Stability of sampled-data, delayed haptic interaction under passive or active operator

This study 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. The authors provide a framework for the system stability analysis, in which the operator is allowed to exhibit passive or active behaviour. In this study, 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.