## 5 Experimental Verification
### Experimental Verification
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(P_{i}\) & **x/cm** & **y/cm** & **z/cm** \\ \hline
1 & 59 & 0 & 15 \\
2 & 57.28 & 2.458 & 13.333 \\
3 & 55.592 & 4.915 & 11.667 \\
4 & 53.839 & 7.373 & 10 \\
5 & 50.863 & 7.753 & 8.333 \\
6 & 48.366 & 9.416 & 6.667 \\
7 & 47.457 & 12.274 & 5 \\
8 & 46.548 & 15.133 & 3.333 \\
9 & 45.638 & 17.992 & 1.667 \\
10 & 45 & 20 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Path points of the end-effector. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(P_{i}\) & **\(\theta_{1}\)/(\({}^{\circ}\))** & **\(\theta_{2}\)/(\({}^{\circ}\))** & **\(\theta_{3}\)/(\({}^{\circ}\))** & **\(\theta_{4}\)/(\({}^{\circ}\))** & **\(\theta_{5}\)/(\({}^{\circ}\))** \\ \hline
1 & 0 & 0 & 0 & 0 & 0 \\
2 & 2.46  
Figure 14 depicts the overall motion state of the pickup manipulator under the obstacle environment. Figure 14a shows the initial state of the pickup manipulator under the obstacle environment. If the pickup manipulator moves in a straight line without obstacle avoidance planning, it will collide with the cylindrical obstacle. Figure 14b shows the end state of the pickup manipulator. The running curve of the pickup manipulator is obtained by using the improved artificial potential field to avoid an obstacle in the obstacle environment and then using the cosine adaptive genetic algorithm to optimize the trajectory. It can be seen from the trajectory curve that the pickup manipulator can successfully avoid the obstacle and smoothly reach the target point along the path of the obstacle avoidance planning, and the trajectory optimization. Figure 15 shows the displacement curve of the end-effector along each coordinate axes. It can be seen from Figure 15 that the trajectory of the end-effector along the coordinate axes during the movement is continuous, without a large fluctuation phenomenon, and the motion law is reasonable. It proves the correctness of the theoretical derivation of the improved artificial potential field method and the cosine adaptive genetic algorithm. (2) Obstacle Environment with the Problems of Local Minimum Value and Unreachable Target Create a work environment with the problems of local minimum value and unreachable target for the pickup manipulator, set the initial point of the end-effector \(X_{o}\) = [60 cm, 0 cm, 15 cm], target point \(X_{g}\) = [45 cm, 10 cm, 15 cm], and the center of obstacle M = [49 cm, 6 cm, 16 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 8.  
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. In order to ensure every joint reaches the joint position in the same time, the longest-running time of the joints is taken as the pickup manipulator running time. The time optimization results in the obstacle environment are shown in Table 9.  
According to the time optimization results in Table 9, the running time of the pickup manipulator in each path point is respectively shortened by 27.11%, 37.38%, 51.08%, 58.42%, 52.52%, 50.59%, 68.69%, 54.5%, and 84.35%. The overall running time is shortened by 53.85%, and the optimization effect is obvious. Combine the path points in Table 6 and the time optimization results of each path point in Table 9 to conduct the motion simulation in ADAMS. Set the simulation time t = 8.31 s and the simulation step size = 200 for simulation, and the result is shown in Figure 16. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Pi** & **x/cm** & **y/cm** & **z/cm** \\ \hline
1 & 60 & 0 & 15 \\
2 & 57.504 & 1.664 & 15 \\
3 & 55.008 & 3.328 & 15 \\
4 & 52.512 & 4.992 & 15 \\
5 & 50.265 & 6.98 & 15 \\
6 & 52.572 & 8.9 & 15 \\
7 & 49.603 & 9.33 & 15 \\
8 & 47.792 & 11.722 & 15 \\
9 & 45.238 & 10.147 & 15 \\
10 & 45 & 10 & 15 \\ \hline \hline \end{tabular}
\end{table}