# Optimization Algorithm for 3D Smooth Path of Robotic Arm in Dynamic Obstacle Environments
## 5 Conclusions  
This study investigates trajectory planning for robotic arms in dynamic obstacle environments and proposes an improved hybrid method that integrates the rapidly exploring random tree (RRT) and artificial potential field (APF) algorithms. Compared to conventional approaches, this method enhances path efficiency, smoothness, and adaptability in dynamic scenarios. The key novelty and contributions of this study include:  
1. Adaptive Angle Guidance for Path Expansion: The proposed expansion strategy enhances the directional efficiency of RRT, reducing redundant nodes and improving the quality of the initial path.  
Figure 16: Search points and trajectory planning demonstration.  
Figure 17: Obstacle avoidance trajectory of robotic arms end effector.  
Figure 15: Simulation experiment environment.  
2. Hybrid Dynamic Path Replanning Strategy: By dynamically adjusting the weight ratios of APF and RRT, the method ensures efficient real-time obstacle avoidance and path optimization.
3. Trajectory Smoothing with Catmull-Rom Interpolation: The integration of this technique enhances path continuity, reducing abrupt directional changes and mechanical stress on the robotic arm.
4. Improved Real-Time Adaptability: The method effectively adjusts to dynamic obstacles, ensuring smoother and shorter paths while maintaining computational efficiency.  
The experimental results validate the effectiveness of the proposed approach. Compared to conventional RRT and APF-based methods, the hybrid method significantly reduces computational overhead while maintaining trajectory smoothness. The ability to adjust the weight distribution between RRT and APF in real time allows the system to dynamically adapt to changing obstacles without excessive recalculations. Furthermore, the integration of Catmull-Rom interpolation improves path continuity and reduces sudden directional changes, ensuring greater motion stability for the robotic arm. These findings provide further insights into real-time motion planning techniques and contribute to the development of efficient robotic arm control strategies in dynamic environments.  
Conceptualization, L.R. and Y.K.; methodology, L.R. and H.J.; software, Y.K. and L.Y.; validation, L.R., Y.K. and H.J.; formal analysis, L.R. and Y.K.; investigation, S.W. and L.Y.; resources, H.J.; data curation, Y.K. and L.Y.; writing--original draft preparation, L.R. and Y.K.; writing--review and editing, H.J.; visualization, Y.K.; supervision, H.J.; project administration, H.J.; funding acquisition, H.J. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Sichuan Province Central Guidance Local Science and Technology Development Special Project, grant number 2024 ZYD0260, titled \"Key Technology Research on Intelligent Welding Robot Systems for High-End Equipment\".  
Not applicable.  
The data that support the findings of this study are available from the corresponding author only for reasonable requests.  
Author [PERSON] was employed by the company Sinomach Heavy Equipment Group Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.  
The following abbreviations are used in this manuscript:  
RRT Rapidly exploring random tree  
Artificial potential field