Expanding the automation level of the freshly introduced fleet of self-propelled Watertruck+ barges, which house fully-rotatable embedded thrusters, might increase their ability to compete with their less sustainable but dominating road-based alternatives. Hydrodynamic motion models, which reveal the manoeuvring capabilities of these barges, can serve as inputs for many pieces of this automation puzzle. No identified motion models or hydrodynamic data seem to be publicly available for the hull design and the novel actuation system configuration of these barges. Therefore, this study offers: (i) decoupled motion model structures for these barges for surge, sway, and yaw, with a focus on the thruster and damping models; (ii) two identification procedures to determine these motion models; (iii) all the experimental data, generated outdoors with a scale model barge to identify (i) based on (ii). In addition, the identified surge models were compared with both computational and empirical data. These comparisons offer more physical insights into the identified model structures and can aid in the model selection for which the desired complexity and accuracy evidently depend on their envisaged application. Finally, this methodology need not be limited to the vessel and actuation types utilised by us.