# Whole-Body Motion Planning for a Six-Legged Robot Walking on Rugged Terrain
## 3 Results
### Experimental Study  
This section discusses the experimental verification of the proposed planning method with our six-legged robotic platform (as illustrated in Figure 8). Specific design and control details about the robot are available in references [5; 21; 25]. The experimental setup is illustrated in Figure 9. The robot is commanded to walk through the specified terrain with a certain initial state. The terrain, which is 3D printed by PLA material, is irregular wave shape. Its size is about \(850\times 800\) mm (width \(\times\) length). The maximum peak height is about \(160\) mm. According to our experimental observations, for the terrain with small obstacles shown in Figure 8, the irregularities can be overcome using fixed motions and reactive control. However, the robot would capsize if the fixed motions are still used for the irregular wave terrain in Figure 9. This is because, severe nonuniform distribution of foot forces and foot slippages would occur when the robot places its feet onto the irregular peaks. As a result, it is necessary to plan the whole-body motion of the robot according to the terrain in advance.  
Figure 8: Physical prototype of the robot.  
Figure 7: Trajectories of all the joints of the robot.  
In the experimental procedure, both the robot and the 3D-printed terrain are placed at the designated locations, and as a result, the terrain information is known for the robot. In addition, a set of footholds are given manually according to the terrain geometry. The maximum foothold height is roughly 19 mm while the minimum height is about 148 mm. Under this circumstance, the proposed planning method is used to produce and calculate the movements of the torso and legs. Then the joint trajectories are obtained by inverse kinematics. In addition, motion control is crucial for the experiment implementation. Various robot control methods have been proposed, effectively improving the performance of robots [26; 27; 28]. In this experiment, our aim is to validate the proposed motion planning method, as a result, each joint is just PD controlled to ensure accurate leg movements, and impedance control is added in each leg-end to deal with ground reaction force. Snapshots of the real-world robot walking over irregular wave terrain are shown in Figure 10. Experiments show that the robot successfully traverses the given terrain.  
Figure 11 shows the trajectory curves of the torso and leg joints during the experiment. The walking details can be learnt from the trend of these curves. Specifically, as shown in Figure 11a, the pitch angle of the robot torso first presents an increasing trend, which corresponds to the initial climbing motion of the robot. Then, the pitch angle shows a decreasing trend, but still maintains positive value, indicating that the front leg or middle leg of the robot has reached the flat terrain shown in Figure 9. The pitch angle becomes roughly 0, indicating that the robot has completely crossed the wave terrain. Small changes of the torso rolling reflect the adjusting effect of the robot during walking.  
Figure 11b shows variations of the joint angles in the left foreleg of the robot. Overall, the three joints display a periodic characteristic, which is consistent with the reciprocating motion of legged locomotion. In addition, the trajectories are also different in each walking cycle, which is, on the one hand, due to the terrain irregularity and thereby the different step lengths of each step. On the other hand, the adjustments of the control system to each joint are also different in the course of motion. Through the walking experiment on irregular wave terrain, the adaptability of the robot on complex terrain is further demonstrated, and the effectiveness of the motion planning mentioned above is illustrated.  
Figure 10: Consecutive snapshots of the walking experiment on irregular wave terrain.  
Figure 9: Schematic of walking experiment on irregular wave terrain.