In this work, a control scheme for human-robot collaborative object transportation is proposed, considering a quadruped robot equipped with the MIGHTY suction cup that serves both as a gripper for holding the object and a force/torque sensor. The proposed control scheme is based on the notion of admittance control, and incorporates a variable damping term aiming towards increasing the controllability of the human and, at the same time, decreasing her/his effort. Furthermore, to ensure that the object is not detached from the suction cup during the collaboration, an additional control signal is proposed, which is based on a barrier artificial potential. The proposed control scheme is proven to be passive and its performance is demonstrated through experimental evaluations conducted using the Unitree Go1 robot equipped with the MIGHTY suction cup.