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The problem of four-fingered robot hand manipulation, while allowing one of the four fingers to slide on the object's surface, is discussed. The paper proposes an on-line optimization algorithm for grasping forces under the constraints of maximal static friction and dynamic friction at the grasping points. Based on the optimal solutions, a dynamic control law is then derived. The control law ensures the tracking of the object trajectory together with the desired sliding motions along the surface of the object. The control law also realizes the desired internal forces. A simulation example to demonstrate the use of the proposed control law is given.