# Omnidirectional Jump of a Legged Robot Based on the Behavior Mechanism of a Jumping Spider
## 4 Results
### Vertical Jump  
In this section, we obtain data on the robot jumping vertically; these data include the joint angle, attitude angle, joint velocity, foot contact force, take-off velocity, trajectory of CoG, jumping height and jumping distance. These data are based on the simulation result under Matlab-Adams, and we can prove the reliability and rationality of vertical jump by analyzing it. Figure 8a,b shows the simulation platform of the virtual jump prototype. At the beginning of the vertical jump, the body slowly moves downward due to a slight flexion of the robot leg, and the robot begins to store energy. During the acceleration phase of the vertical jump, the effective leg length extends quickly, and the robot starts to take off. Figure 8c shows a sketch of the robot jumping vertically. The initial height of the CoG of the robot is 180 mm and the jumping height is 100 mm. In the vertical jumping experiment, we measure the contact force of the foot and the joint force; we observe the change of joint forces to verify whether the motors meet the requirement. During the vertical jumping, each joint of the six legs has the same rotation angle. Here, we can see the set of angle curves of the robot leg in Figure 8c. Coxal joint angles of all legs always remain the same during the vertical jump: they are 0 rad. Before the acceleration phase begins, the femur-patella joint angle, tibia-metatarsus joint angle and metatarasus-tarsus joint angle begin to slowly change, and the robot body slows down and adjusts the attitude. Then, the foot moves down quickly, and the robot starts to accelerate by extending its legs at 0.8 s. At 1.0 s, the height of the CoG is 300 mm, and the robot leaves the ground and takes off. At 1.2 s, the robot rises to its maximum height of approximately 400 mm, the robot completes the task of jumping 100 mm in height. From 0.8 s to \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Symbol** & **Value** \\ \hline Jumping height & \(\mathrm{H_{v}}\) & 100 mm \\ Jumping distance & \(\mathrm{L_{x}(L_{y})}\) & 250 mm \\ Static coefficient & \(\mathrm{u_{S}}\) & 0.35 \\ Dynamic coefficient & \(\mathrm{u_{D}}\) & 0.2 \\ Stiffness & T & 10000 N/m \\ Take-off moment & \(\mathrm{t_{f}}\) & 1 s \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experiment parameters. 1.2 s, the femur-patella joint angle changes by approximately 1.5 rad, the tibia-metatarsus joint angle changes by approximately 1.2 rad and the metatarsus-tarsus joint angle changes by approximately 2.0 rad. As mentioned, the effective length of the robot's legs always changes during the vertical jump. For the robot to achieve stability, the change of the attitude angle is analyzed. The initial attitude angle of the robot is not 0 rad, which is due to the initial pose of the robot in Figure 8e. The roll angle holds at near 0 rad when the robot jumps. The pitch angle holds at 0.002 rad at approximately 0-1 s, and the roll angle increases gradually to 0.01 rad when the robot lifts off the ground. In the process of jumping, the yaw angle of the robot always holds at approximately \(-0.025\) rad. According to the simulation results, the robot has good stability in the vertical jump process. Figure 8f is the contact force of the foot tip for the robot in the vertical jump process. When the robot jumps vertically, it completes the  
Figure 8: (**a**) Simulation platform of the virtual jump; (**b**) sketch of the robot vertically jumping; (**c**) joint angle curves of the robot leg; (**d**) trajectory of center of gravity (CoG); (**e**) attitude angle of robot; (**f**) contact force; and (**g**) joint torque. upward jumping task through the contact force in the \(Z\) direction. The forces all cancel each other out which acts on the entire robot in the X and Y directions. As shown in Figure 8\(f\), the initial contact force is 0 N, which is due to the initial state of the robot. At 0.3-0.8 s, the CoG slowly drops and the contact force remains constant; the contact force of X is approximately 10 N, the contact force of Y is 0.