Delay-Independent L2 Stability of Four-Channel Bilateral Teleoperators with Damping Injection

Abstract

This paper presents an augmented four channel teleoperation architecture with local damping injection, which renders the teleoperation system L 2 stable independent of time delay. It is well known that four channel teleoperation architecture, which is based on the transmission of force and position measurements of both the master and the slave robots, provides perfect transparency, when there is no time delay between the robots. In the presence of delay, four channel systems are not stable and they can not provide transparency. With damping injection, stability is guaranteed independent of the size of the delay, as long as it is constant, and furthermore better transparency with high frequency force feedback can be realized. This is an improvement over conventional methods. As transparency and stability are two conflicting goals, there is a tradeoff that a constant damping is felt in free motion. In this paper stability and transparency analyses are presented and the validity of the method is also confirmed with experiments.

L2 stable transparency optimized two channel teleoperation under time delay

“…By feeding back the disturbance estimate to the system it is possible to realize robust acceleration control with the control law [8]:…”

“…Note that for four channel teleoperation the local force feedback channels C 5 and C 6 in figure 2 are not used and are assumed to be 1. In [8], conventional four channel transparent bilateral teleoperation was realized by choosing the transfer functions for these channels and the local controllers as:…”

“…For stability analysis we will be following the methodology in [8]. The L 2 signal spaces consist of all the functions f : + → which are measurable and satisfy:…”

“…It was shown in [8] that, to satisfy the small gain condition local damping injection is necessary and damping terms must be chosen as a function of human and environment impedance parameters. Furthermore, in the L 2 analysis, the delay operators are irrelevant because the gain of the delay operator is always equal to one.…”

“…In [7] [8], it was shown that with some modifications in the form of local damping injection, delay independent stability and better transparency under time delay can be achieved with four channel control. However in that case the transparency is not ideal; damping makes the system slow and heavy and as delay increases transparency deteriorates further.…”