On one approach to the approximation of solutions to the direct kinematics problem of parallel manipulators

Abstract

Any real continuous bounded function of many variables is representable as a superposition of functions of one variable and addition. Depending on the type of superposition, the requirements for the functions of one variable differ. The article investigated one of the options for the numerical implementation of such a superposition proposed by Sprecher. The superposition was presented as a three-layer Feedforward neural network, while the functions of the first’s layer were considered as a generator of space-filling curves (Peano curves). The resulting neural network was applied to the problems of direct kinematics of parallel manipulators.

Keywords

• parallel manipulators
• kolmogorov’s superpositions
• universal approximation
• space-filling curve