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In this study, an adaptive object deformability-agnostic human-robot collaborative transportation framework is presented. The proposed framework enables to combine the haptic information transferred through the object with the human kinematic information obtained from a motion capture system to generate reactive whole-body motions on a mobile collaborative robot. Furthermore, it allows rotating the objects in an intuitive and accurate way during co-transportation based on an algorithm that detects the human rotation intention using the torso and hand movements. First, we validate the framework with the two extremities of the object deformability range (i.e, purely rigid aluminum rod and highly deformable rope) by utilizing a mobile manipulator which consists of an Omni-directional mobile base and a collaborative robotic arm. Next, its performance is compared with an admittance controller during a co-carry task of a partially deformable object in a 12-subjects user study. Quantitative and qualitative results of this experiment show that the proposed framework can effectively handle the transportation of objects regardless of their deformability and provides intuitive assistance to human partners. Finally, we have demonstrated the potential of our framework in a different scenario, where the human and the robot co-transport a manikin using a deformable sheet.