Cooperative transportation by human and robotic coworkers constitutes a challenging research field that could lead to promising technological achievements. Toward this direction, the present work demonstrates that, under a leader–follower architecture, where the human determines the object’s desired trajectory, complex cooperative object manipulation with minimal human effort may be achieved. More specifically, the robot estimates the object’s desired motion via a prescribed performance estimation law that drives the estimation error to an arbitrarily small residual set. Subsequently, the motion intention estimation is utilized in the object dynamics to determine the interaction force between the human and the object. Human effort reduction is then achieved via an impedance control scheme that employs the aforementioned estimations. The feedback relies exclusively on the robot’s force/torque, position as well as velocity measurements at its end effector, without incorporating any other information on the task. Moreover, an adaptive control scheme is adopted to relax the need for exact knowledge of the object dynamics. Finally, an extension for multiple robotic coworkers is studied and verified via simulation, while extensive experimental results for the single robot case clarify the proposed method and corroborate its efficiency.