Existing work concerning adaptive control of uncertain teleoperation systems only deals with linearly parameterized (LP) dynamic uncertainties. Typical teleoperation system dynamics, however, also posses terms with nonlinearly parameterized (NLP) structures. An example of such terms is friction, which is ubiquitous in the joints of the master and slave robots of practical teleoperation systems. Uncertainties in the NLP dynamic terms may lead to significant position and force tracking errors if not compensated for in the control scheme. In this paper, adaptive controllers are designed for the master and slave robots with both LP and NLP dynamic uncertainties. Next, these controllers are incorporated into the 4-channel bilateral teleoperation control framework to achieve transparency. Then, transparency of the overall teleoperation is studied via a Lyapunov function analysis. Simulation studies demonstrate the effectiveness of the proposed adaptive scheme when exact knowledge of the LP and NLP dynamics is unavailable.

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