# Modeling of Walking-Gait Parameters and Walking Strategy for Quadruped Robots
## 4 Experimental Results and Analysis
### Analysis of Static-Gait Experiment  
The first step was a static-gait experiment. In the experiment, data from each joint was collected and compared with theoretical values, aiming to achieve the planned theoretical values and achieve the planned gait. The speed tests were 3.5 km/h and 4.0 km/h, respectively. According to the static-gait planning, Figure 22 shows the theoretical curve of the changes in the joint angles of each limb during a period. The variation range of the hip joint was [45\({}^{\circ}\), 70\({}^{\circ}\)], and the variation ranges of the knee and ankle joints were [85\({}^{\circ}\), 100\({}^{\circ}\)], both within the predetermined range of structural design. Figure 23 shows the joint angles obtained through data processing based on eight angle sensors and four encoders. The angle sensor measured the angle value between the knee and ankle joints, with a voltage range of [0, 5] (V). The measured angle was [0\({}^{\circ}\), 300\({}^{\circ}\)]. If the collected data is \(a\), then the corresponding angle \(\theta\) is shown in Equation (31):  
\[\theta=\frac{a}{5}\times 300 \tag{31}\]  
The encoder measured the hip joint angles of the four limbs. Due to the motor deceleration ratio of 81, if the collected data is set to \(b\), then the hip joint angle \(\theta\) is Equation (32):  
\[\theta=\frac{b}{4096}\times 360\times\frac{1}{81} \tag{32}\]  
The data collected by each sensor can be obtained from Equations (31) and (32) to obtain the angle values of each joint, as shown in Figure 23.  
Figure 21: Additional components of the experimental system. (**a**) treadmill; (**b**) bracket. Figure 20: Structure of the developed bionic-robot dog. The dotted line in the figure represents the theoretical data of each joint angle, and the solid line represents the experimental data of each joint angle. It can be seen from the figure that the experimental data of the hip joints of each limb was fluctuating near the theoretical data, and the coincidence degree was very high. This was because the angle of the hip joint was processed using the data collected by the encoder, and the error was caused by the performance of the motor, and the error value was very small. Therefore, the rotation angle of the hip joint obtained in the experiment in the figure basically coincided with the theoretical value. The angle data of the knee and ankle joints of the four limbs were collected by the angle sensor. It can be seen from the theoretical analysis that, due to the characteristics of the parallel four-bar mechanism, the angle values of the knee and ankle joints were equal, and the experimental data were consistent with the theoretical analysis. The foot trajectory of the bionic-robot dog was the result of the interaction of various joint angles. The experimental data of the joint angle were close to the theoretical values, which means that the experimental values complied with the planned foot trajectory and realized the planned static gait. The change in attitude angle during static-gait motion was analyzed. Attitude angle is the angle between the ground coordinate system and the center-of-mass coordinate system, including the heading angle, pitch angle, and roll angle, which reflects the attitude change of the robot during walking. The angle of rotation of the center-of-mass coordinate system around the axis of the vertical direction of the ground coordinate system is the heading angle, and it is positive when the head of the bionic-robot dog is deflected to the right. The angle of rotation around the axis on the right side of the body is the pitch angle, and it is positive when the head of the bionic robot is above the horizontal plane. The angle of rotation around the axis of the forward direction is the roll angle, and it is positive when the right side of the body is tilted upward. Figure 24 is the pose data of the bionic-robot dog collected by the inertial-force measurement unit, which show the changes in pitch angle, roll angle, and heading angle in two cycles.