Current industrial robots are often required to perform tasks requiring mechanical interactions with their environment. For tasks that require grasping and manipulation of unknown objects, it is crucial for the robot end-effector to be compliant to increase grasp stability and manipulability. The dynamic interactions that occur between such compliant end-effectors and deformable objects that are being manipulated can be described by a class of nonlinear systems. In this paper, we determine algorithms for grasping and manipulation of these objects by using adaptive feedback techniques. Methods for control and adaptive control of the underlying nonlinear system are described. It is shown that although standard geometric techniques for exact feedback linearization techniques are inadequate, yet globally stable adaptive control algorithms can be determined by making use of the stability characteristics of the underlying nonlinear dynamics.

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