Stability of teleoperation systems under time-varying delays by using Lyapunov-Krasovskii techniques

This paper investigates the stability of a teleoperation system under time-varying communication delays. The system is a laboratory platform consisting on a scale model of a gantry crane, teleoperated by means of a haptic device. This paper focuses on the problems arising from the timevarying nature of the UDP communication delay. First, the actual delay is investigated and bounds on its magnitude and on its time-derivative are estimated, emulating different geographical connections. Second, a recent Lyapunov-Krasovkii technique taken from the literature (Zhao et al. 2007) is applied to the model of the system and stability bounds are obtained for the position error (PE) architecture. The method is applied for different controller parameters and delay bounds, and it is compared to a frequency-domain technique (Kao and Rantzer, 2007), showing reasonably non-conservative results.