Stability of Sampled-Data, Delayed Haptic Interaction under Passive or Active Operator

This paper studies the absolute stability of a sampled-data, m-user haptic virtual environment (HVE) system based on the discrete-time circle criterion. Depending on the task being performed by an operator, the passivity of the operator is influenced. We provide a framework for the system stability analysis in which the operator is allowed to exhibit passive or active behavior. In this paper, the well-known Colgate’s stability condition for a 1-user haptic system with a passive operator is reproduced and then extended to the m-user case while allowing each or all of the operators to behave passively or actively. Another extension to Colgate’s condition comes by allowing communication delays to exist in the system. Simulations and experiments confirm the validity of the proposed conditions for stability of sampled-data, delayed m-user HVE systems.