面向并联机构正运动学方程多根问题的改进差分进化算法

doi:10.3901/JME.2025.19.043

摘要/Abstract

摘要： 耦合并联机构的正运动学方程可转化为具有多根问题的非线性方程组，而在一次运算中求解非线性方程组的多个根是数值计算的主要挑战，提出一种基于个体信息的邻域双策略差分进化算法用于求解该问题。首先，以Stewart并联机构为例，给出了并联机构正运动学方程转化为无约束优化问题的步骤；其次，为改进差分进化算法寻优效率，提出一种自适应子种群策略用于平衡全局搜索能力和局部搜索能力。同时，提出一种个体判断准则将种群个体进行划分，并根据个体反馈信息进行变异策略和控制参数选择。最后，为验证所提方法的有效性与通用性，分别以Stewart并联机构、4-PRP_aU并联机构和5PSS/UPU并联机构正运动学方程求解为例，使用NTDE、NCDE、CADE和MNPSO算法进行求解。实验结果表明，NTDE算法可以准确的求解出并联机构正运动学方程的所有根，并且NTDE算法获得的RR和SR值均优于其他三种比较算法。

关键词: 并联机构, 正运动学方程, 差分进化算法, 自适应子种群, 个体判断准则

Abstract: The forward kinematics equations of a coupled parallel mechanism can be reformulated as a system of nonlinear equations with multi-root. Solving such a system in a single operation poses a significant challenge in numerical computation. A neighborhood two-strategy differential evolutionary algorithm (NTDE) based on individual information is proposed to solve this problem. Firstly, the transformation of the forward kinematic equations of a parallel mechanism into an unconstrained optimization problem is illustrated using the Stewart parallel mechanism as an example. Secondly, to enhance the optimization efficiency of the differential evolution algorithm, an adaptive subpopulation strategy is proposed that balances global and local search capabilities. Additionally, an individual judgment criterion is introduced to differentiate between individuals in the population, while the variation strategy and control parameter selection are informed by feedback. Finally, to validate the effectiveness and generalizability of the proposed method, the forward kinematic equations of the Stewart parallel mechanism, the 4-PRP_aU parallel mechanism, and the 5PSS/UPU parallel mechanism are solved using the NTDE, NCDE, CADE, and MNPSO algorithms as examples. It is demonstrated by the experimental results that the NTDE algorithm effectively identifies all the roots of the forward kinematic equations for the parallel mechanism. Moreover, the RR and SR values obtained using the NTDE algorithm are shown to outperform those of the three comparative algorithms.

Key words: parallel mechanisms, forward kinematics equations, differential evolutionary algorithms, adaptive subpopulation, individual judgement criteria

中图分类号:

TG156

文世坤, 吉爱红, LEE Heow Pueh, 车林仙, 杨志康. 面向并联机构正运动学方程多根问题的改进差分进化算法[J]. 机械工程学报, 2025, 61(19): 43-53.

WEN Shikun, JI Aihong, LEE Heow Pueh, CHE Linxian, YANG Zhikang. Improvement of Differential Evolution Algorithm for Solving the Multi-root in Forward Kinematic Equations of Parallel Mechanisms[J]. Journal of Mechanical Engineering, 2025, 61(19): 43-53.

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