Equivalence between different kinematic models of non-holonomic vehicles is established. Non-holonomic vehicles are shown to be kinematically equivalent to unicycles. A generalized unicycle model is used for stabilization purposes. Globally stabilizing control laws under the presence of kinematic control constraints are derived. The control laws are based on the invariant manifold technique, a control strategy where non-holonomic systems are steered onto manifolds of global and relative local-local controllability. Convergence of the proposed closed-loop strategies are verified by simulations.