## 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
According to the shortest distance change with time in VREP software, the mobile platform and the second link occur collision at \(t=6.2\) s, and the corresponding joint angle is \((90^{\circ},110.7^{\circ},0^{\circ},0^{\circ},0^{\circ})\). When using the typical method and the improved method to detect the self-collision, the larger step size can be used to detect the collision of two components at \(t_{1}^{a}=5\) s and \(t_{1}^{b}=6\) s. When a smaller step size is used, the typical method will detect the collision at \(t_{2}^{a}=6\) s, and the joint angle at this moment is \((90^{\circ},77.4^{\circ},0^{\circ},0^{\circ},0^{\circ})\); the improved method in this paper will detect the collision at \(t_{2}^{b}=10\) s, and the corresponding joint angle is \((90^{\circ},99^{\circ},0^{\circ},0^{\circ},0^{\circ})\). Comparing the typical method, the collision joint angle based on the improved method in this article is closer to the actual joint angle which occur collision. This is due to the more detailed description of the connecting link. By comparing these self-collision detection results with different methods, we can obtain the following:  
(1) Comparing Figures 9c, 10c and 11c, both the improved method and the typical method can effectively achieve self-collision detection, determine the collision location and identify the joint angle of the mobile manipulator robot. (2) Comparing Figures 9a,c, 10a,c and 11a,c, both the improved methods and the typical method can obtain the detection of self-collision before occurring the actual collision between different components, which can prevent the damage caused by the collision phenomenon. (3) Before reaching the inappropriate angle in Figures 9c, 10c and 11c, the manipulator subsystem will inevitably not collide with other components. If shorting the time interval of system movement, we can redefine the angular where the system collides due to the influence of the motion accuracy. However, this result only improves the angle accuracy before self-collision detection. (4) Comparing Figure 10a,c, the mobile manipulator can move to the specified position according to the given joint angles in the Vrep software shown in Figure 10a, but these self-collision detection methods will detect the collision phenomenon in Figure 10c. Therefore, the above methods may incorrectly determine that the collision has occurred, but the actual parts will not collide. This case is caused by the collision of the near-sighted object boundary, and these methods cannot determine that the different parts are in contact without collision. (5) Comparing Figures 9a,c, 10a,c and 11a,c, the improved self-collision detection technology can describe the approaching angle of collision more accurately than the typical method used in article [36]. This is due to the consideration of the deformation of the connecting link. Figure 9: Detection of self-collision between different components of the manipulator subsystem. **(a)** The movement of the mobile manipulator in situation 1 based on the VREP software; **(a1–a9)** The movement of the mobile manipulator before reaching collision location in situation 1 based on the VREP software; **(a10–a12)** The movement of the mobile manipulator after reaching collision location in situation 1 based on the VREP software; **(b)** Distance changes between two components of the manipulator subsystem; **(c1)** Detection of self-collision using the typical method; **(c2)** Detection of self-collision using the improved method; **(c3)** Simplify the detection of self-collision using the typical method; **(c4)** Simplify the detection of self-collision using the improved method. Figure 10: Detection of self-collision between different components of the manipulator subsystem.