A new nonlinear adaptive impedance-based trilateral controller is proposed to ensure the absolute stability of multi-degrees-of-freedom (DOFs) dual-user haptic teleoperation systems subjected to communication delays. Using this strategy, reference impedance models are realized for the trilateral teleoperation system represented by a three-port network to facilitate cooperation of two human operators in order to perform a remote physical task. For this purpose, an impedance model defines the desired haptic interaction between the two human operators, while another impedance model specifies the desired behavior of the slave robot in terms of tracking the mater robots' trajectories during interaction with the remote environment. It is shown that different performance goals such as position synchronization and force reflection can be achieved via different adjustments to the impedance parameters. The sufficient conditions for the trilateral haptic system's absolute stability are investigated in terms of the impedance models' parameters. Accordingly, guidelines for modification of the impedance parameters are obtained to guarantee the absolute stability of the trilateral haptic system in the presence of communication time delays. A trilateral nonlinear version of the model reference adaptive impedance control (MRAIC) scheme is developed for implementing the proposed reference impedance models on the masters and the slave. The convergence of robots' trajectories to desired responses and the robustness against modeling uncertainties are ensured using the proposed controller as proven by the Lyapunov stability theorem. The proposed impedance-based control strategy is evaluated experimentally by employing a nonlinear multi-DOFs teleoperated trilateral haptic system with and without communication delays.

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