L2 stability analysis of four channel teleoperation and experiments under varying time delay

This paper analyses the L
₂
stability of four channel teleoperation systems under time delay. It is a well known fact that four channel architecture provides the best performance when no delay is present on the communication channels. However when delay is present four channel systems can not guarantee stability or good performance. The L
₂
analysis we present using small gain theorem indeed confirms that conventional four channel architecture is unstable when damping is not present in the contact surfaces. We propose the damping injection method for four channel teleoperators in order to make the architecture delay independently stable and we show with the same analysis that indeed L
₂
stability can be achieved given adequate damping injection is applied. We also present experiment results under varying time delay to confirm that the architecture is stable and provides good performance.