Three-Dimensional Hysteresis Modeling of Robotic Artificial Muscles with Application to Shape Memory Alloy Actuators

Being inherently compliant, the robotic artificial muscles are increasingly popular in applications such as safe human-robot interaction, legged robotics, prostheses and orthoses, and soft robotics. Their full utilization is often challenged by the coupled hysteresis among input, strain, and tension force. Although conventional two-dimensional hysteresis models are available, no prior studies on three-dimensional hysteresis models with coupled inputs have been reported for robotic artificial muscles. This paper presents a new approach to capturing the threedimensional hysteresis of robotic artificial muscles by embedding a two-stage Preisach model. The proposed method is applied to shape memory alloy (SMA) actuators. Since direct temperature measurement of the SMA actuator is not available, the concept of temperature surrogate, representing the constant voltage value in Joule heating that would result in a given temperature at the steady-state, is adopted. The proposed approach is utilized to capture the hysteresis among temperature surrogate, contraction length, and force of an SMA actuator. Model verification is further conducted. For comparison purposes, two modeling approaches, namely, the Summed Preisach and the Linear Preisach, are also realized. Experimental results demonstrate that the proposed scheme can effectively characterize and estimate the three-dimensional hysteresis in SMA actuators. This study can be applied towards other robotic artificial muscles such as McKibben actuators and Super-coiled Polymer actuators.