This paper presents a model-reference-based adaptive control (MRAC) strategy for coordinating the actions of multiple omnidirectional mobile robots to transport a shared payload to a predetermined destination along a defined reference trajectory. A cohesive state-space model for the payload is developed, facilitating the streamlined development of control algorithms tailored for cooperative tasks. The distributed adaptive controller dynamically adjusts its parameters to ensure that the system behavior closely emulates that of an ideal reference model. Furthermore, the development of a Lyapunov function serves as a proof of the asymptotic stability of the closed-loop system. The effectiveness of this control methodology is highlighted by a simulation that depicts a scenario involving four omnidirectional mobile robots working in concert to transport a common payload. The simulation results validate the robustness and adaptability of the proposed MRAC method in a practical cooperative transportation scenario.