The problem of stable force-reflecting teleoperation is addressed, where the communication between the master and the slave is subject to multiple time-varying, discontinuous, and possibly unbounded communication delays. A new force reflection (FR) algorithm is proposed, which improves the stability of the system without decreasing its transparency. Based on the estimate of human forces provided by the high-gain input observer, the proposed algorithm restricts the reflected force in such a way that it eliminates the motion of the master induced by the FR signal without changing the human perception of the environmental force. It is shown that the proposed FR algorithm allows us to achieve stability of the system for an arbitrarily high FR gain and arbitrarily low damping and stiffness of the master manipulator. The stability analysis is based on the input-to-output stability small-gain theorem for systems with multiple time-varying communication delays.
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