Navigation Functionalities for an Autonomous UAV Helicopter

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98 APPENDIX A. Fig. 1. The WITAS helicopter descend- Fig. 2. Landing pad with reference pating to the landing pad. tern seen from the on-board camera. proper trade-off between accuracy, range, latency, and rate has to be found optimizing the overall performance of the system. Our method requires a special landing pad (Fig. 2). As unmanned helicopters usually operate from a designated home base this is not a real constraint. A precise and fast pan/tilt camera is used to extend the range of the vision system and decouple the helicopter attitude from the vision field. We developed a single camera solution, as multi-camera systems make the system more complex and expensive and don’t offer significant advantages when using known landmarks. For the experimentation we used a helicopter platform (Fig. 1) which had been developed in the WITAS project [2,1]. Vision-based control of small size autonomous helicopters is an active area of research. A good overview of the state-of-the-art can be found in [7]. Our contribution to the landing problem consists of: (a) many demonstrated landings with a system only based on images from a single camera and inertial data using off-the-shelf computer hardware; (b) a wide envelope of starting points for the autonomous approach; (c) robustness to different weather conditions (wind, ambient light); (d) a quantitative evaluation of the vision system and the landing performance. 2 Vision System The vision system consists of a camera mounted on a pan/tilt unit (PTU), a computer for image processing, and a landing pad (a foldable plate) with a reference pattern on its surface. In this section, we explain the design of the reference pattern, describe the image formation, and present the image processing algorithm. The reference pattern is designed to fulfill the following criteria: fast recognition, accurate pose estimation for close and distant range, minimum size, and minimal asymmetry. We have chosen black circles on white background as they are fast to detect and provide accurate image features (Fig. 2). From
A.3. PAPER III 99 the projection of three circles lying on the corner points of an equilateral triangle the pose of an object is uniquely determined, assuming all intrinsic camera parameters are known. Circles are projected as ellipses, described by the center point ue, the semi-major axis la, the semi-minor axis lb, and the semi-major axis angle θe The pose of the landing pad with respect to the camera coordinate system is estimated by minimizing the reprojection error of the extracted center points and semi-axes of the three ellipses. We use five circle triplets of different size (radius 2 to 32 cm, distance 8 to 128 cm) with common center point to achieve a wide range of possible camera positions. Each triplet is uniquely determined by a combination of differently sized inner circles. A point p ˜x in the landing pad frame is projected on the image plane as follows: ũ = P p ⎛ ⎞ αu 0 u0 0 � cpR ˜x = ⎝ 0 αv v0 0 ⎠ 0 0 1 0 ctp 0T � p˜x 2 p 3 ũ ∈ P ˜x ∈ P 3 1 The extrinsic camera parameters are given by the three Euler angles of the rotation matrix c pR and the three components of the translation vector c tp. We use a camera model with the following intrinsic parameters: ”focal lengths” αu and αv in pixels, principal point (u0, v0), and four lens distortion coefficients . All intrinsic parameters are calibrated using Bouguet’s calibration toolbox [3]. A conic in P 2 is the locus of all points ũ satisfying the homogeneous quadratic equation ũ T C ũ = 0. The transformation of a circle Cp on the landing pad into an ellipse Ci in the image plane is given by[4]: Ci = (H −1 ) T Cp H −1 The homography matrix H is the projection matrix P without third column (z = 0). We calculate the ellipse center and axes from Ci and represent the parameters in a common feature vector c. Fig. 3 shows a data flow diagram of the vision system. Round-edged boxes represent image processing functions, sharp-edged boxes indicate independent processes, and dashed lines show trigger connections. Closed contours are extracted from gray-level images using a fast contour following algorithm with two parameters: edge strength and binarization threshold. The latter is calculated from the intensity distribution of the reference pattern. In the contour list we search for the three biggest ellipses belonging to a circle triplet. Ellipse parameters are estimated by minimizing the algebraic distance of undistorted contour points to the conic using SVD [4,6]. After having found three ellipses, the corresponding contours are resampled with sub-pixel accuracy. A coarse pose is estimated based on the ratio of semi-major axes (1) (2)
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Linköping Studies in Science and T
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Acknowledgements This work would ha
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Contents 1 Introduction 1 2 Overvie
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Chapter 1 Introduction An Unmanned
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of the environment in order to avoi
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Chapter 2 Overview This chapter pre
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2.1. UAV SOFTWARE ARCHITECTURE 7 wh
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2.2. THE UAV HELICOPTER PLATFORM 9
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2.2. THE UAV HELICOPTER PLATFORM 11
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Chapter 3 Simulation 3.1 Introducti
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3.2. HARDWARE-IN-THE-LOOP SIMULATIO
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3.3. REFERENCE FRAMES 17 3.3 Refere
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3.4. THE AUGMENTED RMAX DYNAMIC MOD
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3.4. THE AUGMENTED RMAX DYNAMIC MOD
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3.5. SIMULATION RESULTS 23 3.5 Simu
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3.5. SIMULATION RESULTS 25 Figure 3
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3.5. SIMULATION RESULTS 27 Figure 3
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Chapter 4 Path Following Control Mo
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4.2. TRAJECTORY GENERATOR 31 Figure
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4.2. TRAJECTORY GENERATOR 33 Fig. 4
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4.2. TRAJECTORY GENERATOR 35 be use
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4.2. TRAJECTORY GENERATOR 37 4.2.3
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4.2. TRAJECTORY GENERATOR 39 radius
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4.2. TRAJECTORY GENERATOR 41 Calcul
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4.2. TRAJECTORY GENERATOR 43 Figure
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4.2. TRAJECTORY GENERATOR 45 by the
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Page 83 and 84: BIBLIOGRAPHY 73 [9] E. Frazzoli. Ro
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Page 111 and 112: A.3. PAPER III 101 yes Tbo > Tlim2
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Page 121 and 122: Department of Computer and Informat
Page 123 and 124: No 598 Rego Granlund: C 3 Fire - A
Page 125 and 126: No 1024 Aleksandra Tešanovic: Towa
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Navigation Functionalities for an Autonomous UAV Helicopter

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