## 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 compared the effectiveness of self-collision detection for the mobile manipulator robot after completing the approximation of each component. In the movement, most collisions may occur at other driving joint angles besides the obvious collision angles. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Name** & \multicolumn{4}{c}{**Approximation Object 1**} & \multicolumn{4}{c}{**Approximation Object 2**} \\ \hline
**Time** & \(T_{a}^{1}\) **(s)** & \(T_{b}^{1}\) **(s)** & \(T_{c}^{1}\) **(s)** & \(T_{d}^{1}\) **(s)** & \(T_{a}^{2}\) **(s)** & \(T_{b}^{2}\) **(s)** & \(T_{c}^{2}\) **(s)** & \(T_{d}^{2}\) **(s)** \\ \hline \(T1  
Therefore, we used the joint angles generated by solving the inverse kinematic to study the self-collision detection of the mobile manipulator. Considering the self-collisions phenomenon, the driving joints of the mobile manipulator cannot reach the solved joint angle in the actual movement. Therefore, the kinematic modeling method and self-collision detection technology mentioned in this paper are added to the differential evolution method to optimize the inverse kinematics solution of the mobile manipulator. We can directly choose the traditional differential evolution method proposed in [43] to solve the inverse kinematics problem. Then, the solution result is directly verified by self-collision detection. When it cannot satisfy the collision-free constraint, the inverse kinematics problem is resolved by the differential evolution method and judges the self-collision detection again. When no self-collision occurs, the current solution is saved as the actual control angle. Based on the optimized differential evolution method, the robot can smoothly reach the designated position. To verify the performance of the improved self-collision detection, we compared the method mentioned in this study with the traditional differential evolution method in [43]. Assuming that the corresponding initial joint angle of the mobile manipulator is set to \((0.0,0.5,\pi/4,0,\pi/2,-\pi/4,\pi/4,0.0,0.0,0.0)\), the first desired position is set to \((800,500,1000)\), and the second desired position is set to \((540,-131,974)\). Then, we obtained the collision results by the improved method and the typical self-collision methods. Furthermore, we compared the success rates and the required time for solving the self-collision detection with different methods, which is shown in Table 4. In this table, \(SN_{i}\) represents the number of inverse kinematics solutions, \(CN_{i}\) represents the number of collisions obtained by the self-collision detection method, \(SR_{i}\) represents the success rate of inverse kinematics results without the self-collision, and \(AT_{i}\) represents the time required for self-collision detection in solving the inverse kinematics of the mobile manipulator. Some typical solution results based on the differential evolution method are shown in Table 5, and draw upon some of the solution results, as shown in Figure 8. In Table 5, \(Q_{si}\) represents the solution result without collision based on both methods, \(Q_{fi}\) indicates the solution with self-collision based on the typical method, and \(ME\) is the maximum error between the result position and the actual position. In order to more intuitively identify the location of the collision, the approximate object of the manipulator subsystem uses a red spherical object. However, the approximate object of the mobile platform uses the blue spherical object. Furthermore, we use the approximation with black color to describe the corresponding components when the collision occurs. By comparing the solution results in the Tables 4 and 5, the following can be observed:  
(1) Comparing Figure 8a-f and Table 5, the inverse kinematics of the mobile manipulator have different results for the designated reachable position.