# Optimization Algorithm for 3D Smooth Path of Robotic Arm in Dynamic Obstacle Environments
## 1 Introduction
Artificial potential field (APF) algorithms have been extensively studied in the context of robot path planning. The existing literature [21] primarily focuses on solving the local minimum problem of APF by optimizing and improving the attractive potential function and repulsive potential function or by adding other additional conditions. Bionic algorithms are random algorithms inspired by the intelligent phenomena of biological populations in nature. Based on their principles and path search mechanisms, bionic algorithms can be classified into functional bionic algorithms, informational bionic algorithms, and structural bionic algorithms. Functional bionic algorithms are proposed to simulate the role of a specific physiological function of organisms in foraging, social life, escape, or other biological behaviors. Examples include genetic algorithms, cuckoo search algorithms, sparrow search algorithms, and more. Informational bionic algorithms aim to simulate the basic principles of information transmission and intelligent behavior among organisms' organs, individuals, and populations. These include particle swarm optimization algorithms, bacterial foraging optimization algorithms, artificial bee colony algorithms, gray wolf optimization algorithms, and others. Structural bionic algorithms simulate biological behaviors and functions from a chemical perspective by modeling the secretion and release of trace chemicals by insects, such as ant colony optimization algorithms. The application of artificial intelligence algorithms in path planning leverages machine learning, optimization theory, and intelligent agent technology to enable robots to autonomously adapt to environmental changes and find optimal or near-optimal paths in complex conditions. This often involves bio-inspired neural networks and fuzzy logic. [PERSON] and [PERSON] et al. [22] constructed a Gaussian basis function neural network (GBNN) model with a topological structure that represents the search environment. They used a Gaussian mixture model to extract high-value subregions and quantify future detection rewards. In recent years, researchers have proposed various approaches for robotic arm path planning, including artificial-intelligence-based adaptive path planning, improved rapidly exploring random tree algorithms, artificial potential field methods, and modified A* algorithms. These methods have made significant progress in improving planning efficiency, optimizing computational costs, and enhancing obstacle avoidance capabilities. [PERSON] et al. [23] introduced an AI-based hybrid adaptive path planning method that dynamically adjusts the trajectory in complex environments, making the path more adaptable and flexible. [PERSON] et al. [24] studied an adaptive grinding path planning approach for industrial robotic arms, utilizing parameterized cost estimation and dynamic hierarchical optimization to improve trajectory accuracy and execution efficiency. RRT is widely used in high-dimensional path planning due to its randomness and rapid search characteristics. [PERSON] et al. [25] optimized RRT's search efficiency using goal probability bias and cost functions, while [PERSON] et al. [26] proposed an RRT*-based path planning method that improves trajectory smoothness and reduces computational time. Additionally, APF is commonly used for obstacle avoidance due to its simplicity and real-time capabilities. However, it suffers from local minima and oscillatory paths. [PERSON] et al. [27] explored a six-degree-of-freedom robotic arm path planning method that combines A* and APF, optimizing search strategies to improve obstacle avoidance performance. [PERSON] et al. [28] introduced an improved RRT-Connect method that enhances path smoothness and safety by incorporating obstacle modeling and safety distance calculations. While these studies provide various optimization strategies for robotic arm path planning, certain limitations remain in practical applications.