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This paper analyzes the dynamics and control of pinch motions generated by a pair of two multi-degrees-of-freedom robot fingers with soft and deformable tips pinching a rigid object. It is shown firstly that passivity analysis leads to an effective design of a feedback control signal that realizes dynamic stable pinching (grasping), even if extra terms of Lagrange's multipliers arise from holonomic constraints of tight area-contacts between soft finger-tips and surfaces of the rigid object and exert torques and forces on the dynamics. It is shown secondly that a principle of superposition is applicable to the design of additional feedback signals for controlling both the posture (rotational angle) and position (some of task coordinates of the mass center) of the object provided that the number of degrees of freedom of each finger is specified for satisfying a condition of stationary resolution of controlled position state variables. The details of feedback signals are presented in the case of a special setup consisting of two robot fingers with two degrees of freedom.
Arimoto et al. (Mon,) studied this question.