# Optimization Algorithm for 3D Smooth Path of Robotic Arm in Dynamic Obstacle Environments
## 1 Introduction
In addition to traditional path planning methods, robotic scheduling models have also been explored to address task allocation and path conflict problems. [PERSON] et al. [29] proposed a robotic job-shop scheduling model that simultaneously considers job sequencing and robot movement, ensuring deadlock-free operation by incorporating machine blocking strategies. Similarly, [PERSON] et al. [30] investigated deadlock resolution strategies in robotic cells with post-process inspection systems, proposing avoidance and recovery mechanisms to optimize cycle time and storage costs. These studies highlight the importance of considering robotic movement conflicts and deadlock risks, especially in multi-robot coordination tasks. While these methods provide efficient task scheduling solutions, they do not explicitly address real-time trajectory adjustments for robotic arms in dynamic environments. Despite progress in path planning research, several unresolved issues persist. The ability to adapt trajectories in real time within dynamic environments remains limited. Existing RRT and APF improvements primarily target static or semi-static environments, making real-time path replanning computationally expensive and slow to respond to environmental changes. Balancing trajectory smoothness and obstacle avoidance remains a challenge, as APF-based methods are prone to local minima, leading to infeasible paths,while RRT methods produce discrete paths that may affect the stability of robotic motion. There exists a trade-off between computational efficiency and optimality in current path planning methods, as RRT exhibits slow convergence in large-scale scenarios, while A* incurs high computational costs, making it impractical for high-dimensional spaces. Additionally, robotic arms may experience unstable trajectories and oscillatory paths during obstacle avoidance, impacting the accuracy and safety of task execution. Therefore, optimizing real-time path planning in dynamic environments while improving trajectory smoothness and obstacle avoidance capabilities, and reducing computational costs, remains a critical challenge. This study proposes a hybrid path planning method that integrates RRT and APF, leveraging RRT's global search capability and APF's local obstacle avoidance ability to enhance adaptability and real-time performance. An adaptive adjustment strategy is introduced to optimize trajectory smoothness by incorporating a dynamic potential field weight adjustment mechanism, enabling rapid path updates in complex environments while mitigating the impact of local minima. Computational efficiency is improved through modified sampling strategies and heuristic search methods, reducing redundant computations and accelerating convergence. Additionally, trajectory stability is enhanced by optimizing path smoothing and replanning mechanisms, ensuring a more continuous and feasible trajectory during obstacle avoidance. The proposed method is validated through simulations and experiments, demonstrating its effectiveness across various dynamic environments and confirming its applicability to complex robotic arm path planning tasks.