An Improved Bouc–Wen Model Based on Equitorque Discretization for a Load-Dependent Nonlinear Stiffness Actuator

A novel concept of designing compliant actuators called “small load, low stiffness; large load, high stiffness” was applied and proven effective in human-robot interaction in our previous work. This concept was proposed based on a common scenario of interactive action where humans and some animals can adjust the stiffness of limbs in the light of tasks or contacting the environment. Based on this concept, we developed a new load-dependent nonlinear stiffness actuator (LDNSA) with a compact elastic mechanical structure. However, hysteresis is brought in inevitably along with the nonideal elastic mechanism and assembly errors, which limits the dynamic performance of the LDNSA. In this article, an equitorque discretization to implement real-time compensation is proposed to improve the classical Bouc-Wen model, commonly used to compensate for hysteresis, which is proven effective in controlling the performance of the LDNSA. Afterward, a stability analysis of the hysteresis compensation system with impedance control is also discussed as well as to guarantee the safety of the system. Finally, experiments are conducted to evaluate the performance and advantages of the LDNSA with the proposed hysteresis compensation method. The results show that the proposed model can solve the hysteresis of the LDNSA well. Note to Practitioners-Many VSAs have been developed to realize theoretically both high bandwidth and good safety due to completely decoupling stiffness and load. However, there exists some redundancy range that is rarely used in physical interaction with the environment. To avoid this redundancy, a novel load-dependent nonlinear stiffness actuator (LDNSA) was proposed in our previous work. However, hysteresis is brought in via adopting an nonideal elastic element, which is also common in many automated devices. In this article, we proposed a novel compensation algorithm to deal with the hysteresis, which can be carried out in real time. Experimental results show that compared with the Bouc-Wen model and the PD model, the proposed algorithm can solve the hysteresis of the LDNSA better. The proposed hysteresis compensation methodology can improve the performance of a rehabilitation robot for shoulder training with a modularized LDNSA.