Fractional-order Mathematical Model of Pneumatic Muscle Drive for Robotic Applications

Introduction

Pneumatic muscles are becoming increasingly attractive robotic drives for those applications in which stiffness of a kinematic chain have to be regulated. The stiffness coefficient of the muscle depends mainly on the level of pressure and its initial tension. These values describe the point of work on the static characteristics of the drive. Such a drive could be treated as a regulated spring. However, from the dynamic point of view the muscle is something more than a simple spring. Generally, three-element models (of the type R, L, C) are used in the literature to present the dynamical effects that characterise the drive [6]. It leads to second order differential equations that describe the features of the single muscle or the whole drive in the neighborhood of the static point of work. Sometimes this simple model is not sufficient and some phenomena of the muscle are modeled by additional inertial elements of the first or second order, and the model is characterized by three or four parameters. Precisely speaking, the muscle has to be treated as an element with distributed parameters and to describe its phenomena, partial differential equations could be used. Unfortunately, such an analytical model does not exist in a general case. A finite element method can be applied to derive a numerical model convenient for specific purposes [10].