A new approach to the construction of switching feedback control for a class of non-holonomic systems is presented and its effectiveness is tested on a model of an underwater vehicle. The control strategy proposed has set point stabilization as objective and delivers piecewise constant control sequences. The synthesis method relies on the construction of a pair of guiding functions whose values allow us to determine a desired direction of system motion and permit us to construct a sequence of controls such that the sum of these guiding functions decreases in an average sense. The individual guiding functions are hence not restricted to decrease monotonically but their oscillations are limited and coordinated in a way to guarantee convergence. The approach presented is general and can be employed to control a variety of mechanical systems with velocity constraints.