Navigation Functionalities for an Autonomous UAV Helicopter

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22 CHAPTER 3. SIMULATION substantially the dynamics of our simulator. Of course a small coupling effect between the lateral helicopter motion and yaw channel is neglected during a fast yaw maneuver due to the consistent increase of the tail rotor force. The equations in 3.7 are than rewritten in find form as follows: ˙u = Xuu − qw + rv − gsinθ ˙v = Yvv − ru + pw + gcosθsinφ (3.8) ˙w = Zww + T − pv + qu + gcosθcosφ where Xu, Yv and Zw are the aerodynamic derivatives (accounting for the aerodynamic drag). The value used for the aerodynamic derivatives are Xu = −0.025, Yv = −0.1 and Zw = −0.6. These values have been chosen using an empirical best fit criteria using flight-test data. The main rotor thrust T is given by: T = −g − ∆aZ (3.9) where ∆aZ is given by the fourth transfer function in 3.3. Comparing the equations in 3.8 with other works in the literature as for example in [16] it can be noticed that the rotor flapping terms are missing (the rotor flapping represents the possibility of the helicopter rotor disk to tilt relatively to the helicopter fuselage). On the other hand the flapping dynamics is contained in the transfer functions in 3.3. It was not possible to model the rotor flapping explicitly in the equations 3.8 because it is not observable from the black-box model identification approach used. The fact that the flapping terms are not included in equations 3.8 does not have strong consequences on the low frequency dynamics. On the other hand the high frequency helicopter dynamics is not captured correctly. Therefore the helicopter model derived here cannot be used for high bandwidth control system design. The model anyway is good enough for position and velocity control loop design. In [20] the mathematical formulation for rotor flapping can be found.
3.5. SIMULATION RESULTS 23 3.5 Simulation results The validation of the RMAX helicopter model can be found in [4]. In this section, the validation of the simulation procedure with the control system in the loop will be described. The results of two simulation tests of the PFCM, which will also be described later in the thesis, will be provided. The PFCM is a control function that enables the helicopter to follow 3D path segments. The path segments will be given to the PFCM which is in a closed loop with the simulator. The simulation results will be compared to the same PFCM implemented on the helicopter platform. This is not a validation of the simulator since the control function is in the loop. What is interesting is the analysis of the differences of the closed loop behavior between the flight-test and the simulation. The helicopter is commanded to fly a segment path starting from a hovering condition until reaching a target speed. The path also presents a curvature change. The same control function has been used for the two tests. In Fig. 3.5 and Fig. 3.6 the simulation (dashed line) and flight-test (continuous line) are overlapped on the same graph. The upper-left plot of Fig. 3.5 represents the helicopter path seen from above. The difference in position between the simulation and flight-test is very small, below one meter and cannot be seen in detail from the plot. In the same diagram the velocity components and the total velocity are plotted. This shows that the simulated velocity and the real velocity are quite close. In this test the helicopter was accelerated to 5 m/s forward speed. In Fig. 3.6 the results for the pitch and roll inputs and the attitude angles are presented. The pitch and roll inputs present a steady state error compared to the simulation while the pitch and roll angles are in good agreement. In Fig. 3.7 and Fig. 3.8 the same path segment is tested but the helicopter accelerates until 10 m/s is reached. The simulated position and velocity are still in good agreement with the flight-test experiment while the pitch and roll angles are worse. This is due to the fact that the aerodynamics of the rotor is not modeled. Taking into account such effects is necessary for flight conditions far from hovering. It is interesting to notice that the simulation can predict quite accurately the saturation of the roll input (Fig. 3.8) at around 845 sec. This could be a sign that the helicopter is flying too fast for the current path curvature, and an adjustment in the
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
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Page 23 and 24: Chapter 3 Simulation 3.1 Introducti
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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
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Page 45 and 46: 4.2. TRAJECTORY GENERATOR 35 be use
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Page 67 and 68: Chapter 5 Sensor fusion for vision
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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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