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In this work, we introduce an adaptive control framework for human-robot collaborative transportation of objects with unknown deformation behaviour. The proposed framework takes as input the haptic information transmitted through the object, and the kinematic information of the human body obtained from a motion capture system to create reactive whole-body motions on a mobile collaborative robot. In order to validate our framework experimentally, we compared its performance with an admittance controller during a co-transportation task of a partially deformable object. We additionally demonstrate the potential of the framework while co-transporting rigid (aluminum rod) and highly deformable (rope) objects. A mobile manipulator which consists of an Omni-directional mobile base, a collaborative robotic arm, and a robotic hand is used as the robotic partner in the experiments. Quantitative and qualitative results of a 12-subjects experiment show that the proposed framework can effectively deal with objects of unknown deformability and provides intuitive assistance to human partners.