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In this paper, motion equations for the synchro-drive robot Nomad 200 are solved by using Linde Buzo Gray (LBG) clustering neural networks. The trajectories of the Nomad 200 are assumed to be composed of straight line segments and curves. The structure of the curves is determined by only two parameters, turn angle and translational velocity in the curve. The curves of the trajectories are found by using artificial neural networks (ANN) and the LBG clustered ANN. In this study a clustering method is used to improve the learning and test the performance of the ANN. In general, the LBG algorithm is used in image processing as a quantizer. This is the first publication where the LBG algorithm is successfully used in clustering ANN data sets. Thus, the best training data set of the ANN is achieved and minimum error values are obtained. It is shown that LBG-ANN models are better than the classic ANN models.