Current techniques which have been devised for motion planning and control of compliant multi-fingered grippers are based on the assumption of a constant compliance. The present investigation was undertaken to examine the validity of this assumption. To this end, the variational inequalities approach and the finite element method were used to formulate the general frictional contact problem. A two-step algorithm, which employs Quadratic Programming and non-differential optimization algorithms, is used to solve the resulting variational inequality and to provide the contact characteristics of compliant grippers.

The proposed method is applied to a case study involving a multi-fingered compliant gripper. The equivalent stress contours and the compliance of the system were obtained and analyzed. The proposed approach, which can be applied to any contact problem in robotics, overcomes most of the difficulties and approximations evident in current simplified contact analysis techniques.