Aerial cooperative transportation, involving multiple Unmanned Aerial Vehicles (UAVs) collaborating to transport large or heavy payloads, has become a significant area of research. This growing interest arises from the flexibility, cost-effectiveness, and aerial mobility of UAVs. This study proposes a distributed geometric controller for the cooperative transportation of underactuated UAVs. Each UAV perceives its own pose and the payload configuration, while the others position themselves based on independent perception data. A comprehensive system model is described using manifolds based on Lagrangian dynamics. The nonlinear model serves as a feedforward component, and an estimator is introduced to estimate the rigid payload’s motion using an extended Kalman filter. This estimator eliminates the need for global UAV information, feeding the resulting data into a Proportional-Derivative controller to form a globally coordinated distributed control system. Numerical simulations are conducted to validate the controller’s effectiveness and assess the system performance under the introduction of noise signals.