# Characterization and Joint Control Study of Pneumatic Artificial Muscles
## 1 Introduction  
The pneumatic artificial muscle (PAM) is a pneumatic actuator with biomimetic muscle properties, the original concept of artificial pneumatic muscle was first proposed by [PERSON] in the 1950s [1]. Because its structure is mainly made of rubber, it has no acceleration break point during the filling and deflating process; this property allows flexible change for pneumatic muscle. Due to the cushioning effect of rubber, pneumatic muscles are widely used in medical assistance. Pneumatic artificial muscles are characterized by an enormous power/mass ratio and high flexibility and can be widely used to drive systems with strongly nonlinear motion characteristics; moreover, their inherent flexibility and limited maximum contraction make them very safe and suitable for rehabilitation applications, such as ankle rehabilitation robots and agricultural picking robots [2, 3]. Among them, [PERSON] [4] from Huazhong University of Science and Technology, China, proposed the concept of using this flexible woven actuator system as a pneumatic element and thus put it into the category of pneumatic transmission systems for pneumatic control to build and control this model. They also described the dynamic and static characteristics of the pneumatic artificial muscle system using fluid dynamics and thermodynamics theories. They summarized and proposed that the motion of the pneumatic artificial muscle system can be divided into four processes: the isovolumetric expansion process, the expansion-contraction process, the exhaust extension process and the isovolumetric exhaust process. This segmental approach to the study simplifies the complex pneumatic muscle movements and facilitates modeling pneumatic muscle trajectories. The pneumatic manual muscle is flexible and non-linear, especially when the drive is at low operating pressures and loads. This woven elastic drive is mechanically and mathematically challenging to model accurately. Moreover, because of this non-linearity between pressure and output force, it makes the pneumatic artificial muscle a pneumatic element, and from its emergence to its application, it has gone through a long historical process [5]. In the 1990s, [PERSON] [6] of Harvard University developed an ideal mathematical model ofpneumatic artificial muscles based on the energy conservation law combined with the thermodynamic perfect gas equation of state. The scholar [PERSON] [7] extended the above model and converted it into a new model. However, these two models of pneumatic artificial muscles ignore the effects of friction at the ends of the pneumatic artificial muscles and the elastic change of the material when considering them. Therefore, it leads to a large discrepancy between this ideal model and the actual model. As the application of pneumatic artificial muscles spreads, the research on its modeling has increased. This aspect was investigated by [PERSON] et al. [8], researchers at the U.S. Air Force Laboratory. During the experiment, the pneumatic muscle is equated to a spring, but the stiffness of the equivalent spring can be changed. During the inflation and deflation of pneumatic muscles with different stiffness, a model of pneumatic muscles was fitted by synthesizing a large amount of experimental data. However, due to the other models and manufacturers, each pneumatic muscle requires many experiments to fit the above model before use, which also limits the application of the method. Scholar [PERSON] [9] has also recently developed a mathematical model of pneumatic artificial muscles containing four parameters, which combines empirical and physical theories to explain the connection between static forces and pressures and the stretchability of pneumatic artificial muscles. However, it is also true that this mathematical model only applies to the new Festo air muscles derived from the common McKibben artificial muscles and cannot be used on a large scale and universally to satisfy the general pneumatic artificial muscles.