Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
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A novel approach is presented for adaptive trajectory tracking of robot manipulators using a three-stage hierarchical neural network model involving Support Vector Machines (SVM) and an adaptive unsupervised Neural Network. It involves a novel adaptive Self Organizing feature map (SOFM) in the first stage which aims at clustering the input variable space into smaller subspaces representative of the input space probability distribution and preserving its original topology, while rapidly increasing, on the other hand, cluster distances. Moreover, its codebook vector adaptation rule involves m-winning neurons dynamics and not the winner takes all approach. During convergence phase of the map a group of Support Vector Machines, associated with its codebook vectors, is simultaneously trained in an online fashion so that each SVM learns to positively respond when the input data belong to the topological sub-space represented by its corresponding codebook vector, taking into account similarity with that codebook vector. Moreover, it learns to negatively respond to input data not belonging to such a previously mentioned corresponding topological sub-space. The proposed methodology is applied, with promising results, to the design of a neural-adaptive trajectory tracking controller, by involving the computer-torque approach, which combines the proposed three-stage neural network model with a classical servo PD feedback controller. The results achieved by the suggested hierarchical SVM approach are favorably compared to the ones obtained by traditional (PD) and non-hierarchical neural network based controllers.