zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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.

65K05Mathematical programming (numerical methods)
90C15Stochastic programming
70B10Kinematics of a rigid body