## 6 Experimental Analysis  
To certify the effectiveness of the proposed control strategy in practical robots, the designed controller was applied to a hydraulic quadruped robot developed by the Hydraulic Quadruped Robot Joint Lab of Harbin University of Science and Technology. The experimental platform of the hydraulic quadruped robot is illustrated in Figure 10. The electro-hydraulic servo valve was the SFL212F-12/8-21-40 two-stage force feedback asymmetric servo valve, produced by the 18 th Research Institute of the First Academy of China Aerospace Science and Technology Corporation (Beijing, China). The displacement sensor was the LVDT-PA1 HL60X sensor produced by Fuxin Lisheng Automatic Control Co., Ltd. (Fuxin, China). The force sensor was the WMC-3000 Sensor produced by the Interface Company of America (Phenix City, AL, USA). The IMU was the XW-G15615 produced by Starneto (Beijing, China). In the experiment, the duty cycle of the robot pace gait was 0.5; that is, the swing phase and the support phase were equal in time. The period time was 0.8s, the stride length was 200 mm, and the maximum height of the foot was 50 mm. The experimental process of pace gait motion of the hydraulic quadruped robot is shown in Figure 11. In the picture, the red solid point represents the supporting leg, and the blue one represents the swinging leg. During a motion cycle, a pair of legs of the hydraulic quadruped robot went through lifting, falling and supporting stages. Figure 11: The pacing gait motion of the hydraulic quadruped robot in a gait period. (**a**) Initial stage. (**b**) RF and RH leg are in the support stage. (**c**) All legs are in the supporting stage. (**d**) RF and RH leg are in the lifting stage. (**e**) RF and RH legs are at their highest points. (**f**) Touch down stage. Figure 10: The test platform of hydraulic quadruped robot. The variations of attitude angle and attitude angular velocity of the robot trunk detected by IMU are shown in Figures 12 and 13, respectively. The curves of original controller represent the experimental data obtained without the proposed controller. It only planned the foot trajectory based on the kinematic analysis of the single leg of the quadruped robot, but did not plan and control the centroid of the robot trunk. The curve of centroid-based controller represents the experimental data obtained with the proposed controller. The proposed controller includes foot trajectory planning, and the trajectory planning of the trunk centroid and centroid control of the trunk. During the motion of the hydraulic quadruped robot in pacing gait, since the right leg and the left leg alternately lie in the supporting phase and swing phase, the robot trunk alternately leans to either side. The attitude angles of the robot trunk change slightly in Figure 12. In ten period cycles, when the proposed controller was not used, the roll angle of the hydraulic quadruped robot ranged from 0.6 to 4.5 degrees, and the pitch angle ranged from \(-4.2\) to 1.13 degrees. When using the presented control method, the roll angle ranged from 1.58 to 3.94 degrees, and the pitch angle ranged from \(-3\) to 0.35 degrees. From Figure 13, it can be seen that the attitude angular velocity of the trunk of the hydraulic quadruped robot changed smoothly, by the proposed controller. The results show that the fluctuation of the robot trunk is small during the movement of the robot. As seen from the experimental process, the motion of each leg of the robot is coordinated, and the robot can move smoothly and straight. The availability and rationality of the proposed control method are further proved. Figure 12: Attitude angle curves of the robot trunk. (**a**) Roll angle of the robot trunk. (**b**) Pitch angle of the robot trunk. The position tracking curves of the electro-hydraulic servo actuator of the robot in pacing gait are illustrated in Figures 14 and 15. The reference signals were obtained by cycloid trajectory planning.