The problem of dynamic output stabilization is a very general and important problem in control theory. This problem is completely solved in the case where the system under consideration is uniformly observable. However, usually, nonlinear systems do not share this property: in general, systems are observable or not depending upon the control as a function of time. In this general situation, very little is known about dynamic output stabilization. In this paper, we solve the problem for a classical academic kinematic model for drones whose observability properties are especially bad.