Optimization of Stiffness to Achieve Increased Bandwidth and Torque Resolution in Nonlinear Stiffness Actuators

Nonlinear stiffness actuators with coupled stiffness and load can achieve a tradeoff between high bandwidth in high stiffness and high torque resolution in low stiffness, but numerous studies have focused on the implementation of novel mechanical actuator structures with nonlinear stiffness rather than optimization of the stiffness values to improve the actuator performances. Designing the optimal stiffness profile to simultaneously achieve increased control bandwidth and torque resolution is a critical problem that needs to be resolved. This paper investigates this problem, proposes a quantized comprehensive performance index the perceptivity and responsiveness index (PRI), and achieves increased control bandwidth and torque resolution using a common feedback controller. Minimizing PRI enables nonlinear stiffness actuators to achieve optimal stiffness profiles. Afterward, an optimal stiffness curve and corresponding feedback control gains are obtained for a load-dependent nonlinear stiffness actuator (LDNSA) based on the proposed methodology. Simulations and experiments based on the LDNSA are conducted at the optimal stiffness to verify the proposed method. Remarkably, the results show that the LDNSA with optimal stiffness yields high comprehensive performance including increased bandwidth in the case of low stiffness and increased torque resolution in the cases of large load.