Desirable performance of cooperating manipulators has led to lots of researches and applications of these robotics systems. Among many different scientific issues, object grasping is an important one that many researchers have studied. Type of grasping, grasping point, different type of contact conditions, forces exerted on the object, grasping stability, and object motion measurements are some of the issues that researchers have studied so far. Friction contact condition is one of the contact types that one can find many related researches in the literature. Static and dynamic constraints in this contact condition leads to multi-phase dynamical system which is described by algebraic differential equations with equality and inequality constraints. This irregular form of dynamic equations makes dynamic analysis and control synthesis of the system difficult, if not possible. In this thesis, initially a new form of formulation is developed to illustrate the contact conditions, based on Coulomb friction model. This formulation is used to develop a new set of equations of motion, suitable for dynamic analysis and control synthesis. A control method is proposed based on this formulation and its stability is studied. Then performance of the control system is studied numerically and is compared with a modified conventional control approach and advantage of this new approach to the conventional one is addressed. The formulation is utilized to extend the control approach to an adaptive control system. At the end, an experiment setup is used to evaluate the capability of the proposed control method in real application.