The paper presents a new method of constructing equidistant map projections of a triaxial ellipsoid as a function of reduced coordinates. Equations for x and y coordinates are expressed with the use of the normal elliptic integral of the second kind and Jacobian elliptic functions. This solution allows to use common known and widely described in literature methods of solving such integrals and functions. The main advantage of this method is the fact that the calculations of x and y coordinates are practically based on a single algorithm that is required to solve the elliptic integral of the second kind. Equations are provided for three types of map projections: cylindrical, azimuthal and pseudocylindrical. These types of projections are often used in planetary cartography for presentation of entire and polar regions of extraterrestrial objects. The paper also contains equations for the calculation of the length of a meridian and a parallel of a triaxial ellipsoid in reduced coordinates. Moreover, graticules of three coordinates systems (planetographic, planetocentric and reduced) in developed map projections are presented. The basic properties of developed map projections are also described. The obtained map projections may be applied in planetary cartography in order to create maps of extraterrestrial objects.
Praca dotyczy problemów percepcji i modelowania powierzchni terenu na podstawie danych z miniaturowego skanera laserowego 2D typu Hokuyo URG-04LX, w który wyposażony jest robot kroczący. Otrzymana mapa może być podstawą do planowania ruchu robota po nierównym terenie. Przedstawiono analizę błędów pomiaru odległości w omawianym zadaniu oraz dokonano wyboru konfiguracji systemu sensorycznego, która zapewnia najlepsze warunki akwizycji profilu terenu i redukcję błędów. Zaproponowano metodę budowy rastrowej mapy terenu zawierającą oryginalne algorytmy usuwania błędnych pomiarów oraz zaprezentowano wyniki eksperymentalnej weryfikacji działania tej metody.
EN
This paper considers the problem of terrain perception for a hexapod robot equipped with the compact Hokuyo URG-04LX laser scanner. An analysis of the scanner range measurements uncertainty is presented. Different geometric configurations of the sensing system are analysed, and the one that is best for terrain profile acquisition is chosen. Then, an application of the sensor in local terrain mapping supporting footholds selection is presented, including novel algorithms that remove map artifacts resulting from qualitative errors in range sensing. Experimental results are provided.
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