Isotropy Optimization of Six-Axis Capacitive Force Sensor with a Large Moment-to-Force Ratio

This article presents a structural isotropy optimization method for six-axis capacitive force sensor with a large moment-to-force ratio to minimize its measuring error in the strong cross-axis coupling task scenario. The isotropic index (condition number) was taken as the design criterion to evaluate the sensor’s measuring performance. A single-objective optimized model was established using Box–Behnken experimental design (BBD) and response surface methodology (RSM) to minimize condition number. The optimal values for the geometry dimensions of the elastic body were obtained with the sequential quadratic programming algorithm. The optimized sensor was analyzed numerically and fabricated for experimental verification. As a result of performance optimization, the condition number of the prototype sensor dropped to nearly 1.98, which is close to the solution acquired by the optimal design method. The maximum interference error below 3.32% is a better practical result, compared with other commonly found force sensors, especially considering the higher moment-to-force specification (0.12 $\text{N}\cdot \text{m}$ /N). Finally, to validate the applicability of the optimized prototype, various daily activities were performed to evaluate its dynamic measuring precision of three-dimensional ground reaction force (3-D GRF). The experimental data demonstrate that the prototype sensor can achieve accurate monitoring of 3-D GRF in the strong cross-axis coupling task scenario by applying the isotropy optimization method.