Stability of sampled-data, delayed haptic interaction and teleoperation

This paper proposes a unified framework to study the stability of sampled-data, haptic virtual environment (HVE) systems and sampled-data position-error-based (PEB) bilateral teleoperation systems based on the discrete-time circle criterion. Communication time delay and controller discretization are two major factors that jeopardize the system stability. We provide a framework for the system stability analysis in which both these two destabilizing factors can be addressed. In this paper, first the well-known Colgates stability condition for a 1-user haptic system with a passive operator is reproduced in a different manner and then extended to the case where delay can exist in the communication channel. Then, it is shown that using the same method, the stability of sampled-data position-error-based (PEB) bilateral teleoperation systems can be dealt in a similar manner. Simulation results confirm the validity of the proposed conditions for stability of both sampled-data, HVE and PEB bilateral teleoperation systems.