Self-Sensing Variable Stiffness Actuation of Shape Memory Coil by an Inferential Soft Sensor

Self-sensing actuation of shape memory alloy (SMA) means to sense both mechanical and thermal properties/variables through the measurement of any internally changing electrical property such as resistance/inductance/capacitance/phase/frequency of an actuating material under actuation. The main contribution of this paper is to obtain the stiffness from the measurement of electrical resistance of a shape memory coil during variable stiffness actuation thereby, simulating its self-sensing characteristics by developing a Support Vector Machine (SVM) regression and nonlinear regression model. Experimental evaluation of the stiffness of a passive biased shape memory coil (SMC) in antagonistic connection, for different electrical (like activation current, excitation frequency, and duty cycle) and mechanical input conditions (for example, the operating condition pre-stress) is done in terms of change in electrical resistance through the measurement of the instantaneous value. The stiffness is then calculated from force and displacement, while by this scheme it is sensed from the electrical resistance. To fulfill the deficiency of a dedicated physical stiffness sensor, self-sensing stiffness by a Soft Sensor (equivalently SVM) is a boon for variable stiffness actuation. A simple and well-proven voltage division method is used for indirect stiffness sensing; wherein, voltages across the shape memory coil and series resistance provide the electrical resistance. The predicted stiffness of SVM matches well with the experimental stiffness and this is validated by evaluating the performances such as root mean squared error (RMSE), the goodness of fit and correlation coefficient. This self-sensing variable stiffness actuation (SSVSA) provides several advantages in applications of SMA: sensor-less systems, miniaturized systems, simplified control systems and possible stiffness feedback control.