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Coordinated manipulation of objects by multifingered. robotic hands aims to resolve the redundancy in object level and hand level, increase the rigidity and robustness of grasping, and achieve a good dynamic performance in trajectory control. In the paper a contact space approach and an active joint space approach are explored. The model places the following problems associated with the coordinated manipulation with non-fixed contact into a unified framework: 1. sufficient conditions for the controllability of hand motion including both the velocity of contact coordinates and the object; 2. kinematic measure of robust grasp to generate the coordinated motion of contact coordinates; 3. searching a group of internal forces lying in the strict interior of the friction cone by a LMI method; 4. hybrid control algorithms for simultaneous control of motion of hand and the internal grasping forces; and 5. controlling the internal grasping force to ensure the total contact force lying in the friction cone. Experimental results done on HKUST hands are reported.