A Centralized Adaptive Neuro-Fuzzy Controller for Multi-Lateral Telerehabilitation Systems

In this paper, an adaptive control scheme based on neural-fuzzy network is presented to control multi-lateral telerehabilitation systems. The controller structure is designed in such a way that in the framework of multi-agent systems, it guarantees the synchronization of the position of the operators of the telerehabilitation system. Dynamic parameters of the robots used in telerehabilitation systems are considered unknown. In the following, uncertain dynamic parameters of the operators have been estimated using the neural-fuzzy network and the estimation of these unknown dynamics has been used in the designed controller structure. The structure of the presented controller includes two adjustment matrices <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$U$</tex>. The matrix <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L$</tex> shows how operators (agents) communicate in the framework of multi-agent systems, and by using this matrix in the controller structure, robust synchronization for the position of operators in the telerehabilitation system is achieved. Also, the matrix <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$U$</tex> shows the amount of force felt in each operator's hand caused by other operators, and by using this matrix in the controller structure, transparency is created in the multi-lateral telerehabilitation system. Finally, by properly setting the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$U$</tex> matrices, different scenarios of the telerehabilitation system can be implemented.