Multiobjective Pareto Optimality of a Cross-Beam Six-Axis Force/Moment Sensor With Genetic Algorithm and Approximate Analytical Model

The size optimization of a cross-beam sensor is an application-specific procedure that focuses on improving sensor properties by designing more compact sensors. Six-axis force/moment sensor technology currently lacks an extensive, fast, and accurate size optimization methodology in common sensor diameters that can check sensor body strain output, size, safety, and vibration response for designing custom sensors. Up-to-date research has benefited the finite-element model, reduced optimized sensor dimensions, and narrowed the dimension range to make optimization feasible. Likewise, prior studies that employed analytical methods disregarded equivalent stresses and natural frequencies. This study utilizes a new analytical model that has higher accuracy in an extensive sensor dimension range and respects design safety and vibration frequency. The new optimization problem formulation aims to maximize strain outputs and minimize sensor diameter. Pareto optimization with nondominated sorting genetic algorithm II (NSGA-II), which provides multiple optimal solutions that favor different force and moment axes where an optimal solution is selected according to the designer’s decision-making, is also compared with the weighted sum and goal attainment method with sequential quadratic programming (SQP). The research aims to design a sensor structure with high structural safety and natural frequency through global optimization. The proposed sensor prototype has 0.46% nonlinearity, 0.48% repeatability, 0.26% hysteresis, 0.42% time drift, and 0.74% crosstalk error, resulting in 1.13% accuracy, and the natural frequency of the sensing body is 4144 Hz. Experimental results show excellent consistency between analytical and finite-element models, indicating the presented optimization process is beneficial to sensor design.