An algorithm for the motion planning of the multifingered hand is proposed to generate finite displacements and changes in orientation of objects by considering sliding contacts as well as rolling contacts between the fingertip and the object at the contact point. Specifically, a nonlinear optimization problem is firstly formulated and solved to find the minimum joint velocity and the minimum contact force to impart a desired motion to the object at each time step. Then, the relative velocity at the contact point is found by calculating the velocity of the fingertip and the object at the contact point. Finally, time derivatives of the surface variables and the contact angle of the fingertip and the object at the current time step is computed using the Montana's contact equation to find the contact parameters of the fingertip and the object at the next time step. To show the validity of the proposed algorithm, a numerical example is illustrated by employing the robotic hand manipulating a sphere with three fingers each of which has four joints
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