Modelling and avoidance singular condition - Control of under water vehicle

We present a nonlinear feedback control of position and attitude of an underwater vehicle subject to nonholonomic constraints. Its kinematic model is given by time derivative of position coordinates and of Euler parameters describing the underwater vehicle orientation. One forward velocity and three angular velocities serve as inputs of the vehicle. The method adopts Euler parameters for orientation description and control strategy called variable constraint control (VCC). Euler parameters are employed in order to avoid singularities in orientation description which occur in other representations, such as Euler angles. Since we do not make any coordinate or input transformations, there are no transformation type singularities. Moreover, it is shown by means of theoretical analysis and simulation that singularities occurring during control are avoidable.