Stabilization of asymmetric bilateral teleoperation systems for haptic devices with time-varying delays

This paper invetigates the stabilization issue for a bilateral teleoperation system with time-varying delays. The master and slave manipulators were modeled as linear single degree of freedom systems. The human user force was modeled based on the band limited availability of human motion, and the environmental force was modeled as a spring and damper combination based on the slave position. An impedance matching approach was applied to the master side dynamics, while a static error feedback gain is used to stabilize the slave side dynamics. A Lyapunov functional based on the error dynamics of the system is proposed with consideration for the minimum and maximum level of delays existing in the system. LMI (Linear Matrix Inequality) techniques are used with Jensen´s inequality to determine the static feedback control gain. The cone complementarity algorithm is used to deal with non-linear terms within the LMI. The algorithms, hardware applications to haptic devices are described thoroughly and experimental results with comparisons to simulation results are demonstrated to show the effectiveness of the proposed approach.