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Mathematical Problems in Engineering
Volume 2018, Article ID 9815469, 9 pages
Research Article

A Hybrid Strategy of Differential Evolution and Modified Particle Swarm Optimization for Numerical Solution of a Parallel Manipulator

1State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China
2Lappeenranta University of Technology, 53810 Lappeenranta, Finland

Correspondence should be addressed to Bingyan Mao; moc.361@negoacus

Received 19 July 2017; Revised 8 January 2018; Accepted 22 January 2018; Published 22 February 2018

Academic Editor: Giuseppe Fedele

Copyright © 2018 Bingyan Mao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a hybrid strategy combined with a differential evolution (DE) algorithm and a modified particle swarm optimization (PSO), denominated as DEMPSO, to solve the nonlinear model of the forward kinematics. The proposed DEMPSO takes the best advantage of the convergence rate of MPSO and the global optimization of DE. A comparison study between the DEMPSO and the other optimization algorithms such as the DE algorithm, PSO algorithm, and MPSO algorithm is performed to obtain the numerical solution of the forward kinematics of a 3-RPS parallel manipulator. The forward kinematic model of the 3-RPS parallel manipulator has been developed and it is essentially a nonlinear algebraic equation which is dependent on the structure of the mechanism. A constraint equation based on the assembly relationship is utilized to express the position and orientation of the manipulator. Five configurations with different positions and orientations are used as an example to illustrate the effectiveness of the proposed DEMPSO for solving the kinematic problem of parallel manipulators. And the comparison study results of DEMPSO and the other optimization algorithms also show that DEMPSO can provide a better performance regarding the convergence rate and global searching properties.