Lambert W Function Controller Design for Teleoperation Systems

Stability and transparency play key roles in a bilateral teleoperation system with communication latency. This study developed a new method of controller design, based on the Lambert W function for the bilateral teleoperation through the Internet. In spite of the time-delay in the communication channel, system disturbance, and modeling errors, this approach causes the slave manipulator tracks the master appropriately. Time-delay terms in the bilateral teleoperation systems result in an infinite number of characteristic equation roots making difficulty in the analysis of systems by traditional strategies. As delay differential equations have infinite eigenspectrums, it is not possible to locate all closed-loop eigenvalue in desired positions by using classical control methods. Therefore, this study suggested a new feedback controller for assignment of eigenvalues, in compliance with Lambert W function. Lambert W function causes the rightmost eigenvalues to locate exactly in desired possible positions in the stable left hand of the imaginary axis. This control method led to a reduction in the undesirable effect of time-delay on the communication channel. The simulation results showed great closed-loop performance and better tracking in case of different time-delay types.