Navigation Functionalities for an Autonomous UAV Helicopter

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34 CHAPTER 4. PATH FOLLOWING CONTROL MODE The path generated in this way can have discontinuity of the second order derivative at the segment joints. This can lead to a small path tracking error especially at high speed. The 12 parameters are passed as input arguments to the PFCM which then generates the reference geometric segment used for control purposes. The generation of the path segment in the PFCM is done using the matrix formulation in 4.2 with the boundary condition vector explicitly written on the right hand side. The parameter s ranges from s = 0 which corresponds to the starting point P (0) to s = 1 which corresponds to the end point P (1) of the same segment. When the helicopter enters the next segment the parameter is reset to zero. P n (s) = � s3 s2 s 1 � ⎡ ⎤ ⎡ 2 −2 1 1 ⎢ −3 3 −2 −1 ⎥ ⎢ ⎥ ⎢ ⎣ 0 0 1 0 ⎦ ⎣ 1 0 0 0 P (0) P (1) P ′ (0) P ′ (1) ⎤ ⎥ ⎦ (4.2) For control purposes the tangent and the curvature need to be calculated. The path tangent T n is: T n (s) = � 3s2 2s 1 0 � ⎡ ⎤ ⎡ 2 −2 1 1 P (0) ⎢ −3 3 −2 −1 ⎥ ⎢ ⎥ ⎢ P (1) ⎣ 0 0 1 0 ⎦ ⎣ P 1 0 0 0 ′ (0) P ′ ⎤ ⎥ ⎦ (4.3) (1) The path curvature K n is: Q n (s) = � 6s 2 0 0 � ⎡ ⎤ ⎡ 2 −2 1 1 ⎢ −3 3 −2 −1 ⎥ ⎢ ⎥ ⎢ ⎣ 0 0 1 0 ⎦ ⎣ 1 0 0 0 K n (s)= T n (s) × Q n (s) × T n (s) |T n (s)| 4 P (0) P (1) P ′ (0) P ′ (1) ⎤ ⎥ ⎦ (4.4) In the guidance law the curvature radius which is R n = 1/K n will be used. Since T n and R n are expressed in the navigation frame, in order to
4.2. TRAJECTORY GENERATOR 35 be used in the guidance law, they have to be transformed into the body frame using the rotation matrix C b n defined in section 3.3. At this point the geometric parameters (tangent and curvature) of the path segment are known. Now these parameters can be used in the guidance law provided that the path segment parameter s is known. The method as to how to find s will be discussed in the next section. 4.2.2 Feedback method When the dynamic model of the helicopter is known, it is in principle possible to calculate beforehand at what point in the path the helicopter should be at a certain time. By doing this the path segment would be time dependent. In this way at each control cycle the path parameters (position, velocity and attitude) would be known and they could be used directly for control purposes. Then the helicopter could be accelerated or slowed down if it is behind or ahead of the actual control point (which is the point of the path where the helicopter should be at the relative time). The generation of a time dependent trajectory is usually a complex problem. An additional complication is that the trajectory has to satisfy obstacle constraints (to find a collision free path in a cluttered environment [18]). The alternative approach used here is the following. Instead of accelerating or slowing down the helicopter, the control point will be accelerated or slowed down using a feedback method. In this way the path is not time dependent anymore and so the problem of generating a collision free path can be treated separately from the helicopter dynamics. Of course the path generated must be smooth enough to be flown with a reasonable velocity and this has to be taken into account at the path planning level. The fact that the helicopter kinematic and dynamic constraints are not taken into account at the path planning level might lead to a path which forces the helicopter to abrupt brake due to fast curvature change. This problem can be attenuated using some simple rules in the calculation of the segment boundary conditions [18]. The algorithm implemented in this thesis finds the control point by searching for the closest point of the path to the helicopter position. The problem could be solved geometrically simply by computing an orthogonal
Page 1: Linköping Studies in Science and T
Page 5: Acknowledgements This work would ha
Page 9 and 10: Contents 1 Introduction 1 2 Overvie
Page 11 and 12: Chapter 1 Introduction An Unmanned
Page 13 and 14: of the environment in order to avoi
Page 15 and 16: Chapter 2 Overview This chapter pre
Page 17 and 18: 2.1. UAV SOFTWARE ARCHITECTURE 7 wh
Page 19 and 20: 2.2. THE UAV HELICOPTER PLATFORM 9
Page 21 and 22: 2.2. THE UAV HELICOPTER PLATFORM 11
Page 23 and 24: Chapter 3 Simulation 3.1 Introducti
Page 25 and 26: 3.2. HARDWARE-IN-THE-LOOP SIMULATIO
Page 27 and 28: 3.3. REFERENCE FRAMES 17 3.3 Refere
Page 29 and 30: 3.4. THE AUGMENTED RMAX DYNAMIC MOD
Page 31 and 32: 3.4. THE AUGMENTED RMAX DYNAMIC MOD
Page 33 and 34: 3.5. SIMULATION RESULTS 23 3.5 Simu
Page 35 and 36: 3.5. SIMULATION RESULTS 25 Figure 3
Page 37 and 38: 3.5. SIMULATION RESULTS 27 Figure 3
Page 39 and 40: Chapter 4 Path Following Control Mo
Page 41 and 42: 4.2. TRAJECTORY GENERATOR 31 Figure
Page 43: 4.2. TRAJECTORY GENERATOR 33 Fig. 4
Page 47 and 48: 4.2. TRAJECTORY GENERATOR 37 4.2.3
Page 49 and 50: 4.2. TRAJECTORY GENERATOR 39 radius
Page 51 and 52: 4.2. TRAJECTORY GENERATOR 41 Calcul
Page 55 and 56: 4.2. TRAJECTORY GENERATOR 45 by the
Page 59 and 60: 4.3. OUTER LOOP CONTROL EQUATIONS 4
Page 61 and 62: 4.4. EXPERIMENTAL RESULTS 51 Up [m]
Page 63 and 64: 4.5. CONCLUSIONS 53 1 + s 1 C(s) =
Page 65 and 66: 4.5. CONCLUSIONS 55 Vel [m/s] 20 18
Page 67 and 68: Chapter 5 Sensor fusion for vision
Page 69 and 70: composed of three accelerometers an
Page 71 and 72: 5.1. FILTER ARCHITECTURE 61 filter
Page 73 and 74: 5.1. FILTER ARCHITECTURE 63 north,
Page 75 and 76: 5.2. EXPERIMENTAL RESULTS 65 Figure
Page 77 and 78: 5.2. EXPERIMENTAL RESULTS 67 Figure
Page 79 and 80: 5.2. EXPERIMENTAL RESULTS 69 by the
Page 81 and 82: 5.3. CONCLUSION 71 vision system st
Page 83 and 84: BIBLIOGRAPHY 73 [9] E. Frazzoli. Ro
Page 85 and 86: Appendix A 75
Page 87 and 88: A.1. PAPER I 77 is a three-dimensio
Page 89 and 90: A.1. PAPER I 79 The reference point
Page 91 and 92: A.1. PAPER I 81 Path Av Err Max Err
Page 93 and 94: A.2. PAPER II 83 From Motion Planni
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A.2. PAPER II 85 From Motion Planni
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A.3. PAPER III 97 A.3 Paper III Aut
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A.3. PAPER III 99 the projection of
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A.3. PAPER III 101 yes Tbo > Tlim2
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A.3. PAPER III 103 immediately afte
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A.3. PAPER III 105 altitude [m] 20
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A.3. PAPER III 107 Fig. 10. Flight
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Department of Computer and Informat
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No 598 Rego Granlund: C 3 Fire - A
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No 1024 Aleksandra Tešanovic: Towa
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Navigation Functionalities for an Autonomous UAV Helicopter

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