω results from the fact that the constructed matrices are not well defined at according to the definition in ( 16) and (17). Then, we set the additional angular velocity to be 0 at .…”