  We study the controllability of a Partial Differential Equation of transport
type, that arises in crowd models. We are interested in controlling it with a
control being a vector field, representing a perturbation of the velocity,
localized on a fixed control set. We prove that, for each initial and final
configuration, one can steer approximately one to another with Lipschitz
controls when the uncontrolled dynamics allows to cross the control set. We
also show that the exact controllability only holds for controls with less
regularity, for which one may lose uniqueness of the associated solution.
