# Controllable Height Hopping of a Parallel Legged Robot
## 5 Simulation and Experiment
### Constant Height Hopping  
The aim of the constant-height hopping experiment was to prove the feasibility of the height control method proposed in Section 4.3 and its adaptability to different ground levels.  
Figure 7: Framework for simulation and fitting relation between takeoff stiffness, bottom height, and final jumping height.  
First, the robot leg was controlled using VMC and height control strategy for constant height hopping. Subsequently, we set the robot leg hopping continuously on a stool (stool height: 0.48 m) at a constant height of 0.5 m (relative to the stool). Next, the stool was removed between the toe and the ground. The leg then fell to the ground and maintained its height at 0.5 m relative to the ground. The entire process is shown in photographs in Figure 9, where we see that the leg can maintain a constant height relative to its stance phase, even when the floor height changes. Data records of this process are presented in Figures 10 and 11.  
Figure 8: Data recorded during single landing–jumping motion. From top to bottom: leg length; motor current of Joint 1; toe velocity in vertical direction; and toe acceleration in vertical direction. In the graph, black circles represent the moment of change in leg length and motor current. Obviously, the motor current can be used to detect the touchdown information earlier than the leg length.  
Figure 9: Photographs of robot leg during continuous constant height hopping. Initially, the leg is hopping on a stool; at 1.68 s, the stool was removed and the leg then fell to the ground.  
In Figure 10, one short solid line represents the calculated summit height (based on internal sensor data and the identified g' according to (13), which is also similar to external sensor results but with lower accuracy) of the previous period. Because the calculated value can only be updated after each touchdown, the value at the current time represents the previous period's summit height. The black arrow labeled \"Horizon changed\" indicates the moment of stool removal. After this moment, the leg has an unusual height because the flight time was accidentally prolonged. However, the specific value of this height is meaningless because the stool's height is unknown. In the next period, the robot returned to its target height of 0.5 m. Figure 11 shows that, after the stool was removed, the leg length and the motor current changed dramatically, and the motor produced more power to maintain the virtual model for impact mitigation. The leg then recovered rapidly to its normal situation and still realized height control in subsequent periods, which verified its impact resistance and its adaptability to variable horizon heights. From the motor current curve shown in Figure 11, we found that the current in the touchdown phase fluctuated slightly after the horizon changed. After analysis, we believe that this resulted from the difference in physical stiffness between the stool and the floor. Consequently, the stability and adaptability of the constant height control approach on variable-level terrain was verified.  
Figure 11: Data recorded during constant height hopping: (top) leg length; and (bottom) motor current of joint 1.  
Figure 10: Summit hopping height during continuous constant height hopping. The black dashed line is the set target summit height; orange short solid lines represent actual calculated heights based on the measured hang times. At the initial moment, the measured value is zero because the leg’s summit height cannot be calculated before the first touchdown.