Approximating a solution set of nonlinear inequalities

Evtushenko, Yu. G.; Posypkin, Mikhail; Rybak, Larisa; Turkin, Andrei

doi:10.1007/s10898-017-0576-z

Cited by 41 publications

(12 citation statements)

References 21 publications

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“…The second planar parallel manipulator (3-RPR) [22,[24][25][26] is shown in Figure 5 and consists of three variablelength links attached to a movable triangular platform and hinged on a fixed platform. The system of kinematic equations (and inequalities) for a given manipulator can be written as follows: Therefore, to obtain an unambiguous solution, the restriction φ = π/4 was introduced and the only assembly was taken as the workspace.…”

Section: Parallel Manipulatorsmentioning

confidence: 99%

“…The approximation results can be seen in Table 2. The form of the functions x(η), y(η) can be seen in Figure 10 It should be noted that the proposed approach (like neural networks of a different architecture) is not by far the best tool for direct kinematics problems, it is also necessary to consider analytical and numerical methods of solution [25][26][27]29].…”

Section: Numerical Experimentsmentioning

confidence: 99%

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

Gorchakov

Mozolenko

2020

Open Computer Science

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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.

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Section: Parallel Manipulatorsmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

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

Gorchakov

Mozolenko

2020

Open Computer Science

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“…A system for solving global optimization problems with Branch and Bound method was proposed in [2]. Research on processing nonlinear inequalities was made in [3]. Some research on complexity and scalability of this method was made in [4,5].…”

Section: Introductionmentioning

confidence: 99%

Tool for Simulating Branch and Bound Computations

Ignatov

Gorchakov

2020

Open Computer Science

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The paper describes a simulator of parallel Branch and Bound (BnB) method. Several subdomain trees for benchmark functions are analyzed, a characteristic Gaussian-like distribution is discovered. An algorithm of artificial tree generation is formulated according to this criterion. The process of simulator modeling is described, several computational experiments are conducted. Their results show a hyperbolic decrease trend for modeled time as the number of computational units grows, which is concluded to be similar to real systems.

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“…Despite the variety of methods, the solution of the direct problem is reduced to solving a system of nonlinear equations that a priori require knowledge of a large number of parameters related to the structural features of the parallel structure mechanism, the location of the hinges, and so on. Numerical methods are used to solve the system of equations [18,19].…”

Section: Introductionmentioning

confidence: 99%