A Power-Function-Based Hysteresis Modeling Method for Precise Torque Control of Nonlinear Compliant Actuators

Compliant actuators are suitable for reliable human–robot interaction applications due to their inherent flexibility and safety. However, a limitation of this type of actuator is that nonlinear hysteresis exists especially for those actuators with nonlinear stiffness, which makes accurate system modeling difficult and further degrades force/torque tracking performance. Most hysteresis models are developed with black-boxes and the parameters of these models are obtained with optimization algorithms. However, they are applicable to accurate hysteresis modeling only for a specific hysteresis nonlinear curve, lacking the versatility when dealing with nonlinear torque curves with multiple loops at different amplitudes. In this article, a compliant actuator with nonlinear stiffness is developed and a novel hysteresis modeling method is proposed for the modeling of hysteresis curves with multiple loops; thus, a precise torque control of the actuator can be achieved. In our modeling method, a “virtual deformation” concept is defined to linearize the torque curves of the actuator. The torque curves are segmented into ascending, descending, and transition subcurves. A novel model based on a power function is designed with the model parameters adjusted to fit the multiple torque curves at different amplitudes. Experimental results show that the root-mean-square errors of the estimated torque are reduced by 53.1% and 9.4% and the computation cost is reduced by 95.2% and 66.7% when compared with the nonlinear backlash model and the modified Maxwell-slip-based model, respectively. Tests of the torque tracking verify the performance of our proposed inverse model.