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Zastosowanie algorytmów opartych na rachunku różniczkowym niecałkowitego rzędu do wyznaczania ścieżki ruchu platformy mobilnej

Autonomous mobile vehicles which can determine the safe path to the predefined goal can be very useful in different situations, e.g. areas affected by a natural disasters, with different kinds of obstacles.

The aim of the project was development of new algorithms for fast and secure path planning for mobile vehicles. Following the designated path autonomous vehicle should reach a predefined target without hitting stationary obstacles. In the proposed algorithms, based on the a priori known positions and shapes of the obstacles, the generalized potential which indicates the level of danger in the vicinity of obstacles is determined. Discrete function of four variables: the position x, y of the obstacle, υ the order of fractional sum and the value of the charge q is used to model stationary obstacles. In the map each pixel of the obstacle is regarded as a charged point which generates an electric field with a specified potential. Their sums create the resultant electric potential. The value of generalized resultant potential in the given point is informs about the possibility of hitting an obstacle.

The safe path for the vehicle is determined based on the equipotential surfaces and positions of the start and finish point. The three methods for path finding were proposed: first based on the square mask with odd dimensions (3, 5 or greater). The second is based on circular mask defined by the Bresenham discrete circles (for different radii of the circles multidirectional masks can be obtained). The third method is based on flooding the potential fields (analogously to the image segmentation method called Watershed).

In order to compare developed algorithms the testing station was built. The station allows to study the movement of the real mobile platform in the virtual environment. The path is determined by the proposed algorithms in the computer generated world and next is sent to the real mobile platform which follows the path. It allows to the evaluation of the proposed methods. Additionally the impact of the different terrain characteristics on the realization of the trajectory can be studied. The testing station consists of three modules: central unit (generates the virtual world), engine test stand (maps the wheel movements of the real mobile platform into virtual world) and control module of the mobile platform.

All goals declared in the project were realized successfully. In addition, Authors were inspired to determine the directions for the further works, such as applying different values of charges or using two-argument function of charge distribution. This will allow for more accurate modeling of obstacles using method of the potential fields.

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