Accurate multivariable arbitrary piecewise model regression of McKibben and Peano muscle static and damping force behavior

Abstract

Machines that efficiently and safely interact with the uncertainty of the natural world need actuators with the properties of living creatures’ muscles. However, the inherent nonlinearity of the static and damping properties that the most promising of these muscle-like actuators have makes them difficult to control. Our ability to accurately control these actuators requires accurate models of their behavior. One muscle-like actuator for which no accurate models have been specifically developed is the Peano muscle. This paper presents and validates a model generation algorithm, multivariable arbitrary piecewise model regression (MAPMORE), that produces accurate models for predicting the static and damping force behavior of Peano muscles, as well as of the popular McKibben muscle. MAPMORE builds a training data processing, muscle-specific model term dictionary, and piecewise function fusion framework around Billings et al's forward regression orthogonal least squares estimator algorithm. We demonstrate that MAPMORE's static and damping force models have a normalized root mean square error (NRMSE) of 48%–88% of the NRMSE of the most accurate of Peano and McKibben muscles’ existing models. The improved accuracy of MAPMORE's models for these artificial muscles potentially aids the muscles’ ability to be accurately controlled and hence is a step towards enabling machines that interact with the real world. Further steps could be made by improving MAPMORE's accuracy through the addition of hysteresis operator and lagged terms in the damping force dictionary.