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Dynamic and robust control of fingertip grasping is essential in robotic hand manipulation. This study introduces detailed kinematic and dynamic mathematical modeling of a two-fingered robotic hand, which can easily be extended to a multifingered robotic hand and its control. The Lagrangian technique is applied as a common procedure to obtain the complete nonlinear dynamic model. Fingertip grasping is considered in developing the detailed model. The computed torque controller of six proportional derivative (PD) controllers, which use the rotation angle of the joint variables, is proposed to linearize the hand model and to establish trajectory tracking. An impedance controller of optimized gains is suggested in the control loop to regulate the impedance of the robotic hand during the interaction with the grasped object in order to provide safe grasping. In this impedance controller, the gains are designed by applying a genetic algorithm to reach minimum contact position and velocity errors. The robustness against disturbances is achieved within the overall control loop. A computer program using MATLAB is used to simulate, monitor, and test the interactional model and the designed controllers.

Interactional Modeling and Optimized PD Impedance Control Design for Robust Safe Fingertip Grasping