In this paper, a state space dynamical model for the differential drive path tracking system of an AGV (Automated Guided Vehicle) is developed. In order to guarantee desirable control specifications for a wide range of possible masses (50 < M < 1000kg), the payload mass is considered as uncertainty in the model. Robust stability domain in the controller parameter space via randomization technique is analysed. Two sets of controller parameters are selected and experimentally tested on a commercial vehicle, showing performances in agreement with the analysis.