The focus of this paper is (i) to derive a suitable dynamic model for a self-reconfigurable pavement sweeping robot PANTHERA and (ii) to design a robust controller for the same to tackle uncertainties stemming from the reconfiguration process, external disturbances and from actuator saturation. To meet the first objective, an Euler-Lagrangian dynamic model is proposed to incorporate the effects of configuration changes on the system dynamics. Based on this model, the second objective is met via designing a singular perturbation based robust controller which can tackle the aforementioned uncertainties without violating the actuation limits. To circumvent the vulnerability toward actuator saturation, the proposed controller is built on contraction theory, which, compared to a conventional Lyapunov theory based design, allows to improve closed-loop tracking performance without reducing the singular perturbation parameter. Experimental results on the PANTHERA reconfigurable robot validate the effectiveness of the proposed controller over the state of the art.