A passivity criterion for N-port multilateral haptic systems

This paper presents a criterion for passivity of n-port networks, which can be used to model multilateral systems involving haptic information sharing between a number of users. Such systems have recently found interesting applications in both cooperative haptic teleoperation and haptics-assisted training. The criterion presented in Theorem 1, which is necessary and sufficient for passivity of the n-port network, imposes 2n conditions on the immitance parameters of the network and on the residues of the immitance parameters at their imaginary-axis poles. It is shown that when n = 2, the proposed conditions reduce to the well-known Raisbeck's passivity criterion for two-port networks. Another special case for which the proposed criterion has been simplified corresponds to three-port networks. Finally, the passivity of a dual-user haptic system for control of a single teleoperated robot is investigated.