CASPIAN JOURNAL
MANAGEMENT AND HIGH TECHNOLOGIES
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Read | Karpasyuk Vladimir K., Karpasyuk Igor V. // Caspian journal : management and high technologies. — 2012. — №1. — pp. 125-131. |
Karpasyuk Vladimir K. - Doctor of science (Physics and Mathematics), Astrakhan State University, 20a Tatishchev Str., Astrakhan, 414056, Russia, karpasyuk@aspu.ru.
Karpasyuk Igor V. - Candidate of science (Physics and Mathematics), Astrakhan State Technical University, 16 Tatishchev Str., Astrakhan, 414025, Russia, i.karpasyuk@astu.org.
The paper studies actual problem of the modeling of real processes in dynamical environment on the basis of algorithms which realize required strategies for given aims achievement. Mathematical model of minimal time controllable motion of material point between starting and end states in the plane containing moving or immovable impenetrable round zones is proposed. The straight-line regular motion of such obstacles is allowed. Equations of motion are obtained in the presence of maximum control constraint. The friction force, directly proportional to the velocity, is taken into consideration. Starting and end values of the velocity are assumed to be zero. Equations of motion are integrated under the condition for maximum acceleration. Different basic variants of possible configurations of the environment are given. Algorithms of mobile object motion control in determinate workspace for each variant are described. Differences of global and local methods of trajectories planning are observed. Computer program for modeling of the motion in stationary and non-stationary workspace is described. Comparison of the modeling results for global and local control is given. Adequacy of mathematical model and reliability of results are justified.
Key words: mathematical modeling,controllable motion,obstacles avoidance,time minimization,determinate dynamical environment,friction of motion,system of differential equations,global and local control,algorithm,computer experiment