# Omnidirectional Jump of a Legged Robot Based on the Behavior Mechanism of a Jumping Spider
## 3 Methods
### Locomotion Planning
#### 3.2.2 Attitude Planning  
In the jump process of the robot, the reasonable initial attitude angle of the robot can affect the jumping height and distance. The initial jumping posture mainly includes the pitch angle, yaw angle and roll angle of the robot when taking off. By controlling the pitch angle of the robot, the maximum height and maximum distance of the robot can be reached when the robot jumps forward. The roll angle affects the sideways jump, while the yaw angle can adjust the jumping direction of the robot, allowing the robot to jump towards the target. During vertical jumps, the yaw angle and pitch angle of the robot are 0\({}^{\circ}\). The initial joint position and angles of each leg of the robot are the same, correspondingly. The robot can jump vertically by reacting to the ground. Before the robot begins jumping sideways, the body leans to the left due to a slight flexion of the left legs, and the robot has a certain roll angle of \(\theta_{r}\) in the jumping direction. Meanwhile, the yaw angle and pitch angle are zero. A simple model of the robot's posture during a sideways jump is shown in Figure 7a. When the robot jumps to the right, the effective length of the three left legs of the robot is larger than that of the right legs in the initial state to satisfy a certain proportion. Therefore, we can obtain  
\[\mathrm{Z_{I}}=\mathrm{K_{I}}\mathrm{Z_{r}}, \tag{22}\]  
where \(\mathrm{Z_{I}}\) is the Z coordination of the three left legs opposite to the base coordinate {O}. \(\mathrm{Z_{r}}\) is for the right legs. \(\mathrm{K_{I}}\) is a constant, and it is determined by the initial attitude of the robot.  
When the robot jumps forward, the forelegs extend and the hind legs flex during their contact phase, and the middle legs remain in slight extension. Therefore, the robot has a certain pitch angle in the jump direction; the pitch angle is \(\mathrm{\theta_{p}}\). The roll angle and raw angle are 0\({}^{\circ}\). The simple model of the robot posture of the forward jump is shown in Figure 7b. At the beginning of the jump, the effective length of the forelegs of the robot is larger than that of the middle legs in the initial state; meanwhile,  
Figure 7: Simplified model of the robot posture. (**a**) Sideways jump: The red solid line indicates the transverse axis of the robot body, the green solid line indicates the left leg of the robot body, the blue solid line indicates the right leg, the purple dashed line indicates the effective length, and the black circles indicate the joints. (**b**) Jump forward: Green solid lines indicate the hind legs of the robot body, the blue solid line indicates the foreleg, and the yellow solid line indicates the middle leg.  
the effective length of the middle legs of the robot is larger than that of the hind legs in the initial state, and they satisfy two proportions:  
\[\left\{\begin{array}{l}\mathrm{Z_{f}=K_{2}Z_{m}}\\ \mathrm{Z_{m}=K_{2}Z_{h}}\end{array}\right., \tag{23}\]  
where \(\mathrm{Z_{h}}\) is the Z coordination of the hind legs opposite to the base coordinate {O}; \(\mathrm{Z_{f}}\) is the forelegs; and \(\mathrm{Z_{m}}\) is the middle legs. \(\mathrm{K_{2}}\) is a constant and it is determined by the initial attitude of the robot.