Abstract: This paper addresses the issue of overly conservative angular velocity and angular acceleration in segmented polynomial trajectory planning for robotic arms, and the traditional egret swarm optimization algorithm is easy to fall into the local optimum when optimizing the trajectory of the robotic arm, which results in longer movement completion time. To solve this problem, an improved egret swarm optimization algorithm (IESOA) is proposed for time-optimal trajectory planning of the robotic arm. Firstly, Sinusoidal chaotic mapping is introduced to enhance population diversity. Secondly, the long-tailed distribution jumping mechanism of Lévy flight is utilized to avoid the algorithm from falling into a local optimum, thus improving the algorithm?s global search capability. Finally, adaptive t-distribution is employed to dynamically adjust the algorithm?s degree of freedom parameter [v], balancing global exploration with local exploitation, thereby enhancing both optimization accuracy and convergence efficiency. To evaluate the superiority of algorithm, the improved algorithm is compared with five similar algorithms including the traditional ESOA for convergence analysis, Wilcoxon rank-sum tests, and robotic arm trajectory planning experiments. The results demonstrate that, compared with other algorithms, IESOA provides superior optimization accuracy and stability across single-peak, multi-peak, and fixed-dimension multi-peak functions.  Moreover, in the robotic arm trajectory planning simulations, the trajectory curve optimized by IESOA is smooth, without abrupt changes. Additionally, the running time and its standard deviation outperform those comparison algorithms, validating the superiority and robustness of IESOA in solving the time-optimal trajectory planning problem.

Key words: robotic arm, trajectory planning, improved egret swarm optimization algorithm, Lévy flight, Wilcoxon rank sum test

摘要： 针对机械臂轨迹规划任务中角速度和角加速度的选择过于保守，且采用传统白鹭群优化算法优化机械臂运行轨迹时易陷入局部最优，进而导致整个动作的完成时间过长等问题，提出一种改进白鹭群优化算法（IESOA），并将其应用于机械臂时间最优轨迹规划任务中。引入Sinusoidal混沌映射作为种群初始化方法以增强种群多样性；利用莱维飞行的长尾分布跳跃机制避免算法陷入局部最优，提升算法的全局搜索能力；采用自适应[t]分布动态调整自由度参数[v]，在提高优化精度与收敛效率的同时平衡算法的全局搜索与局部开发能力。为验证改进算法的优越性，将改进后的算法与包含传统ESOA在内的5种同类算法进行收敛性分析、Wilcoxon秩和检验以及机械臂轨迹规划对比分析。实验结果表明，相较于对比算法，IESOA在单峰、多峰函数以及固定维数多峰函数上均有较好的寻优精度和稳定性。同时，在机械臂轨迹规划实验验证中，经IESOA优化后的机械臂轨迹曲线平滑且无突变，运行时间及其标准差均优于对比算法，验证了IESOA在解决机械臂时间最优轨迹规划问题中的优越性和鲁棒性。

关键词: 机械臂, 轨迹规划, 改进白鹭群优化算法, 莱维飞行, Wilcoxon秩和检验