Exponential stabilization of a nonholonomic underwater vehicle with constant desired configuration

Presents a feedback control law which gives exponential stabilization of a nonholonomic underwater vehicle to a constant desired configuration. This is achieved by transforming the kinematic model into a chained form, and applying a control scheme for exponential stabilization of chained form systems. The nonholonomic vehicle under consideration is described by a kinematic model with three angular velocities and one translational velocity component as inputs. The kinematic model of the underwater vehicle is given in SE(3) by a position vector and a rotation matrix. Due to the difference in topology, the transformation into chained form is not global, but has singularities for large angular deviations. This problem is discussed, and conditions for avoiding the singularities are derived