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This paper focuses on the optimization of the truncated power series for the inverse kinematics solution that was obtained in the earlier work for a six-legged robot. The inverse solutions were used to approximate the displacement angle for input values for the three servos S1, S2, and S3 using the three desired parameters R, Z, and angle ?. The truncated solution was complex and mathematically tedious, requiring 16 coefficients to be used to compute S1 and 165 coefficients to compute S2 and 145 for S3. In this research, a neural network was used to replace the highly complex power expansions. Single neural networks were used to compute S1, S2, and S3 separately. The networks were optimized such that each network had eight hidden layers. The neural networks provided good accuracy in the solutions they obtained. Most importantly, the approach reduced the high demand for mathematical resources significantly below the resources required by the power series method. The goal of this research is to use the results reported in this paper in the implementation of a field-programmable gate array (FPGA).