# A Method for Precise Tracking Control of Pneumatic Artificial-Muscle-Driven Exoskeletal Robot
## 4 Results and Discussion
### Discussion of Intermediate Variables in the Process of Upper Limb Exoskeleton Transportation  
(1) Load Variation Analysis. In the process of carrying objects using the Upper Limb Exoskeleton, the interaction force and friction force between the load and the Upper Limb Exoskeleton will change with a change in the elbow joint angle. In order to maintain the balance of objects, the torque  
Figure 11: Schematic diagram of the Upper Limb Exoskeleton assisting process. provided by the elbow joint will also change. According to the right-hand rule, the torque is negative, as shown in Figure 12a. At the initial stage of handling, the torque provided by the elbow joint fluctuates slightly and changes gently. After 2 s, the torque provided by the elbow joint increases approximately in direct proportion with the increase in the angle. After 4 s, the torque changes tend to be gentle and tend toward a certain value, and the motion curve is smooth, indicating that the torque fluctuation during the movement of the elbow joint is small and has no excessive impact on the arm. According to the principle of torque equivalence and the inverse model of pneumatic muscle output force, the torque of the elbow joint is converted into the pneumatic muscle pressure value. As shown in Figure 12b, the pneumatic muscle pressure value and the torque of the elbow joint show similar changes. (2) Kinematic and Dynamic Simulation Analysis. In the process of carrying the Upper Limb Exoskeleton, the control object is the pneumatic muscle pressure. The change in pneumatic muscle pressure is transformed into the length change of the pneumatic muscle, and then, the angle of the elbow joint is changed to drive the movement of the elbow joint. The change in the length of the pneumatic muscle during the assistance process is shown in Figure 13a. At the beginning, the pneumatic muscle is at its original length, so the change is 0. Then, with the process of handling, the pneumatic muscle begins to compress, and the compression changes gently at the beginning. After 0.5 s, the change speed increases, and the speed reaches the maximum at 2.5 s. After that, the approximate symmetrical speed change table is small, and tends to be flat after 4.5 s. It is proven that when the elbow joint angle is changed by the quintic polynomial, the aerodynamic muscle shape variable also changes similarly. The length change process of the pneumatic muscle can be obtained by calculating the sum of the shape variable and the original length of the pneumatic muscle, as shown in Figure 13b. The change speed and acceleration of pneumatic muscle length are shown in Figure 13c,d. The output of the control system in this paper is the control torque that needs to be compensated by the elbow joint in the process of carrying the Upper Limb Exoskeleton, and its change within the control time is shown in Figure 14. It can be seen from the control rate that the elbow joint torque needs to be compensated according to the difference between the target angle and the actual angle. The image is a smooth curve, which proves the compensation performance of the control system. The control torque of the elbow joint changes gently at the initial time, because the load is predicted at the initial time, the elbow joint provides the corresponding torque, and the control torque also changes gently due to the gentle change in the elbow joint angle, which changes rapidly after 1.5 s and tends to be constant after 4.5 s. The corresponding pneumatic muscle control air pressure process according to the principle of torque equivalence and the inverse model of pneumatic muscle  
Figure 12: Load change diagrams of left and right arms during handling. **(a)** Load torque process of elbow joint. **(b)** Pneumatic muscle loading pressure process. output force is shown in the figure. At the beginning, because of the load prediction, the elbow joint is offset by the load force brought about by the power, so the initial control air pressure value is 0.