UMA APLICAÇÃO DA EQUAÇÃO DE LAPLACE NA AUTOMAÇÃO

Abstract

This work deals with the application of the qualitative theory of partial differential equations in automation, with emphasis on the theory of harmonic functions. The problem of this study involves a need for motion of a robot to a goal, deflecting from certain obstacles inserted in a square. To achieve these objectives, qualitative properties of harmonic functions, known as the mean-value property and the maximum principle, were used. The application was followed by modeling the problem in the softwares Excel and AutoCAD. The modeling showed that in fact the robot moved to the goal. The use of Excel was important, because this software has a tricolor scale resource, which transmits a two-dimensional representation of the study, that is, the illustration of the robot trajectory through the variation of colors along of square. AutoCAD, on the other hand, enabled the generation of three-dimensional simulations through the use of surfaces.