We present a hybrid systems solution to the problem of trajectory tracking for a four-wheel steered four-wheel driven mobile robot. The robot is modelled as a non-holonomic dynamic system subject to pure rolling, no-slip constraints. Under normal driving conditions, a nonlinear trajectory tracking feedback control law based on dynamic feedback linearization is sufficient to stabilize the system and ensure asymptotically stable tracking. Transitions to other modes are derived systematically from this model, whenever the configuration space of the controlled system has some fundamental singular points. The stability of the hybrid control scheme is finally analyzed using Lyapunov-like arguments.