This paper addresses the problem of physical human-robot collaboration for object manipulation. In particular, we consider a human-robot architecture where the human has exclusive knowledge of the object's desired trajectory and the robot tries to assist actively, by carrying the object's load in order to reduce the human effort that is required to achieve the desired tracking behavior. The robot estimates the human's desired motion via a prescribed performance estimation law that drives the estimation error to an arbitrarily small residual set. This estimation is further employed in the object dynamics equation to compute the interaction force between the human and the object. Subsequently, an impedance control scheme is designed based on the aforementioned estimations, achieving significant reduction on the required human effort, despite the uncertainty in the robot dynamics. The feedback relies exclusively on the robot's force/torque, position as well as velocity measurements and no a priori explicit information on the task is required. Finally, extensive experimental results clarify the proposed method and verify its efficiency.