Attitude stabilization with a nonholonomic constraint

The authors present a piecewise continuous feedback law for attitude stabilization of a rigid body which can rotate around only two axes. The angular velocity around the third axis is constrained to be zero. This is a controllable nonholonomic system for which the attitude cannot be stabilized by a smooth feedback law. It is shown that the kinematic equations can be transformed into the same model structure as the one used to describe a mobile wheeled robot with two degrees of freedom. A piecewise continuous feedback law can then be used as in the mobile robot case with exponential convergence to stabilize the attitude of the rigid body.<>