Bayesian Optimization with Multi Constraints for Planar Rotary Spring Design

This paper combines Bayesian optimization with the theoretical mathematical model to propose a new and efficient design and optimization algorithm for a planar rotary spring to be included in the design of a series elastic actuator. Although the planar rotary spring has a compact structure, the complexity of its structure makes it challenging to design such a kind of spring that meets the required torque and stiffness. To overcome this challenge, the torsional stiffness model of a planar rotary spring is established based on the bending beam theory, and is solved by the generalized shooting method as the evaluation method. Next, Bayesian Optimization is used to optimize the arm's Archimedean spiral-based trajectory with the goal of finding the optimal design that minimizes the spring mass. The simulation and experimental results showed the validity of the proposed method. Compared with the initial valid parameter, the mass of the optimized results is reduced by 92.04% with 40 iteration steps. The prototype of the optimized model weights 10g. The stiffness error between the experimental calibration and finite element method (FEM) simulation is 3.05Nm/rad. The study highlights the potential efficiency of designing the planar rotary springs with complex curve structures by combining Bayesian Optimization and mathematical models.