# Optimization Algorithm for 3D Smooth Path of Robotic Arm in Dynamic Obstacle Environments
## 4 Experiment Results  
To validate the effectiveness of the trajectory planning algorithm proposed for dynamic obstacle environments, several experimental data statistics are presented in this section to demonstrate the algorithm's efficacy. These include comparative experiments on path performance between the proposed algorithm and other algorithms, statistical comparisons of path lengths from multiple simulation experiments, and comparisons of average convergence time and average number of turning points in multiple simulation experiments. To verify the effectiveness of the trajectory planning algorithm proposed in this study for dynamic obstacle environments, the following experiments are conducted: validation of the effectiveness of the dynamic trajectory planning algorithm proposed in this study and comparative experiments with the performance of other algorithms. Among the validation experiments, there are two sub-experiments: verification of the effectiveness of the local path replanning algorithm and robustness verification for dynamic obstacles of different speeds. Notably, the trajectory planning algorithm in this experiment utilizes point cloud data obtained from online resources and does not include experimental demonstrations. Finally, regarding the trajectory planning of robotic arms in obstacle environments studied in this paper, simulation experiments are conducted on robotic arms for trajectory planning. To validate the effectiveness of the random tree guided path back-to-source update algorithm proposed in this study for static environments, comparisons were conducted in the MATLAB (R2024a) environment between the RRT* algorithm, the RRT-Connect algorithm, the Lazy-RRT algorithm, and the proposed random tree back-to-source path update algorithm. The experimental space was \(100\times 100\times 100\) (cm\({}^{3}\)), with the initial point located at (5, 5, 5) and the target endpoint at (95, 95, 95), and a step size of 5. A total of 3000 iterations were performed, with 30 repeated simulation experiments. Firstly, a comparison of the algorithm's effectiveness with other improved RRT algorithms is presented, using one of the simulation results as an example, as shown in Figure 9. Figure 9a shows the effectiveness of the traditional RRT* algorithm, Figure 9b shows the RRT-Connect algorithm, Figure 9c shows the Lazy-RRT algorithm, and Figure 9d shows the improved random tree guided path back-to-source update algorithm based on the RRT* algorithm proposed in this study. From the figures, it can be seen that the traditional RRT* algorithm has numerous calculation nodes, the Lazy-RRT algorithm has some optimizations over the RRT* algorithm, and the path smoothness of the RRT-Connect algorithm is lacking. The proposed random tree guided path back-to-source update algorithm reduces redundant points while also increasing the smoothness of the path. Then, the comparison of motion path lengths among the aforementioned algorithms is presented in Figure 10 below. From the figure, it can be concluded that in 30 experiments, the random tree guided path back-to-source update algorithm proposed in this study exhibits the best path planning performance in most cases compared to other algorithms. Figure 9: Obstacle avoidance performance of various algorithms in 3D space: (**a**) RRT star algorithm, (**b**) RRT-Connect algorithm, (**c**) lazy RRT algorithm, (**d**) improved random tree guided path back-to-source update algorithm. Finally, considering that the application scenario in this paper requires real-time calculation for robotic arm movement, a comparison of path convergence time and path turning points is also conducted, as shown in Table 1 below.