[Studies in Computational Intelligence 481] Artur Babiarz, Robert Bieda, Karol Jędrasiak, Aleksander Nawrat (auth.), Aleksander Nawrat, Zygmunt Kuś (eds.) - Vision Based Systemsfor UAV Applications (2013, Sprin

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196 D. Cedrych et al. where , (6) ,…, , , , , , (7) , ∞, , 1,2,…,2 In (7) and are equal to and correspondingly which are defined in (2). This set defines the vertices of the graph (6). Second part of the graph model is the set of edges . It defines mutual, spatial relations between elements defined by as well as costs of transitions between any given pair of vertices. Calculation of costs is a crucial part of the model creation. All the process of planning is based on the graph representation so the quality of the model is critical for this process. In this the cost between two elements of the set is calculated as: , 1 , (8) where denotes Euclidean distance between ith and jth vertex, and: , is a sum of altitudes read from the map (\ref{fig:2}) along the line that connects vertex ith with vertex jth. This mapping is done according the following rule: 0 (10) , If the line that connects vertex ith with vertex jth crossed the state border line (9), the sum is set to a relatively big number to prevent the algorithm for searching paths that crosses the border lines. As a result of determining costs of transitions between all pairs of vertices the cost matrix is created. It is denoted as: 2.6 Solution (9) , , 1,2,…,2 (11) For the representation given by (11) searching the path of minimal cost is performed. There are many effective algorithms for minimal path search [5] but in this study the Dijkstra's algorithm was chosen. Since the graph defined by (11) is the complete one, always exists the path connecting vertices and .As a result of the graph search the path that connects those vertices is found: ,…, , , , 2 2 (12) each element of the set (12) is a point in a 2D space. Next stage consists of transforming this solution into 3D space. This process is done by attributing each point of the (12) with appropriate altitude. This is done in the following way: For each
Probabilistic Approach to Planning Collision Free Path of UAV 197 pair , of points from the set (12) it is checked if for any point that lays on the line between , the height is lower than $H_0$. If yes, the point is attributed with the coordinate Δ and this point is added to the solution. As a result of this iterative procedure the final solution defined in 3D space is determined: , ,…, , (13) where each element , 1,2,… defines a point in 3D space that has coordinates ( , , ). 2.7 Indices of the Quality of Generated Solution Here we introduce three indices for rating founded solution. It is reasonable to assume that UAV energy consumption increases with the incease of trajectory. It also increases for frequent changes of the altitude of UAV during the mission. The following are three proposed indices: • - is the length of the path in 2D space. • - is the length of the path in 3D space. • - is the sum of changes of absolute values of UAV altitudes. 3 Simulations In this chapter we present simulation results. The following are the main assumptions that were followed during the simulation process: • The reference altitude (priory stated height ) of UAV is set to = 1500 m, 1600 m and 1700 m. • The minimal distance between UAV and the terrain surface ('safety margin') is set to = 50 m. • The number of randomly generated points is set to = 30. Below three sets of figures are shown for different altitudes. For readers convenience in these figures the state border lines are represented by canyons. Figures 4 and 5 are for = 1500 m, figures 6 and 7 for = 1600 m, figures 8 and 9 for = 1700 m. In the following tables the indices values are presented. For each altitude 5 solutions were generated. Table 1 shows the values of indices for = 1500 m, table 2 is for = 1600 m and finally, table 3 is for = 1700 m. It is observed, that the values of indices are decreasing with increase of .
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Studies in Computational Intelligen
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Aleksander Nawrat · Zygmunt Kuś E
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“In God We Trust, All others we o
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VIII Preface valuable information i
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Contents Part I: Design of Object D
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Contents XIII Technology Developmen
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XVI List of Contributors Adam Czorn
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XVIII List of Contributors Henryk M
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XX List of Contributors Józef Wron
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2 Design of Object Detection, Recog
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4 A. Babiarz et al. 1 Introduction
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6 A. Babiarz et al. The description
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10 A. Babiarz et al. o o o “micvo
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12 A. Babiarz et al. a) b) Fig. 7.
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14 A. Babiarz et al. • The camera
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18 A. Babiarz et al. a) b) Fig. 11.
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Recognition and Location of Objects
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118 D. Bereska et al. Fig. 2. Image
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120 D. Bereska et al. Fig. 4. Ortho
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Omnidirectional Video Acquisition D
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Part III Design of Vision Based Con
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Vision System for Group of Mobile R
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Vision System for Group of Mobile R
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344 Conclusions Control algorithms
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[Studies in Computational Intelligence 481] Artur Babiarz, Robert Bieda, Karol Jędrasiak, Aleksander Nawrat (auth.), Aleksander Nawrat, Zygmunt Kuś (eds.) - Vision Based Systemsfor UAV Applications (2013, Sprin

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