Feedback Control of a Nonholonomic Underwater Vehicle With a Constant Desired Configuration

In this article we present a feedback control law which gives exponential convergence of a nonholonomic underwater vehicle to a constant desired connguration. This is achieved using a piecewise smooth feedback control law which is based on previous work on the control of nonholonomic mobile robots in the plane. The kinematic model of the underwater vehicle is given in SE(3) by homogeneous transformation matrices, and attitude deviations are given by Euler parameters. This gives a global description without singularities. It is also shown how controllability and stabilizabil-ity of the nonholonomic underwater vehicle can be analyzed in SE(3) without the use of local charts. The inputs of the system are the three angular velocity components and the forward velocity.