# A Method for Precise Tracking Control of Pneumatic Artificial-Muscle-Driven Exoskeletal Robot
## 1 Introduction  
Exoskeletal robots for upper limbs combine human physical strength with mechanical power, integrating techniques such as bionics, mechanics, transducing, control, and algorithms in themselves [1; 2; 3], thus becoming intelligent devices that can enhance work efficiency and life quality. In recent years, they have also been intensively researched, both domestlically and abroad [4; 5; 6]. Upper extremity exoskeletons offer several advantages in the field of mechanical boosting, which generally refers to enhancing or augmenting human physical capabilities. By providing mechanical assistance to the upper body, exoskeletons help reduce muscle fatigue. This is valuable in professions that involve repetitive or prolonged use of the upper extremities, such as construction, agriculture, and manufacturing, as it can help prevent overexertion and musculoskeletal injuries. In Europe, three-fifths of workers suffer from work-related diseases, of which 60% are musculoskeletal diseases. In total, 40% of these diseases are upper limb-related. During industrial lifting, workers are required to hold weights above their heads for an extended period. The torque generated by gravity and impounding of the elbows and shoulders of workers weighs 50% of their body weight. Therefore, exoskeletal robots have a significant effect in the domain of industrial lifting and rehabilitation from sports injuries [7; 8]. Most exoskeletal devices use electrical, hydraulic, or pneumatic actuators. Safety, conformability, controllability, and power-weight ratio should be taken into consideration when selecting actuators to assistwith lifting. Many researchers favor electrical motors for their controllability. For example, [PERSON] et al. proposed a novel design of a hand exoskeleton system [9]. The optimization of the exoskeleton device was achieved through a procedure targeting the natural finger workspace and capabilities. [PERSON] et al. proposed an upper extremity exoskeleton mounted on a wheelchair [10]. This new device is dedicated to regular and efficient rehabilitation training for weak and injured people without the continuous presence of a therapist. However, its weight is an obvious downside. Hydraulic actuators have an outstanding power-weight ratio, while possible leaking of hydraulic fluid can cause a lot of problems in medical aseptic environments [11]. In contrast thereto, pneumatic actuators possess a favorable power-weight ratio but cause no medical pollution. A pneumatic muscular actuator (PMA) is light and conformable itself. Such conformability softens the counterforce against resistance. In the meantime, a pneumatic muscle is similar to skeletal muscle in terms of biomechanical biconical results [12]. This renders the PMA the best choice for assisting with goods lifting. The pneumatic muscle assembly consists of three main elements: the outer braided sleeve, the flexible inner bladder, and end-fittings at each of its two ends. This study takes a self-assembled McKibben-style pneumatic muscle as an example, as shown in Figure 1. A PMA operates primarily by inputting pressured air into the bladder, causing it to expand, and applying a radial outward force to the surrounding braided sleeve, which transforms the aforementioned force into axial adduction (or displacement) of the muscle. However, hysteresis, as an inherent characteristic of soft actuators, can seriously affect the accuracy of closed-loop control and practical application [13]. This non-linear characteristic can be observed in the output force through a non-singular and non-convex hysteresis curve [14]. Existing models cannot accurately describe this phenomenon [15], and so far, there is no versatile method to model this hysteresis of soft actuators [16]. However, soft actuators have been more commonly employed on upper limbs in recent years. In 2018, [PERSON] proposed a new 7-DOF upper limb robot exoskeleton [17]. Each arm includes force and torque transducers to detect human motion.