## 5 Experimental Verification
### Experimental Verification  
2.1 The Comparative Experiment of the Improved Artificial Potential Field Method and the Rapidly-Exploring Random Tree* Method  
Create a work environment for the pickup manipulator, set the initial point of the end-effector \(X_{0}=\) [1 cm, 18 cm], target point \(X_{g}=\) [60 cm, 60 cm], and the center of obstacle M = [50 cm, 50 cm] to conduct the simulation experiment in MATLAB. The improved artificial potential field method is adopted for obstacle avoidance planning to obtain the path points of the end-effector, and the results are showed in Table 2. The rapidly-exploring Random Tree* (RRT*) method is adopted for obstacle avoidance planning to obtain the path points of the end-effector, and the results are showed in Table 3.  
Figure 12 shows the path point obtained by the improved artificial potential field method for obstacle avoidance planning. When the end-effector is not affected by obstacles, the improved artificial potential field method can plan a straight-line trajectory to reduce the running distance and improve the working efficiency of the pickup manipulator. When the manipulator is affected by obstacles, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\mathbf{P_{i}}\) & \(\mathbf{x/cm}\) & \(\mathbf{y/cm}\) & \(\mathbf{P_{i}}\) & \(\mathbf{x/cm}\) & \(\mathbf{y/cm}\) \\ \hline
1 & 1 & 18 & 14 & 32.772 & 40.617 \\
2 & 3.444 & 19.74 & 15 & 35.216 & 42.357 \\
3 & 5.888 & 21.48 & 16 & 37.66 & 44.097 \\
4 & 8.332 & 23.219 & 17 & 40.104 & 45.837 \\
5 & 10.776 & 24.959 & 18 & 42.548 & 47.577 \\
6 & 13.22 & 26.699 & 19 & 44.992 & 49.316 \\
7 & 15.664 & 28.439 & 20 & 47.436 & 51.056 \\
8 & 18.108 & 30.179 & 21 & 47.708 & 54.044 \\
9 & 20.552 & 31.918 & 22 & 50.407 & 55.352 \\
10 & 22.996 & 33.658 & 23 & 53.107 & 56.66 \\
11 & 25.44 & 36.398 & 24 & 55.807 & 57.968 \\
12 & 27.884 & 37.138 & 25 & 58.507 & 59.276 \\
13 & 30.328 & 38.878 & 26 & 60 & 60 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Path points of the end-effector obtained by the improved artificial potential field method. Figure 11: Force of improved local minimum value. 2.2 Simulation Experiment of the Improved Artificial Potential Field Method and Cosine Adaptive Genetic Algorithm  
(1) General Obstacle Environment  
Create a work environment for the pickup manipulator, set the initial point of the end-effector \(X_{0}\) = [59 cm, 0 cm, 15 cm], target point \(X_{g}\) = [45 cm, 20 cm, 0 cm], and the center of obstacle M = [53 cm, 10 cm, 20 cm] to conduct the simulation experiment in MATLAB. The improved artificial potential field method is adopted for obstacle avoidance planning to obtain the path points of the end-effector, and the results are showed in Table 4. The established Kinematics model is used to calculate the joint angle, and the results are shown in Table 5.  
The primary selection of the running time between the path points is 2 s, and the established cosine adaptive genetic algorithm is used to optimize the time of the trajectory planning. The time optimization results of each joint at each path point are shown in Table 6. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(P_{i}\) & **Joint 1/(s)** & **Joint 2/(s)** & **Joint 3/(s)** & **Joint 4/(s)** & **Joint 5/(s)** \\ \hline
1 & 0 & 0 & 0 & 0 \\
2 & 0.5577 & 1.0568 & 1.8787 & 1.2329 & 0.4697 \\
3 & 0.5577 & 0.5284 & 1.1448 & 0.9100 & 0.4697 \\
4 & 0.5871 & 0.3523 & 0.9687 & 0.7632 & 0.4697 \\
5 & 0.3229 & 0.5284 & 1.2329 & 0.9393 & 0.2642 \\
6 & 0.5284 & 0.1761 & 0.9687 & 0.7926 & 0.4403 \\
7 & 0.6458 & 0.5284 & 0.2055 & 0.4110 & 0.5284 \\
8 & 0.6458 & 0.5577 & 0.4110 & 0.3229 & 0.5284 \\
9 & 0.6458 & 0.5871 & 0.5284 & 0.2348 & 0.5284 \\
10 & 0.5577 & 0.5871 & 0.5871 & 0.0587 & 0.4697 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Time optimization results of the pickup manipulator at each path point.