## 4 The Improved Self-Collision Detection Technology
### Comparison of the Performance of Self-Collision Detection
#### 5.3.3 Comparison of the Judgment of Self-Collision Detection
We select the typical method and the improved method proposed in this study to determine the detection of a collision between the mobile platform and the manipulator subsystem. The specific results are shown in Figure 11(c1,c2). To accurately recognize the collision, we also select the driving joint angle at the time of the collision and the joint angle at the previous time to control the mobile manipulator robot, and the overall time is \(t_{2}=20\) s.The specific results are shown in Figure 11(c3,c4). According to the basic structure of the mobile manipulator robot, the manipulator subsystem will inevitably collide with the other components of the mobile manipulator robot. The possible collisions of the mobile manipulator robot are described in Figures 9-11. Figure 9 shows the result of the movement of the mobile manipulator and the change of the shortest distance of the collision components in situation 1. According to the movement result of the mobile manipulator and the shortest distance change with time, the sixth motor and the first link were occurring collision between Figure 9(a9,a10) in VREP software. When two components collide, the shortest distance between the surfaces of the two parts is zero. From Figure 9b, we can get that the time of occurring self-collision is \(t=8.65\) s, and the corresponding joint angle is \((90^{\circ},0^{\circ},155.7^{\circ},155.7^{\circ},0^{\circ},0^{\circ})\). When using the basic method and the improved method to detect the self-collision of the mobile manipulator, the larger step size can be used to detect the collision of two components at \(t_{1}^{a}=8\) s and \(t_{1}^{b}=9\) s. When a smaller step size is used, the typical method will detect the collision at \(t_{2}^{a}=18\) s, and the joint angle at this moment is \((90^{\circ},0^{\circ},142.2^{\circ},142.2^{\circ},0^{\circ},0^{\circ})\); the improved method in this paper will detect the collision at \(t_{2}^{b}=4\) s, and the corresponding joint angle is \((90^{\circ},0^{\circ},147.6^{\circ},147.6^{\circ},0^{\circ},0^{\circ})\). The collision joint angle based on the improved method is closer to the actual joint angle when the collision occurs. Figure 10 shows the result of the movement of the mobile manipulator and the change of the shortest distance of the collision components in situation 2. In the simulation of  
VREP software, the manipulator subsystem reaches the designated position smoothly according to Figure 10a. However, the shortest distance of the manipulator subsystem and the carrying load is becoming to zero between \(t=7.7\) s, the corresponding joint angle is \((26^{\circ},90^{\circ},0^{\circ},-90^{\circ},0^{\circ},0^{\circ})\), and the robot's motion results are shown in Figure 10a.b. When using the basic method and the improved method to detect the self-collision of the mobile manipulator, the larger step size can detect the collision of two components at \(t_{1}^{a}=6\) s and \(t_{1}^{b}=6\) s. When a smaller step size is used, the typical method will detect the collision at \(t_{2}^{a}=11\) s, and the joint angle at this moment is \((40.05^{\circ},90^{\circ},0^{\circ},-90^{\circ},0^{\circ})\); the method in this paper will detect the collision at \(t_{2}^{b}=15\) s, and the corresponding joint angle is \((38.25^{\circ},90^{\circ},0^{\circ},-90^{\circ},0^{\circ})\). In the second simulation with the VREP software, the manipulator subsystem can move close to the edge of the carrying load without collision. However, we use the spherical element to approximate the manipulator subsystem and the carrying load for practical applications, the typical method and the improved method will be judged as a collision occurs before the manipulator subsystem touches the edge of the carrying load. Therefore, the results of the self-collision detection based on the two methods are quite different from the actual collision joint angle. Figure 11 shows the result of the movement of the mobile manipulator and the change of the shortest distance of the collision components in situation 3.