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**On the use of differential evolution for forward kinematics of parallel manipulators.**
*(English)*
Zbl 1157.65392

Summary: 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.

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.

### MSC:

65K05 | Numerical mathematical programming methods |

90C15 | Stochastic programming |

70B10 | Kinematics of a rigid body |

### Keywords:

evolutionary strategy; differential evolution; forward kinematics; parallel manipulator; numerical examples; optimization algorithm; genetic algorithm; particle swarm optimization; convergence
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\textit{X.-S. Wang} et al., Appl. Math. Comput. 205, No. 2, 760--769 (2008; Zbl 1157.65392)

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### References:

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