Hybrid dynamical modeling of shape memory alloy actuators with phase kinetic equations

Shape memory alloy morphing actuators are a type of composite soft actuator with many attractive properties such as large deformation, small form factor, self-sensing ability, and physical reservoir computing potential. These actuators are composed of active shape memory alloy wires and a passive material to magnify the overall deflection. However, the dynamic modeling of these actuators is difficult due to both shape memory alloy characteristics and the nonlinearity of the passive layer. Here, a hybrid dynamical model is proposed that couples the phase kinetics and thermal modeling for the shape memory alloy with a dynamic Cosserat beam model. This hybrid model is benchmarked against experimental linear and morphing actuators resulting in a root mean squared error of 0.87 mm for the linear actuator and root mean squared error of 1.34 and 1.42 mm for the two morphing actuator configurations evaluated in this work. This model applies continuous phase kinetic equations in a comprehensive hybrid dynamical model to accurately simulate the hysteretic transition of the alloy, which is then coupled to a high deformation beam model. This work can expand the capability and design of novel morphing actuators to achieve specified dynamic characteristics for increased application in robotic fields.