# Design and Control of a Pneumatic Muscle Servo Drive Containing Its Own Pneumatic Muscles
## 1 Introduction  
A pneumatic muscle is a type of single-acting cylinder which, under the influence of an increase in internal pressure, increases its volume by increasing its diameter while reducing its length. Changing the length of the cylinder is used as a working movement [1]. The basic physical quantities describing the behavior of a muscle in a steady state are internal hypertension \(p\) muscle length \(l\) and the force generated by the \(F\) muscle. In 1957, Dr. [PERSON]. [PERSON] used the pneumatic muscle he had developed to propel his limbs. This muscle consisted of an elastic bladder placed freely inside a braid of inextensible fibers. At the ends, the braid and the bladder were connected which allowed for the transfer of the forces generated by the muscle and the working medium, which was carbon dioxide. This muscle is often referred to as \"[PERSON]'s muscle\". In 1980, the Bridgestone Rubber Company commercialized the pneumatic muscle on a massive scale by introducing a muscle that was an improvement on Dr. [PERSON]'s design. Currently, pneumatic muscles are mainly offered by two companies: since 1987, Shadow Robot Company has been producing and selling muscles modeled on the [PERSON] project, while in 1999, Festo, a well-known manufacturer of pneumatic devices, introduced pneumatic muscles that could be tailored to individual applications. It is fundamentally different in structure from [PERSON]'s muscle. In the Festo project, the braid and the rubber bladder are fused along the entire length of the muscle. The view of the muscle in this version is shown in Figure 1. This solution significantly increases the resistance of the muscle to mechanical damage and increases its durability. However, it has the disadvantage of a lower relative shortening of the muscle and, hence, less effective working movement is generated by the muscle. Work is underway in many research centers around the world to analyze artificial pneumatic muscles and to determine mathematical models describing their behavior. These models can be broadly divided into static and dynamic, as well as into positional models, where the key is to determine the length of the muscle, and force models, where it is crucial to determine the force generated by the muscle. The first stage of the analysis of pneumatic muscles is often the determination of their static characteristics in the form of isobaric, isotonic and isometric characteristics and their dynamic characteristics in the form of thedependence of the force generated by the muscle on time as the object's response to a step change in internal pressure. The methodology of their determination and the characteristics of the muscles modeled on the [PERSON] design, Festo muscles and many original designs are presented, among others, have been previously described [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12]. In the article [5], [PERSON] and his team presented the research methodology and determined the static characteristics: isobaric, isotonic and isometric of Festo pneumatic muscles and Shadow Robot Company muscles. In publications describing the static models of muscles, the research mainly concerns the determination of the relationship between internal overpressure, the length of the muscle and the force generated by the muscle in relation to the geometric parameters of the muscle. Research was also carried out on the determination of dynamic models of both [PERSON]'s and Festo's muscles, as well as on other structures developed in various research centers, and on the development of positional and force control methods using the presented mathematical models. These issues were extensively discussed, inter alia, in the research of [13; 14; 15; 16; 17; 18]. Due to the significant friction between the fibers of the braid and between the braid and the rubber bladder, there is a hysteresis phenomenon in the muscles modeled on the [PERSON] design. It concerns both the shortening of the muscle and the force generated by it.