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

In this article we present a feedback control law that gives exponential convergence of a nonholonomic underwater vehicle to a constant desired configuration. This is achieved using a piecewise smooth feedback control law that 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 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.

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