Contact stability is a major concern when the tip of a manipulator contacts with a stiff surface in a manipulation task. Better understanding of the contact dynamics problem can help deal with the contact stability problem. This paper studies the frictional contact problem of manipulators from the perspective of the recent development of relative contact dynamics. With the presented approach, the contact stability of a robot’s tip can be characterized by two critical parameters A and B. It is shown that parameter A depends on the robot’s configuration and friction coefficient only and parameter B is a function of the configuration, speed and the control forces/torques. By examination of the signs of the two parameters, one can determine whether the tip contact is in a stable contact, unstable contact, or separation condition. Such a characterization of the tip contact stability of a manipulator by just examining two parameters provides a new perspective or means for dealing with contact tasks of a manipulator. A simulation example using a planar manipulator is presented to demonstrate the conclusive relationship between the two key parameters and the contact stability conditions.

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