Data-Driven Position and Stiffness Control of Antagonistic Variable Stiffness Actuator Using Nonlinear Hammerstein Models

In this paper, an optimal PID controller is introduced for an antagonistic variable stiffness actuator (AVSA) based on Hammerstein models. A set of Hammerstein models is developed for the AVSA using the voltage difference method. For each stiffness level, linear and nonlinear Hammerstein models are identified using the least squares method. Experimental results confirm that the outputs of the Hammerstein models fit the measured data better than linear models, as Hammerstein models can incorporate nonlinear effects such as friction. A genetic algorithm is utilized to find optimal PID gains for different stiffness levels and reference position amplitudes. The final gains are obtained by linearly interpolating the optimal gains obtained. To demonstrate the effectiveness of the proposed design, several scenarios with different reference positions and stiffness profiles are provided. Specifically, square, sinusoidal, and sawtooth waves are used for reference positions and stiffness values. The robustness of the proposed approach is further analyzed by applying a disturbance force on the actuator link. The results are compared with the linear method, showing that the proposed design can handle soft transitions in stiffness variation and ensure perfect tracking.