This paper introduces a bipedal robot joint constructed from pneumatic artificial muscles. This joint utilizes the flexibility of pneumatic artificial muscles to effectively control the impact of the landing foot during rapid walking or running in bipedal robots. The working principle of the pneumatic artificial muscles and the hardware architecture of the joint system constructed from them are detailed. A control software system built based on this hardware joint is also introduced. Bipedal robots have better mobility in unstructured environments compared to conventional mobile robots, thus attracting widespread attention from researchers. Controlling robots to achieve rapid walking speeds and running gaits remains one of the most challenging problems in the field of bipedal robotics. When a robot walks or runs rapidly, the swinging foot generates a large impact force upon landing. This force causes the landing foot to bounce or causes a large jump at the zero-moment point, resulting in reduced stability margin and falls. This phenomenon is called the impact effect, and it is a factor limiting the improvement of walking speed and running in bipedal robots. Pneumatic artificial muscles are a new type of actuator developed in recent years, with McKibben-type pneumatic muscles being the most widely used. It possesses advantages such as compliance, a high power-to-mass ratio, and similar force and length characteristics to human muscles. Due to its controllable compliance, pneumatic artificial muscles can effectively solve the impact problem of landing feet in bipedal robots. Therefore, using pneumatic artificial muscles as actuators for bipedal robots shows great promise. However, artificial muscles exhibit highly nonlinear characteristics and hysteresis, making their construction and control difficult. Currently, research on bipedal robots based on pneumatic artificial muscles is still in its early stages, with only a few bipedal robot projects having conducted research in this area. This paper utilizes MeKibben pneumatic artificial muscles to construct a single-degree-of-freedom artificial joint similar to a biological antagonistic joint. The hardware of this system includes a pneumatic drive subsystem, a sensor subsystem, and a control subsystem. A software system was built on this hardware system to achieve trajectory tracking and control of this artificial joint. Based on the work in this paper, we can further study and solve the modeling and control problems of pneumatic artificial muscles and joints, laying the foundation for the design and construction of bipedal robots based on pneumatic artificial muscle actuators. 1. Hardware and Software Design of Pneumatic Artificial Muscle Joint System 1.1 Pneumatic Artificial Muscle McKibben The McKibben pneumatic artificial muscle is a flexible pneumatic actuator invented by American physician Joseph L. McKibben and named after him. The main body of the McKibben pneumatic artificial muscle consists of an outer woven mesh and an inner elastic rubber tube. Its structure is shown in Figure 1. Figure 1 shows the muscle structure, where Pi is the input air pressure, the magnitude of which is controlled by the controller according to the actual working conditions. When the input air pressure increases, the inner rubber tube expands. Due to the high stiffness of the outer woven mesh, it can hardly stretch, limiting the muscle to radial deformation (diameter increases, length shortens), generating axial contractile force; while when the input air pressure Pi decreases, the artificial muscle stretches (relaxes), and the muscle stiffness and driving force decrease accordingly. The muscle stiffness can be achieved by controlling the air pressure inside the rubber tube. This muscle has variable stiffness characteristics and can be equivalent to a variable stiffness spring. 1.2 Single-DOF Joint System Since pneumatic artificial muscles can only provide unidirectional driving force, two muscles are needed to form an antagonistic rotational joint in a manner similar to biological antagonists to achieve force closure of the manipulator arm. This paper utilizes McKibben pneumatic artificial muscles as actuators to build a single-DOF antagonistic joint system. The hardware of this system consists of a pneumatic drive subsystem, a sensor subsystem, and a control subsystem. The system structure diagram is shown in Figure 2. 1.2.1 Pneumatic Drive Subsystem The pneumatic drive subsystem consists of an air source, a pressure servo proportional valve, McKibben pneumatic artificial muscles, and the mechanism. Compressed gas with a pressure of 0.6–0.9 MPa is provided by the air source. The compressed gas is delivered into the pneumatic artificial muscle through a conduit via the servo proportional valve. Each muscle is connected to a servo proportional valve and has an outlet valve and an inlet valve. The gas pressure in the muscle can be controlled by controlling the voltage applied to the servo proportional valve. The pressurized pneumatic muscle outputs contractile tension and drives the joint rotation of the mechanism. Therefore, the joint torque required for trajectory tracking can be achieved by controlling the muscle pressure. The McKibben pneumatic artificial muscle used in this system is the FESTO MAS-20-300N model, with a working pressure range of 0–0.6 MPa, a maximum working frequency of 3 Hz, a maximum contraction of 25% of the muscle length, a theoretical force of 300 N at 0.6 MPa, and a repeatability of less than 1%. The pressure servo proportional valve receives the voltage input from the control terminal and controls the air pressure inside the muscle by adjusting the inflation valve and the air intake valve. This system uses the SMC ITVOO5C-2ML model pressure proportional valve. The input range of this valve is 0–5 VDC, and the output pressure is between 0.001 and 0.9 MPa. 1.2.2 Sensor Subsystem The sensor subsystem consists of a force sensor and a linear displacement sensor. The linear displacement sensor can measure the amount of muscle contraction, and based on this contraction, trajectory tracking control can be performed using muscle and joint models. Force sensors measure muscle tension. Based on the linear relationship between this tension and joint torque, the joint torque can be calculated, thus completing the servo closed-loop control of the joint. The force sensor used in this system is the BK-2F high-precision S-shaped force/weighing sensor from the 7O1 Institute of China Aerospace Science and Technology Corporation. Its maximum force measurement range is 80kg, with an accuracy of 0.05%. After being amplified by a TS-2 amplifier, the output voltage range is -5V to +5V. The linear displacement sensor uses a WDL-type straight-slide conductive plastic potentiometer. 1.2.3 Control Subsystem The control subsystem consists of an industrial control computer (IPC), an A/D acquisition card, and a D/A converter card. The software control system runs on the industrial control computer and converts digital control quantities into analog quantities through a D/A converter. This analog quantity is used to control the output air pressure of the pressure servo proportional valve. The A/D converter acquires data from the force sensor and the linear displacement sensor and provides the industrial control computer with digital signals that can be processed by software. The D/A converter used in this system is a PCL-726 6-channel analog output card. It provides six 12-bit double-buffered analog output channels to meet the needs of muscle servo control. The MD acquisition card uses a PCL-813B 12-bit 32-channel A/D card, which provides 32 channels of isolated DC voltage measurement with accuracy sufficient for system requirements. 1.3 Software System The pressure of two muscles in the anterolateral joint driven by the pneumatic artificial muscle is the control variable of the system. Since the system controls the motion of one degree of freedom through two free variables, it constitutes a redundant drive system. It can be proven that this system can independently control the joint torque and joint stiffness. The former is related to the pressure difference between the two muscles, and the latter is related to the sum of the muscle pressures. By controlling the joint torque, accurate joint trajectory tracking can be achieved, while by controlling the joint stiffness, the impact of the landing foot and system energy consumption can be reduced. This paper develops the control software and operation interface for the pneumatic artificial muscle joint system in an industrial control computer. Through this software system, functions such as setting muscle model parameters, stable closed-loop control, and real-time display and recording of sensor return values ​​can be realized. The main part of the software includes a trajectory planning module and a pressure control module. The trajectory planning module implements the upper-level joint trajectory planning and calculates the joint torque required to achieve the desired joint trajectory based on the joint model. The pressure control module performs the lower-level calculation, and its input is the desired joint torque obtained from the upper-level planning. The pressure calculation module calculates the pressure required to control muscle movement based on the actual model of the pneumatic artificial muscle, and its output is the desired muscle pressure value. The intelligent PID control algorithm module performs intelligent PID control based on this desired pressure value and the actual muscle pressure data collected by A/D converter, thereby realizing closed-loop control. Its output is converted into the actual control voltage output to the hardware system through numerical and D/A circuits. The block diagram of the software system is shown in Figure 3. 2. Experiment and System Application 2.1 Pneumatic Joint System Model In order to achieve accurate servo control of the antagonistic joint driven by the pneumatic artificial muscle built in this paper, the pneumatic artificial muscle must first be modeled. Due to its nonlinear and time-varying characteristics, and the hysteresis phenomenon during operation, the MeKibben pneumatic artificial muscle is difficult to model and control. Most existing studies on McKibben pneumatic artificial muscles use the theoretical model proposed by Chou and Hannaford based on the principle of virtual work. This model provides an ideal estimate of muscle output; however, its direct application to actual control does not yield good results. In this study, the three-dimensional muscle dynamics model proposed by Reynolds et al. is adopted, approximating the pneumatic muscle as a dynamic system composed of a nonlinear damping factor, a nonlinear spring factor, and a nonlinear contractile force factor connected in parallel. The model equation is: where x is the muscle contraction length, and x=0 when the muscle is fully extended. K0 and K1 are spring factor coefficients, B0 and B1 are damping factor coefficients, and F0 and F1 are contractile force factors. For the pneumatic artificial muscle used in this paper, the parameters of the three-dimensional muscle model in equation (1) can be accurately estimated through experiments on this system. When the muscle pressure p is between 200 kPa and 650 kPa, the model coefficients obtained through experiments can achieve satisfactory approximation results. Using this three-dimensional muscle model, the software system introduced in this paper performs closed-loop trajectory tracking control on the joint, and its control accuracy is better than that of the traditional theoretical model. 2.2 System Application This paper applies the system to a single-DOF antagonistic joint system for robots, which utilizes McKibben pneumatic artificial muscles with flexible actuators as the driving source. This allows for further research on the modeling and control of McKibben-type pneumatic artificial muscles. Through experiments on this system, and based on accurate estimation of the ternary muscle model parameters, closed-loop joint trajectory tracking control was achieved using the control software system implemented in this paper. Further work will focus on two key issues based on the existing platform and closed-loop control method. First, we will study trajectory tracking control with controllable joint stiffness. Optimizing the joint stiffness of this redundant system will allow the robot to reduce energy loss by better utilizing the passive dynamic characteristics of its joints. Second, we will study how to reduce the impact of impacts by controlling joint stiffness, thus providing theoretical preparation for building bipedal robots driven by pneumatic muscles.