STRATEGIES FOR DETERMINING THE PARAMETERS OF AN INACCESSIBLE POINT OF AN OBJECT

Abstract

In the present research the strategies to the determination of the parameters of an inaccessible point of an object is developed. The common issues are revealed and essential steps of their resolution are identified.

The essence of the problem is an objective contradiction between a requirement for the location of points A and B of the centers of the sighting tubes of optical devices in the same horizontal plane P₁ and the lack of a real possibility to perform such to achieve this an identical one-level arrangement without error.

The aim of the study is to develop strategies for determining the position of an inaccessible point of an object in the minimum domain between intersecting sighting rays as well as an adaptive algorithm for determining the values of the parameters of an inaccessible point under the given absolute and relative errors.

To achieve this aim, the following problems are formulated and solved in the paper: 1. Develop strategies for determining the position of the inaccessible point of the object in the minimum domain between the intersecting sighting rays. 2. Carry out an experimental test of the developed strategies.

In the proposed optimizing approach, the three-dimensional geometrical model with crossed directional rays for the determination of coordinates of the inaccessible point of an object is developed. It is discussed that points С and C', coordinated of which to be determined, locates in domain [C_DM, C_EM], [C'_D'M, C'_E'M] of the minimum distance ρ_min between crossed directional rays.

The optimizing problem of the determination of coordinates of an inaccessible point of an object in space is reduced to a problem of the determination of the minimum distance between two crossed directional rays.

It’s known from the theory of function of multiple variables that function ρ = f (t_C'D', t_C'E') reaches its extremum ρ_min when its partial derivatives by each variable are equal to zero.

Three strategies for selecting the position of the inaccessible point C (x_C, y_C, z_C) in the found minimum region [C_DM, C_EM] are proposed. The required point C' (x_C', y_C', z_C') can be located, for example, in the middle of the minimum segment [C'_D'M, C'_E'M].

The proposed approach is verified using real experimental data.

Keywords: an object, point, extremum, directional ray, collimating ray, coordinates, strategies, geometrical model, analytical model.