University of Bologna Department of Electronics, Computer Science and Systems Prototyping, Modeling and Control of a Class of VTOL Aerial Robots Ph.D. Thesis by: Roberto Naldi Tutor: Prof. Lorenzo Marconi XX Ciclo University of Bologna Department of Electronics, Computer Science and Systems Prototyping, Modeling and Control of a Class of VTOL Aerial Robots Ph.D. Thesis by: Tutor: Roberto Naldi Prof. Lorenzo Marconi XX Ciclo Dott. Ing. Roberto Naldi CASY - DEIS - University of Bologna Viale Pepoli 3/2, 40136 Bologna. Phone: +39 051 2093788 Fax: +39 051 2093073 Email: [email protected] This thesis has been written in LATEX. Acknowledgments: ThisworkhasbeenpartiallyfundedbyMIUR(Ministerodell’istruzione,dell’universit`a e della ricerca). Copyright c 2008 by Roberto Naldi. All rights reserved. (cid:13) No part of this publication may bereproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording or any information storage and retrieval system, without permission in writing from the author. 3 There are many people which I have to thank for many help, inspiration and friend- ship received in these years. First of all I would like to thank Lorenzo, which has been a great mentor and most of all has teach me the beauty of the research. I don’t know how to thank enough Andrea (”Asla”), which is the real author of all the ex- perimental work, and, most of all, which has divided with me long days spent on the flying field and in the lab looking for new crazy flying ideas. I’m grateful to Luca, which has joined our group later but his contribution to this work is very important, and in practice he is one of the coauthors. Many thanks also to all my friends here at CASY: Andrea, Luca (again), Gi- anni (thank you for the many beers together!), Riccardo, Luca ”Hamilton”, Matteo (”MarcoCartini”), Alessandro, Raffaella, Manuel(both), Gianluca, Davide(”Manolo”, the first one to work with autonomous helicopters here at Bologna), ... which have been first of all real friends. A special thank also to Michelangelo and Emanuele, which have been with me at Boston, turning that period into a great experience (”it was really a kind of cool....”). Also I have to thank Emilio, for the great opportunity given me to visit MIT, and of course Amit, Ricardo, Marco, Ketan, Alessandro, Sertac, John, Navid... Many thanks also to my friends Lorenzo, Laura, Davide, ... for having been a support under many circumstances. A special thank to Claudia, for having been near me in these years despite many difficulties. No words to say what she has done for me. Of course I’m in debt with my family, my mother an my father in particular, and all my incredible cousins, which have always supported me. Roberto To my father... Contents 1 Introduction 13 1.1 Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2 Nonlinear Robust Control of a Miniature Helicopter 21 2.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3 The framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3.1 Helicopter Model . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3.2 Helicopter Model for Control Purpose . . . . . . . . . . . . . 27 2.3.3 The Control Problem . . . . . . . . . . . . . . . . . . . . . . 29 2.4 Control Structure and Main Results . . . . . . . . . . . . . . . . . . 30 2.4.1 Vertical Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 30 2.4.2 Engine Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.4.3 Lateral, Longitudinal and Attitude Dynamics . . . . . . . . . 35 2.5 Tuning of the Control Law . . . . . . . . . . . . . . . . . . . . . . . . 48 2.6 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.7 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.7.1 Helicopter Framework . . . . . . . . . . . . . . . . . . . . . . 57 2.7.2 Flight Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3 Prototyping, Modelling and Control of a Ducted-Fan MAV 65 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.2 Dynamical Model of the Ducted-Fan MAV . . . . . . . . . . . . . . . 67 3.3 The Control Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.4 Control Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.4.1 Vertical Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 75 3.4.2 Lateral, Longitudinal and Attitude Dynamics . . . . . . . . . 76 3.4.3 Attitude controller . . . . . . . . . . . . . . . . . . . . . . . . 77 3.4.4 Lateral and longitudinal controller . . . . . . . . . . . . . . . 79 3.4.5 The tuning procedure . . . . . . . . . . . . . . . . . . . . . . 82 3.5 The Experimental Framework . . . . . . . . . . . . . . . . . . . . . . 83 3.5.1 The Aircraft Prototype . . . . . . . . . . . . . . . . . . . . . 85 6 Contents 3.5.2 Communication and Interaction Algorithms . . . . . . . . . . 89 3.6 Experimental Results. . . . . . . . . . . . . . . . . . . . . . . . . . . 93 3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4 Modelling and Control of VTOL UAVs Interacting with the Envi- ronment 105 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 4.2 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 4.2.1 Aerodynamic Simplifications . . . . . . . . . . . . . . . . . . 107 4.2.2 Free Flight Model . . . . . . . . . . . . . . . . . . . . . . . . 108 4.2.3 Tracking for the Approximate Dynamics . . . . . . . . . . . . 110 4.2.4 Constrained Model . . . . . . . . . . . . . . . . . . . . . . . . 110 4.2.5 Interaction with a Horizontal Fixed Surface . . . . . . . . . . 111 4.2.6 Interaction with a Vertical Fixed Surface . . . . . . . . . . . 112 4.2.7 A Hybrid Dynamical Model of the Overall Dynamics . . . . . 113 4.3 Take-Off Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 4.3.1 Hybrid Take-Off Controller . . . . . . . . . . . . . . . . . . . 119 4.4 Interaction with Rigid Vertical Surfaces . . . . . . . . . . . . . . . . 120 4.4.1 Equilibrium Analysis and Design Hints. . . . . . . . . . . . . 121 4.4.2 Tracking Control Law . . . . . . . . . . . . . . . . . . . . . . 122 4.4.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . 125 4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 5 Modelling and Control of a Ducted-Fan in Fast Forward Flight 129 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 5.2 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 5.3 Linear Approximations of the Level-Flight Dynamics . . . . . . . . . 137 5.3.1 Simplified Linear Model . . . . . . . . . . . . . . . . . . . . . 138 5.4 Design of the Control Law . . . . . . . . . . . . . . . . . . . . . . . . 139 5.5 Analysis of the Transition Maneuver . . . . . . . . . . . . . . . . . . 141 5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 A The Onboard Hardware Architecture and Sensor Fusion 149 A.1 IMU/GPS sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 A.1.1 The State Estimation Architecture . . . . . . . . . . . . . . . 150 A.2 Embedded ARM computer . . . . . . . . . . . . . . . . . . . . . . . 153 List of Figures 1.1 A classification of the Unmanned Aerial Vehicle: VTOL, V/STOL and fixed wing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1 The different subsystems which define the dynamics of a small scale helicopter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.2 Interconnection of the dynamics of the helicopter. . . . . . . . . . . . 29 2.3 Cascade control structure with inner attitude loop and outer lat- eral/longitudinal loop. . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.4 The equivalent interconnection behind the stability analysis of the outer loop.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.5 The two maneuvers used in the simulations. . . . . . . . . . . . . . . 52 2.6 The position of the helicopter during the first maneuver in the simu- lations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.7 The attitude of the helicopter during the first maneuver in the simu- lations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.8 The control inputs of the helicopter during the first maneuver in the simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.9 The states of the flapping dynamics and of the engine dynamics of the helicopter during the first maneuver in the simulations. . . . . . 54 2.10 The position of the helicopter during the second maneuver in the simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.11 The attitude of the helicopter during the second maneuver in the simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.12 The control inputs of the helicopter during the second maneuver in the simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.13 The states of the flapping dynamics and of the engine dynamics of the helicopter during the second maneuver in the simulations. . . . . 56 2.14 The CASY small scale helicopter. . . . . . . . . . . . . . . . . . . . . 58 2.15 The maneuver described during the experiments in the flying field. . 59 2.16 The nominal feed-forward throttle command as a function of the col- lective pitch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2.17 Photograms of an autonomous maneuver accomplished by the heli- copter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 8 LIST OF FIGURES 2.18 The trajectory accomplished by the CASY helicopter during a flight test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 2.19 The attitude of the CASY helicopter during a flight test. . . . . . . . 62 2.20 The control inputs of the CASY helicopter during a flight test. . . . 62 3.1 Prototype design of the ducted-fan MAV. . . . . . . . . . . . . . . . 67 3.2 Flaps subsystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.3 The experimental set-up. . . . . . . . . . . . . . . . . . . . . . . . . 70 3.4 Interconnection oftheforcesandtorquesgeneration mechanismswith the rigid body dynamics.. . . . . . . . . . . . . . . . . . . . . . . . . 73 3.5 Functional representation of the on-board and ground functions. . . 84 3.6 Ground station interface. . . . . . . . . . . . . . . . . . . . . . . . . 84 3.7 The avionics hardware inside the ducted-fan. . . . . . . . . . . . . . 85 3.8 The thrust of the power subsystem as a function of the motor regu- lator input (PWM signal). . . . . . . . . . . . . . . . . . . . . . . . . 88 3.9 The datapacket of the trajectory mode. . . . . . . . . . . . . . . . . . 91 3.10 A trajectory defined by means of a trajectory mode interaction. The four way-points are given by two different data packets. . . . . . . . 91 3.11 The datapacket of the ROV mode. . . . . . . . . . . . . . . . . . . . 93 3.12 The position of the ducted-fan MAV during the first hover flight test. 95 3.13 The velocity of the ducted-fan MAV during the first hover flight test. 95 3.14 The attitude of the ducted-fan MAV during the first hover flight test. 96 3.15 Thecontrolinputsoftheducted-fanMAVduringthefirsthoverflight test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 3.16 The ROV mode commands of the ducted-fan MAV during the first hover flight test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 3.17 Sequence of photograms taken from an autonomous translation. The ducted-fan UAV is controller through the joypad in ROV mode. . . 97 3.18 The latitude and longitudinal position of the ducted-fan MAV during the second translation flight test. . . . . . . . . . . . . . . . . . . . . 98 3.19 The position of the ducted-fan MAV during the second translation flight test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 3.20 The velocity of the ducted-fan MAV during the second translation flight test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 3.21 The attitude of the ducted-fan MAV during the second translation flight test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 3.22 The control inputs of the ducted-fan MAV during the second trans- lation flight test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 3.23 The ROV mode commands of the ducted-fan MAV duringthe second translation flight test. . . . . . . . . . . . . . . . . . . . . . . . . . . 100 3.24 The latitude and longitudinal position of the ducted-fan MAV during the third flight test. . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 3.25 The position of the ducted-fan MAV during the third flight test. . . 101