How can the accuracy of parameter computation in complex kinematic systems be further improved?

Increasing Accuracy of Solution of Transcendental Equation

Problem: Given a complex kinematic system with parameters that are difficult to measure accurately, the goal is to compute these parameters from a set of measurements using auto-calibration. The objective is to increase the accuracy of the computed parameters.

Approximation Method: The solution utilizes an approximation class that iteratively searches for the minimal deviation point for a given variable within a specified range and step size. The solution is further refined by reducing the range and step size near the minimal point, recursively increasing accuracy.

Current Accuracy: Simulation results show that the accuracy is still not sufficient, with errors ranging from 0.1 mm to 0.5 mm. The number of measurement points and recursion levels have limited effects.

Possible Solutions:

1. Iterative Approximation: Consider implementing a more sophisticated iterative approximation algorithm, such as the Levenberg-Marquardt algorithm, which can potentially achieve higher precision.

2. Weighted Deviations: Explore weighting the deviations based on angular distance from 0 degrees. This may help improve accuracy by emphasizing the more reliable measurements.

3. Different Model: Re-evaluate the kinematic model. The proposed transcendental equation may not be the most accurate representation of the system. Consider alternative models that better capture the physics of the system.

4. Improved Measurement Techniques: Focus on improving the measurement accuracy of y0, z0, and a0. This could involve using more precise sensors or calibrating the existing ones.

5. Mechanical Improvements: Examine the mechanical design of the system for possible sources of error. Address any issues such as vibrations or tube eccentricity.

6. Additional Data Points: Explore increasing the number of measurement points, but only up to a point where stability is maintained. Too many points can lead to instabilities in the results.

7. Alternative Approaches: Consider exploring different approaches to the problem, such as utilizing machine learning algorithms or optimization techniques like genetic algorithms.

Edit:

• Further Accuracy Improvement: Estimating y1, which corresponds to the intersection of the arm and tube movement axis, and using it to calculate a0, z0, and y0 has significantly enhanced accuracy, with precision now around 0.03 mm.
• Explanation of Approximation Search: The approximation search narrows down the range of a single variable by incrementally adjusting its value and selecting the step that produces the smallest error. This process is repeated recursively, reducing the range and step size to gradually increase accuracy.

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