Hybrid dynamic model for shape memory alloy linear and unimorph actuators

Shape memory alloy morphing actuators are a type of soft actuator with many attractive properties. These actuators exhibit large deformation, small form factor, self-sense ability, and physical reservoir computing potential, while also being inexpensive. These morphing actuators are composed of active shape memory alloy wires and a passive base layer that is used to magnify the overall deflection. Although morphing actuators have great potential, the modeling of shape memory alloy 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 & thermal modeling for the shape memory alloy with a dynamic Cosserat nonlinear beam model. This hybrid model is benchmarked against linear and morphing experimental actuators. The model resulted in a root mean squared error of 1.48 mm and 1.63 mm for the morphing actuator configuration for two different actuators. This model can expand the capability and design of novel morphing actuators for a designed deformation profile for use in soft robotics.

Methods
An Edgertronic SC2+ camera (Sanstreak Corp., San Jose, CA) is used to record the movement of the actuator for both the linear and bending actuation at a frame rate of 100 Hz. Reflective markers are adhered to the actuators in order to track their motion. For the linear SMA actuator, the reflective makers are placed on the ends of the wire in order to measure the length of the SMA wire during testing. For the bending actuators, reflective markers are adhered on the side of the actuator at the locations of the offset holders. These markers are used to track the configuration of the actuator at locations of approximately 10 mm. An N6705C DC power analyzer (Keysight, Santa Rosa, CA) was used to supply the input power to heat the SMA wire. This power supply also has a built in waveform generator and data logger. The waveform generator was used to test the results for a variety of input current waves for the linear actuator. The data logger recorded the current output of the device, which is then used as an input for the dynamic model. Visual markers were used to sync the power data with the visual data from the camera. The camera begins to record and then the input waveform is started. When the waveform begins recording, an LED light is triggered "ON''. The LED is in view of the camera and used to sync the start of the input power data with the frame from the high speed camera at which the input waveform began. MATLAB's Image Processing Toolbox was used to process the visual data from the camera and calculate the x and y positions of the reflective markers attached to the actuators at every frame.