Quantifying Measurement Uncertainty using Weighted Least Squares for Force Measurement in Biomimetic Robot Development

Abstract

Robotics is one area where biomimetics, a field devoted to mimicking natural systems to address difficult human problems, has made great strides. Precise force measurement and analysis are vital to this field because they are necessary to reproduce and comprehend natural phenomena. This study addresses the challenge of accurate force measurement by developing a load cell-based device. It specifically assesses the impact of the taring process on measurement accuracy. The Weighted Least Squares (WLS) method is employed to thoroughly quantify the uncertainty of the device, ensuring reliability. The findings suggest that the single-input taring process contributes to variations in standard deviation, with accuracy peaking near the tared value and decreasing as the mass deviates from it. The linear calibration equation derived from WLS showed minimal variation in estimated mass values, with uncertainties u_a = 2  10^-6 and u_b = 8  10^-4. However, the expanded uncertainty increased with the input mass, largely due to the inherent uncertainty of the mass balance. Despite this, the hysteresis of the system was negligible, and its sensitivity of 0.01 N/g made it suitable for detecting small force fluctuations in biomimetic models. The study concludes that while the relative value of the maximum combined uncertainty, U_Lc = ±0.2% FSS, exceeds the reference specifications of the load cell, it remains adequate for applications requiring moderate precision. Future research will reduce mass balance uncertainty and consider environmental factors, thereby improving system effectiveness in biomimetic research.