Improvement of Differential Evolution Algorithm for Solving the Multi-root in Forward Kinematic Equations of Parallel Mechanisms

doi:10.3901/JME.2025.19.043

Abstract

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

CLC Number:

TG156

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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