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As widely analyzed, the approximations made in the simple inverse kinematics solution are not accurate enough to meet the requirements for the SCU (Superconducting Undulator).
To enhance the overall accuracy of the solution, two approaches are followed:
Error function
This approach aims to improve the accuracy of the inverse kinematics (IK) by identifying an error function that models the IK errors as a function of the quadrupole orientation and position. By determining this ideal function for all degrees of freedom, we can apply corrections to the IK solution, thereby increasing its accuracy.
Concept
Error Mapping:
Multidimensional Matrix:
Optimization:
Implementation Steps
Initialization:
- Define simulation parameters and geometric properties.
- Set test positions for all DOFs.
Simulation Loop:
- Iterate over all combinations of test positions.
- For each combination, solve the inverse kinematics.
- Run the simulation model and capture the output.
- Calculate the average positions and orientations.
- Store the results for analysis.
Optimization:
- Use the collected data to optimize the error function.
- Apply the optimized error function to correct the IK solution.
This algorithm is repeated two times: one to find an error function that corrects for X and Y and then a final one that computes the fine error for pitch roll and yaw.