## 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
In theory, these solutions have the same validity for inverse kinematics, but some driving joints cannot reach the solved angle due to self-collision constraints. Therefore, the optimized differential evolution algorithm can reach the designated position without considering other collision avoidance technology. (2) Comparing Figure 8c,f, The optimized differential evolution method can guarantee collision-free results. Due to the high-precision kinematic modeling and effective self-collision detection, the solutions which included the self-collision phenomenon can be entirely discarded, and the actual results fully meet the actual requirement. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Method** & \multicolumn{2}{c}{**Typical Self-Collision Detection**} & \multicolumn{2}{c}{**Improved Self-Collision Detection**} \\ \hline
**Name** & \(SN_{1}\) & \(CN_{1}\) & \(SR_{1}\) & \(AT_{1}\) **(s)** & \(SN_{2}\) & \(CN_{2}\) & \(SR_{2}\) & \(AT_{2}\) **(s)** \\ \hline Task1 & 100 & 73 & 27.00\% & 1.9053 & 100 & 63 & 37.00\% & 1.6700 \\ Task2 & 100 & 86 & 14.00\% & 1.9353 & 100 & 65 & 35.00\% & 1.7081 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison performance of self-collision detection in practical application. when a collision occurs, these self-collision detection technologies were used to judge the collision status, which can also identify the joint angle of the manipulator subsystem when a collision occurs. These simulations are illustrated below. **Situation 1:** To study the collision between the components of the manipulator subsystem, we set the initial angle of the manipulator subsystem as \((90^{\circ},0^{\circ},18^{\circ},18^{\circ},0^{\circ},0^{\circ})\), and the final desired joint angle is \((90^{\circ},0,180^{\circ},180^{\circ},0^{\circ},0^{\circ})\), the motion time of each joint is \(t_{1}=10\) s, and the overall joints use uniform motion. To obtain the actual movement and determine the collision results, we first carry out a simulation experiment in the VREP-EDU software, and solve the shortest distance of two components which will occur collision during the movement, which is shown in Figure 9a,b. Then, we use the typical method and the improved method proposed in this study to determine the detection of a collision between different components of the manipulator. The specific results are shown in Figure 9(c1,c2). To accurately recognize the collision, we 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 9(c3,c4). **Situation 2:** To study the collision between the carrying load and the manipulator subsystem, we set the initial angle of the manipulator as \((90^{\circ},90^{\circ},0^{\circ},-90^{\circ},0^{\circ},0^{\circ})\), the final desired joint angle is \((0^{\circ},90^{\circ},0^{\circ},-90^{\circ},0^{\circ},0^{\circ})\), and the motion time of each joint is \(t_{1}=10\) s, and the overall joints use uniform motion. We use the typical method and the improved method proposed in this study to determine the detection of a collision between the carrying load and the manipulator subsystem. The specific results are shown in Figure 10(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 10(c3,c4). **Situation 3:** To study the collision between the mobile platform and the manipulator subsystem, we set the initial angle of the manipulator as \((90^{\circ},0^{\circ},0^{\circ},0^{\circ},0^{\circ},0^{\circ})\), the expected final angle is \((90^{\circ},180^{\circ},0^{\circ},0^{\circ},0^{\circ},0^{\circ})\), the motion time of each joint is \(t_{1}=10\) s, and the overall joints move at a uniform speed.