Navigation Functionalities for an Autonomous UAV Helicopter

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36 CHAPTER 4. PATH FOLLOWING CONTROL MODE projection from the helicopter position to the path. The problem which arises in doing this is that there could be multiple solutions. For this reason a method has been adopted which finds the control point incrementally and searches for the orthogonality condition only locally. The reference point on the nominal path is found by satisfying the geometric condition that the scalar product between the tangent vector and the error vector has to be zero: E • T = 0 (4.5) where the error vector E is the helicopter distance from the candidate control point. The control point error feedback is calculated as follows: ef = E • T /|T | (4.6) that is the magnitude of the error vector projected on the tangent T . The vector E is calculated as follows: E = p cp,n−1 − p heli (4.7) where p cp,n−1 is the control point position at the previous control cycle and p heli is the actual helicopter position. The control point is updated using the differential relation: Equation 4.8 is applied in the discretized form: dp = p ′ · ds (4.8) sn = sn−1 + ef | dp cp ds |n−1 (4.9) where sn is the new value of the parameter. Equations 4.6 and 4.9 can also be used iteratively in order to find a more accurate control point position. In this application, it was not necessary. Once the new value of s is known, all the path parameters can be calculated.
4.2. TRAJECTORY GENERATOR 37 4.2.3 Outer loop reference inputs In this section, the method used to calculate the reference input or set-point for the outer control loop will be described in detail. Before proceeding, a description as to how the PFCM takes into account some of the helicopter kinematic constraints will be provided. PFCM kinematic constraints The model in 3.8 will be used to derive the guidance law which enables the helicopter to follow a 3D path. The sin and cos can be linearized around θ = 0 and φ = 0 since in our flight condition, the pitch and roll angles are between the interval ∼ ±20 deg. This means that we can approximate the sin of the angle to the angle itself (in radians) and the cos of the angle to 1. By doing this from the first and second equation of 3.6 it is possible to calculate the body angular rate p and q: q = ˙ θ + rφ (4.10) p = ˙ φ − rθ where the product between two or more angles has been neglected because it is small compared to the other terms. Using the same considerations and substituting 4.10 it is possible to rewrite the system in 3.8 in the following form: ˙u = Xuu − ( ˙ θ + rφ)w + rv − gθ ˙v = Yvv − ru + ( ˙ φ − rθ)w + gφ (4.11) ˙w = Zww + T − ( ˙ φ − rθ)v + ( ˙ θ + rφ)u + g At this point we can add the condition that the helicopter has to fly with the fuselage aligned to the path (in general this condition is not necessary for a helicopter, it has been adopted here to simplify the calculation). The constraints which describe this flight condition (under the assumption of relatively small pitch and roll angles) are:
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 and 44: 4.2. TRAJECTORY GENERATOR 33 Fig. 4
Page 45: 4.2. TRAJECTORY GENERATOR 35 be use
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
Page 95 and 96: A.2. PAPER II 85 From Motion Planni
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A.2. PAPER II 87 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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