# Research on the Path Planning Algorithm of a Manipulator Based on GMM/GMR-MPRM
## 5 Simulation and Experimental Analysis
### Experiment and Analysis  
In order to verify the effectiveness of the GMM/GMR-MPRM algorithm, a path planning experiment platform for the pick-and-place task of a manipulator was built. The manipulator used in this experimental platform was ABB IRB1200, with a maximum load of 7 kg and a maximum working radius of 700 mm. The manipulator was installed on the workbench, and a pneumatic gripper was installed at the end of the manipulator to complete tasks such as picking and placing and assembly. A Kinect V2 was also installed on the workbench to detect the position and size of the obstacle. The experimental platform is shown in Figure 8. In this experimental scene, the manipulator needed to pick up the axle from the container and place it in another container. In the process of the demonstration, the teacher performed teaching six times, and six different teaching trajectories were obtained, as shown in Figure 9. When the task occurred, a white spherical obstacle with a diameter of 50 mm was placed on the task path. The position and size of the obstacle were obtained by the Kinect V2, and the position of the obstacle was (299.75 mm, \(-\)40.03 mm, 240.11 mm).  
Figure 6: The recurrent scene with two new obstacle.  
Figure 7: Path planned by the GMM/GMR-MPRM.  
Because there was an obstacle in the experimental scene, if the pick and place task were executed directly according to the path planned by the GMM/GMR, it would cause  
Figure 8: The experimental platform.  
Figure 9: Teaching trajectory of the experimental task.  
the manipulator to collide with the obstacle. However, the obstacle did not affect all the feasible space of the teaching path, but only part of the feasible space. Therefore, the GMM/GMR-MPRM algorithm can be used for trajectory planning. The number of Gaussian components in the GMM was set as \(K=10\). The quantity of resampling based on covariance was set as \(n_{\Sigma}=100\). The quantity of resampling based on the distance was set as \(n_{0}=300\). The adjustment coefficient of the Euclidean and probability distances was \(\lambda=0.7\). The order of the B-spline was set as \(p=3\). The control loop rate of IRB1200 was 10 Hz.  
Figure 10 is the path planning process of the manipulator using the GMM/GMR-MPRM algorithm: (a,b) the manipulator first moves to the initial position and then moves to the top of the container; (c) the manipulator descends to the grasping position and grabs the shaft; (d,e) after the grasping is completed, the manipulator is raised to a certain height and then moved to the vicinity of the obstacle; (e-h) there is a feasible space in front of the obstacle, and the GMM/GMR-MPRM algorithm plans a feasible path in this space; the manipulator bypasses the front side of the obstacle; (h-j) after the manipulator completes the obstacle avoidance, the manipulator continues to move to the top of the container along the GMR path, moves downwards, and opens the claw to release the shaft, then the shaft is placed into the container.  
The experimental results showed that the GMM/GMR-MPRM algorithm provided the manipulator better adaptability when the task recurred, that is when a new obstacle appeared in the recurring scene, the path planning could be completed without teaching again.