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• NN data generator: This script generates the dataset used in during the training phase
• NN training: This scripts trains both networks (direct and inverse kin) for the selected datasets
• Space explorer NN: This script explore the space and compute computes the inverse kinematics error as for the previous approach

Comparison

Both approaches solve the problem of computing an accurate inverse kinematic function. However, there is a winner in terms of simplicity, flexibility and generality. But first let's have a look at the results 

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The first plot represents the error for the quadrupole position (X and Y) computed with the analytical solution of the inverse kinematics, the second represents the same error but with inverse kinematics based on the optimized error function and, finally, the third one is the one based on the feedforward neural network

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These plots are the same as before except for the fact that these represent the orientation errors.

Both the error function optimization and the feedforward NN show almost the same performances for the position while, on the orientation side, the feedforward nn outperforms if compared with the other.

For this reason and for the fact is capable of modeling uncaught behavior defined in the function error, the Feedforward NN is the favourite approach to solve this problem.