Distributed haptic cooperation with passive multirate wave communications

This paper investigates the use of passive multirate wave communications for distributed haptic cooperation between two users connected over a network with constant delay and low transmission rate. The paper develops the lifted state space model of the haptic cooperation system and uses it to compute the maximum stable gains for the users´ feedback loops and for the coordination of the virtual object distributed across the network. The multirate stability analysis predicts that: an order of magnitude larger coordination gains can be used when the two users are connected via passive wave communications than when they are connected via powerdomain communications or via traditional wave-domain communications; the maximum coordination gain stays unaffected by constant and symmetric network delays. A larger maximum coordination gain independent of the network delays provides increased and robust coherency of the shared virtual object. Experiments in which two users manipulate a shared virtual cube together validate the multirate stability analysis.