A haptic interface conveys a kinesthetic sense of presence to a human operator interacting with a computer generated environment. Historically, human-computer interaction has taken place through one-directional channels of information. Haptic interaction is fundamentally different in that kinesthetic energy flows bi-directionally, from and to the human operator. The human grasp may be responsible for stabilizing or destabilizing the overall system. Since the haptic display actively generates physical energy, instabilities can damage hardware and even pose a physical threat to the human.

A number of authors have proposed an artificial coupling between a haptic display and a virtual environment to create stable interaction. Colgate et. al. (Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, Pittsburgh, PA, 1995 ) introduced the idea of a virtual coupling which guarantees stability for arbitrary passive human operators and environments. Zilles and Salisbury (Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, Pittsburgh, PA, 1995) presented a heuristically motivated "god-object" approach which greatly simplifies control law design. These implementations can be grouped together as special cases of a virtual coupling network, a two-port interface between a haptic display and a virtual environment. This network can play the important role of making the stability of a haptic simulation independent of human grasp impedance and of the details of virtual environment design. The above-mentioned work focuses exclusively on impedance-type haptic displays. No similar work on virtual couplings has appeared for admittance displays and very little exists in explicit criteria for the design of virtual coupling networks.

This work extends the concept of a virtual coupling to admittance displays and attempts to treat the problem of stable haptic interaction in a more general framework. Linear circuit theory is used to develop necessary and sufficient conditions for the stability of a haptic simulation, assuming the human operator and virtual environment are passive. These equations lead to an explicit design procedure for virtual coupling networks which give maximum performance while guaranteeing stability. By decoupling the haptic display control problem from the design of virtual environments, the use of a virtual coupling network frees the developer of haptic-enabled virtual reality models from issues of mechanical stability.