On the use of differential evolution for forward kinematics of parallel manipulators

Differential evolution (DE) is a real-valued number encoded evolutionary strategy for global optimization. It has been shown to be an efficient, effective and robust optimization algorithm, especially for problems containing continuous variables. We have applied a DE algorithm to solve forward kinematics problems of parallel manipulators. The forward kinematics of a parallel manipulator is transformed into an optimization problem by making full use of the property that it is easy to obtain its inverse kinematics and then DE is used to obtain a globally optimal solution of forward kinematics. A comparison of numerical simulation results of a pneumatic 6-SPS parallel manipulator with DE, genetic algorithm and particle swarm optimization is given, which shows that the DE-based method performs well in terms of quality of the optimal solution, reliability and speed of convergence. It should be especially noted that the proposed method is also suitable for various other types of parallel manipulators, which provides a new way to solve the forward kinematics of parallel manipulators.

[1]  Yunfeng Wang.  An Incremental Method for Forward Kinematics of Parallel Manipulators , 2006, 2006 IEEE Conference on Robotics, Automation and Mechatronics.

[2]  Zhang Guo-wei.  Direct Kinematic Problem Based on RBFNN of Parallel Manipulator , 2004 .

[3]  Wei Sun,et al.  Iterative Learning Controller for Trajectory Tracking Tasks Based on Experience Database , 2005, ICMLC.

[4]  Rong-Song He,et al.  Improving real-parameter genetic algorithm with simulated annealing for engineering problems , 2006, Adv. Eng. Softw..

[5]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .

[6]  M. Petko,et al.  Mechatronic design of a parallel manipulator for milling , 2005, Proceedings, 2005 IEEE/ASME International Conference on Advanced Intelligent Mechatronics..

[7]  Michael R. Lyu,et al.  A hybrid particle swarm optimization-back-propagation algorithm for feedforward neural network training , 2007, Appl. Math. Comput..

[8]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[9]  Zafer Bingul,et al.  Hybrid genetic algorithm and simulated annealing for two-dimensional non-guillotine rectangular packing problems , 2006, Eng. Appl. Artif. Intell..

[10]  Fuan Wen,et al.  Displacement analysis of the 6-6 stewart platform mechanisms , 1994 .

[11]  Wei Song,et al.  Genetic Algorithm-Based Text Clustering Technique , 2006, ICNC.

[12]  Peng-Yeng Yin,et al.  A particle swarm optimization approach to the nonlinear resource allocation problem , 2006, Appl. Math. Comput..

[13]  Zheng Chun.  Forward kinematics of a general Stewart parallel manipulator using the genetic algorithm , 2003 .

[14]  Patrick Brézillon,et al.  Lecture Notes in Artificial Intelligence , 1999 .

[15]  Chyi Hwang,et al.  Optimal approximation of linear systems by a differential evolution algorithm , 2001, IEEE Trans. Syst. Man Cybern. Part A.

[16]  Bing Yu,et al.  Training radial basis function networks with differential evolution , 2006, 2006 IEEE International Conference on Granular Computing.

[17]  Michele Lacagnina,et al.  A Novel Parallel Manipulator Architecture for Manufacturing Applications , 2003 .

[18]  Russell C. Eberhart,et al.  A discrete binary version of the particle swarm algorithm , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[19]  Pratik J. Parikh,et al.  A hybrid strategy to solve the forward kinematics problem in parallel manipulators , 2005, IEEE Transactions on Robotics.

[20]  Dimitris E. Koulouriotis,et al.  Comparing simulated annealing and genetic algorithm in learning FCM , 2007, Appl. Math. Comput..

[21]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..