Navigation Functionalities for an Autonomous UAV Helicopter

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20 CHAPTER 3. SIMULATION the body yaw angular rate increment (deg/sec) and ∆AZ the acceleration increment (g) along the Zb body axis. ∆AIL, ∆ELE, ∆RUD and ∆T HR are the control input increments taken relative to a trimmed flight condition. The control inputs are in YACS unit and range from -500 and +500. These transfer functions describe not only the dynamic behavior of the YACS but also the dynamics of the helicopter (rotor and body) and the dynamics of the actuators. Since the chain composed by the YACS, actuators and helicopter is quite complex it is important to remember that the estimated model has only picked up a simple reflection of the system behavior. The identification was done near the hovering condition so it is improper to use the model for different flight conditions. In spite of this, simulations up to ∼10 m/s have shown good agreement with the experimental flight-test results. 3.4.2 Helicopter equations of motion The aircraft equations of motion can be expressed in the body reference frame with three sets of first order differential equations [7]. The first set represents the translational dynamics along the three body axes: X = m( ˙u + qw − rv) + mgsinθ Y = m( ˙v + ru − pw) − mgcosθsinφ (3.4) Z = m( ˙w + pv − qu) − mgcosθcosφ where X, Y , Z represent the resultants of all the aerodynamic forces; u, v, w the body velocity components; p, q, r the body angular rates; m and g the mass and the gravity acceleration; φ and θ the pitch and roll angles. The second set of equations represents the aircraft rotational dynamics: L = Ix ˙p − (Iy − Iz)qr M = Iy ˙q − (Iz − Ix)rp (3.5) N = Iz ˙r − (Ix − Iy)pq where L, M, N represent the moments generated by the aerodynamic forces acting on the helicopter; Ix, Iy, Iz the inertia moments of the helicopter.
3.4. THE AUGMENTED RMAX DYNAMIC MODEL 21 The third set of equations represents the relation between the body angular rates and the Euler angles: ˙φ = p + qsinφtanθ + rcosφtanθ ˙θ = qcosφ − rsinφ (3.6) ˙ψ = qsinφsecθ + rcosφsecθ These three sets of nonlinear equations are valid for a generic aircraft. The transfer functions in 3.3 can be used now in the motion equations. From the Laplace domain of the transfer functions, it is possible to pass to the time domain. This means that from the first three equations in 3.3 we derive φ(t), θ(t) and r(t) which can be used in 3.6 in order to find the other parameters p(t), q(t), ψ(t). The equations in 3.5 will not be used in the model because the dynamics represented by these equations is contained in the first three transfer functions in 3.3. The motion equations in 3.4 can be rewritten as follows: ˙u = Fx − qw + rv − gsinθ ˙v = Fy − ru + pw + gcosθsinφ (3.7) ˙w = Fz − pv + qu + gcosθcosφ where Fx, Fy, Fz are the forces per unit of mass. In this set of equations some of the nonlinear terms are small and can be neglected for our flight envelope, although for simulation purposes, it does not hurt to leave them there. Later when the model will be used for control purposes the necessary simplifications will be made. The tail rotor force is included in Fy and it is balanced by a certain amount of roll angle. In fact every helicopter with a tail rotor must fly with a few degrees of roll angle in order to compensate for the tail rotor force which is directed sideway. For the RMAX helicopter the roll angle is 4.5 deg in hovering condition with no wind. The yaw dynamics in our case is represented by the third transfer function in 3.3. For this reason we do not have to model the force explicitly. By doing that we find in our model a zero degree roll angle in hovering condition which does not affect
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
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Page 27 and 28: 3.3. REFERENCE FRAMES 17 3.3 Refere
Page 29: 3.4. THE AUGMENTED RMAX DYNAMIC MOD
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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 and 46: 4.2. TRAJECTORY GENERATOR 35 be use
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
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Page 61 and 62: 4.4. EXPERIMENTAL RESULTS 51 Up [m]
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Page 71 and 72: 5.1. FILTER ARCHITECTURE 61 filter
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Page 75 and 76: 5.2. EXPERIMENTAL RESULTS 65 Figure
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5.3. CONCLUSION 71 vision system st
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BIBLIOGRAPHY 73 [9] E. Frazzoli. Ro
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Appendix A 75
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A.1. PAPER I 77 is a three-dimensio
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A.1. PAPER I 79 The reference point
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A.1. PAPER I 81 Path Av Err Max Err
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A.2. PAPER II 83 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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