There have been many researches on object grasping in cooperating systems assuming no object slippage and stable grasp and the control system is designed to keep the contact force inside the friction cone to prevent the slippage. However undesired slippage can occur due to environmental conditions and many other reasons. In this research, dynamic analysis and control synthesis of a cooperating system, considering slipping conditions are performed. Equality and inequality equations of the frictional contact conditions are replaced by a single second order differential equation with switching coefficients in order to facilitate the dynamical modeling and control synthesis. Using this new modeling of friction, a conventional approach in grasping control is modified and presented to control any undesired slippage of the end-effectors on the object.
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