Modelling and Control of the Crazyflie Quadrotor for Aggressive and Autonomous Flight by Optical ...

153 Pages·2017·6.33 MB·English

Modelling and Control of the Crazyflie
Quadrotor for Aggressive and
Autonomous Flight by Optical Flow
Driven State Estimation
Marcus Greiff

Department of Automatic Control
MSc Thesis
TFRT-6026
ISSN 0280-5316
Department of Automatic Control
Lund University
Box 118
SE-221 00 LUND
Sweden
© 2017 by Marcus Greiff. All rights reserved.
Printed in Sweden by Tryckeriet i E-huset
Lund 2017
Abstract
The master thesis seeks to develop a control system for the Crazyflie 2.0
unmannedaerialvehicletoenableaggressiveandautonomousflight.Forthis
purpose, different rigid-body models are considered, differing primarily in
their parametrisation of rotation. The property of differential flatness is ex-
plored and several means of parametrising trajectories in flat output space
areimplemented.Anewmethodofrotorcontrolwithparameterestimationis
developed and geometric controllers are implemented for rigid-body control.
Finally, state estimation is accomplished through a scalar-update extended
Kalmanfilter,whereinformationfromtheinternalmeasurementunitisfused
with positional information from camera systems, ultra-wide band systems,
optical flow measurements and laser ranging measurements. Capable of sus-
taining flight with any combination of the previously mentioned sensors, the
real-time implementation is showcased using polynomial motion-planning to
avoid known obstacles.

Acknowledgements
I would like to express my sincere thanks to the Professors Anders Roberts-
son and Bo Bernhardsson as well as Ph.D. student Fredrik Bagge Karlsson
for valuable advice and helpful theoretical discussions throughout the course
of the thesis. I also wish to thank Professor Karl-Johan ˚Astr¨om for helpful
discussions on the complementary filtering and enthusiastic encouragement.
In addition, would like to thank the members of Bitcraze AB individually.
Firstly, Arnaud Taffanel, for his patience and help with the EKF implemen-
tationandinputonthefirmwarearchitecture.Secondly,MarcusEliasson,for
helpwiththedesignanddevelopmentoftheexpansionboardsrelatingtoop-
ticalflowandlaserranging.Thirdly,TobiasAntonsson,forhelpfuldiscussions
on the rotor-loops and debugging of the Crazyflie radio. Fourthly, Kristof-
fer Richardsson, for discussions on the firmware implementation and ideas
relating to organisation of labour. Finally, Bj¨orn Mauritz, for support and
encouragement throughout the project. I would also like to thank Michael
Hamer, for his prior work on the extended Kalman filter, helpful discus-
sions on the control system throughout the thesis and help with tuning the
geometric controller. Finally, I would like to thank Daniel Nilsson, for his
contribution to the ROS implementation in the Kinect vision project.

Contents
1. Introduction 1
1.1 Outline of thesis . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Goals of thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Modelling 4
2.1 Tait-Bryan rigid-body dynamics . . . . . . . . . . . . . . . . 4
2.2 Quaternion rigid-body dynamics . . . . . . . . . . . . . . . . 11
2.3 Rotor dynamics and coupling . . . . . . . . . . . . . . . . . 14
2.4 Implementation considerations . . . . . . . . . . . . . . . . . 17
2.5 Open loop response . . . . . . . . . . . . . . . . . . . . . . . 21
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3. Motion planning 24
3.1 Differential flatness . . . . . . . . . . . . . . . . . . . . . . . 26
3.2 Generation of flat output trajectories . . . . . . . . . . . . . 32
3.3 Parametrization of flat outputs . . . . . . . . . . . . . . . . 38
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4. Rotor control 44
4.1 Open loop control . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2 Closed loop rotor control . . . . . . . . . . . . . . . . . . . . 45
4.3 Rotor adaptation and estimation . . . . . . . . . . . . . . . 50
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5. Rigid-body control 54
5.1 Saturations and controllability . . . . . . . . . . . . . . . . . 55
5.2 Tait-Bryan parametrised control . . . . . . . . . . . . . . . . 57
5.3 Geometric control . . . . . . . . . . . . . . . . . . . . . . . . 63
5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6. Inner state estimation 69
6.1 Model independent estimation . . . . . . . . . . . . . . . . . 70
6.2 Model based state estimation . . . . . . . . . . . . . . . . . 75
6.3 MOCAP positioning . . . . . . . . . . . . . . . . . . . . . . 78
Contents
6.4 UWB positioning . . . . . . . . . . . . . . . . . . . . . . . . 84
6.5 Optical flow and laser positioning . . . . . . . . . . . . . . . 92
7. Conclusions and summary 102
Bibliography 104
A. Modelling appendix 111
A.1 Identification of mappings . . . . . . . . . . . . . . . . . . . 111
A.2 Continuous time DC motor parameters . . . . . . . . . . . . 113
A.3 Coriolis matrix definition . . . . . . . . . . . . . . . . . . . . 115
A.4 Gimbal lock avoidance with Tait-Bryan angles . . . . . . . . 116
A.5 Quaternion rotations and relation to Tait-Bryan angles . . . 119
A.6 Quaternion rate of change . . . . . . . . . . . . . . . . . . . 121
A.7 Quaternion state-space representation . . . . . . . . . . . . . 122
A.8 Linearised systems . . . . . . . . . . . . . . . . . . . . . . . 123
A.9 Closed form system integration with constant terms . . . . . 124
A.10Cross product identities. . . . . . . . . . . . . . . . . . . . . 125
A.11Time derivative of the rotation matrix . . . . . . . . . . . . 126
B. Controller appendix 127
B.1 Set-point weighed PID . . . . . . . . . . . . . . . . . . . . . 127
B.2 MRAC with MIT synthesis . . . . . . . . . . . . . . . . . . . 128
B.3 Linear quadratic reaulators . . . . . . . . . . . . . . . . . . . 130
C. State estimation appendix 132
C.1 Cramer-Rao lower bound in TOA . . . . . . . . . . . . . . . 132
C.2 Robust protocols considering clock drift. . . . . . . . . . . . 133
C.3 The Extended kalman Filter . . . . . . . . . . . . . . . . . . 136
C.4 Multi-camera LS regression. . . . . . . . . . . . . . . . . . . 138
Index of Acronyms
Acronym Description
UAV Unmanned Aerial Vehicle
EKF Extended Kalman Filter, a state estimator using system
dynamics
PID Proportional-Integral-Derivative regulator
LQR Linear-Quadratic Regulator
UWB Ultra-Wideband, referring to radio communication with a
large bandwith
TOA Time Of Arrival, a term used to describe a class of UWB-
positioning algorithms
MRAC ModelReferenceAdaptiveControl,hereforSISO systems
with MIT-rule synthesis
GA Genetic Algorithm, used in the motion-planning of the
rotor-craft
CIR ChannelImpulseResponse,usedtodeterminetime-stamps
in the TOA methods
RLS RecursiveLeast-Squares,hereforon-linearparameteriden-
tification
LS Least-Squares, referring to any problem formulated and
solved in a least-squares sense
TSP The Travelling Salesman Problem, an integer-
programming problem
IMU Inertial Measurement Unit, contains a 3-axis gyroscope, a
3-axis accelerometer and a 3-axis magnetometer
Contents
Acronym Description
PD Proportional-Derivative control
PWM Pulse-Width Modulation, used in the rotor control
MOCAP Motion capture, here referring to camera systems
TWR Two-Way Ranging, a protocol for communication in the
UWB-system
TDOA TimeDifferenceOfArrival,atermusedtodescribeaclass
of UWB-positioning algorithms
SO(3) Isometric rotations in R3 with fixed origin
CRLB Cramer-RaoLowerBound,alowerboundforanyunbiased
estimator
DW1000 The radio chip implemented in the LPS
SISO Single-Input Single-Output, a class of dynamical systems
SFD Start of Frame Delimiter, used to time-stamp packets in
the UWB-network
SDS-TWR Symmetric-Double-Sided Two-Way Ranging, a communi-
cation protocol
QR Referring to the QR-decomposition of
matrices
MSE Mean Squared Error
LPS LocoPositioningSystem,anUWB-systembeingdeveloped
by Bitcraze
DC Direct Current, with respect to the brushed motors imple-
mented in the UAV
SE(3) Euclidean group of isometric rotations in R3 with fixed
origin and fixed-sign determinant
ROS TheRobotOperatingSystem,ameta-operatingsystemfor
robotics
LP Low-Pass, referring to a filter which attenuates high fre-
quency spectral content
AHRS Attitude Heading and Reference Systems, a category of
complementary filters
MIT Massachusetts Institute of Technology
ZOH Zero-OrderHold,anapproximationusedwhendiscretising
continuous systems