Impedance Control Realization of Screw Stiffness Matrix in Virtual Fixtures

This paper presents a novel approach to determine and realize the virtual fixture stiffness matrix. Generally, for characterizing the stiffness matrix, stiffness of each direction needs to be known. Here, by the help of screw theory, stiffness matrix is obtained and afterwards, an impedance control strategy is employed to realize it. In addition, the extension of the proposed virtual fixture algorithm for passive and non-passive environments is also discussed. This task is feasible by use of a force sensor that measures environment force. Stability analysis of switching modes of virtual fixtures is shown by a unique Lyapunov function. Finally, simulation results on a surgical maxillofacial robot is presented which verifies the efficiency of the proposed algorithm.