Passivity And Absolute Stability Analyses Of Trilateral Haptic Collaborative Systems

Trilateral haptic systems can be modeled as three-port networks. Analysis of coupled stability of a three-port network can be accomplished in either the passivity or the absolute stability frameworks assuming all three ports are connected to passive but otherwise unknown terminations. This paper first introduces our recent results in terms of extending Raisbeck's passivity criterion and Llewellyn's absolute stability criterion to general three-port networks -- both criteria are founded on the properties of a positive real Hermitian matrix. Next, we show that the absolute stability criterion is less conservative than the passivity criterion. Then, to show how the two criteria may be utilized at the system design stage, we apply them to the problem of designing controllers for a dual-user haptic teleoperation system and a triple-user collaborative haptic virtual environment. Using the two criteria, controllers are then designed and compared in terms of conservatism in simulations and experiments.