# Studies regarding the Use of Pneumatic Muscles in Precise Positioning Systems
## 1 Introduction  
Nowadays, the use of pneumatic muscles is more and more common due to the advantages they have. A pneumatic muscle actuator (PMA) is a flexible tube made of an aramid fiber-reinforced rubber composite material. The elastomer is a chloroprene rubber and forms a matrix that integrates a 3D mesh of inelastic aramid fibers laid out in a diamond pattern. The working principle of a pneumatic muscle is correlated to its construction. Depending on the internal pressure applied to the pneumatic muscle, it increases in diameter and decreases in length. The development of the pneumatic muscle is correlated to the necessity of obtaining alternatives for actuators, such as a simple or diaphragm cylinder, especially in the case of large dimensions, which involves higher weight and difficulties in stroke controlling. Even if the first mention of an artificial muscle was in 1930, when the Russian inventor [PERSON] developed the pneumatic muscle [1], interest in these types of actuators increased, and many other types have appeared. In 2002, the company Festo submitted a patent for \"Actuating means\", a braided pneumatic muscle with robust end-fittings that allow it to be easily commercialized [2]. Later, the companies Shadow Robot Company and Merlin Systems Corporation produced braided pneumatic muscles on a commercial scale [3]. The applications of the pneumatic muscle are mostly found in industrial and medical domains such as industrial manipulators [4, 5], robotic arms [6, 7], and assistive devices for rehabilitation [8, 9, 10, 11]. Pneumatic muscle actuators have numerous strengths, such as low weight, low workspace requirement, high flexibility to construct [8, 12], adaptable installation possibilities, minimum consumption of compressed air, accessibility of different measurements, low cost, and being safe for human use [8, 13]. These strengths are why it is recommended to be used as an actuator instead of electrical or hydraulic ones. A weakness is the nonlinearity caused by the elastic, viscous properties of the inner rubber tube, the compressibility of air, and the structure of the complex behavior of the PMA outer covering [12]. Control accuracy of the pneumatic muscle depends on its behaviors in functioning as inelastic (namely hysteresis) or mechanical. Paper [14] focused on the coupled deformation-diffusion response of fiber-reinforced polymeric gels based on the existence of the embedded fibers in a swellable polymer matrix, leading to anisotropy in the overall behavior. In [15], an experimental characterization and continuum modeling of inelasticity in filled rubber-like materials was presented. The results showed that the viscous stiffness exhibited strain-stiffening behavior during loading/unloading, and that stress-softening while experiencing a successive stretch did not affect the non-equilibrium behavior. [PERSON] and [PERSON] [16] developed a thermo-mechanically coupled large deformation constitutive model that quantitatively captures thermal recovery of the stretch-induced stress softening (Mullins effect) of elastomeric materials. Furthermore, [PERSON] et al. [17] showed that viscoelasticity provides stabilization that delays the onset of instability under monotonic loading and may fully suppress instabilities under sufficiently fast cyclic loading, which may be desirable for many applications. Hysteresis, as a common nonlinear phenomenon that appears in numerous systems, has been studied by numerous researchers. Studies were made on piezoelectric-actuated stages [18; 19], magnetostrictive actuators [20; 21], and pneumatic actuators [22; 23; 24]. In the case of pneumatic muscles, the analysis of force/length hysteresis or pressure/length hysteresis can be made in an isobaric or isotonic contraction test [4; 25]. Some modeling methods have been proposed for establishing the hysteresis phenomenon in the pneumatic muscle actuator analysis. The Maxwell-slip model [26] was used as a lumped-parametric quasi-static model proposed to capture the force/length hysteresis of a PMA.