Passive Stability And Actuation Of Micro Aerial Vehicles

161 Pages·2017·25.52 MB·English

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Publicly Accessible Penn Dissertations
2016
PPaassssiivvee SSttaabbiilliittyy AAnndd AAccttuuaattiioonn OOff MMiiccrroo AAeerriiaall VVeehhiicclleess
Matthew Piccoli Piccoli
University of Pennsylvania, [email protected]
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Commons
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Piccoli, Matthew Piccoli, "Passive Stability And Actuation Of Micro Aerial Vehicles" (2016). Publicly
Accessible Penn Dissertations. 2529.
https://repository.upenn.edu/edissertations/2529
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Micro Aerial Vehicles (MAVs) have increased in popularity in recent years. The most common platform,
the quadrotor, has surpassed other MAVs like traditional helicopters and ornithopters in popularity mainly
due to their simplicity. Yet the quadrotor design is a century old and was intended to carry people. We set
out to design a MAV that is designed specifically to be a MAV, i.e. a vehicle not intended to carry humans
as a payload. With this constraint lifted the vehicle can continuously rotate, which would dizzy a human,
can sustain larger forces, which would damage a human, or can take advantage of scaling properties,
where it may not work at human scale. Furthermore, we aim for simplicity by removing vehicle controllers
and reducing the number of actuators, such that the vehicle can be made cost effective, if not disposable.
We begin by studying general equations of motion for hovering MAVs. We search for vehicle
configurations that exhibit passive stability, allowing the MAV to operate without a controller or actuators
to apply control, ideally a single actuator. The analysis suggests two distinct types of passively stabilized
MAVs and we create test vehicles for both.
With simple hovering achieved, we concentrate on controlled motion with an emphasis on doing so
without adding actuators. We find we can attain three degree of freedom control using separation of time
scales with our actuator via low frequency for control in the vertical direction and high frequency for
control in the horizontal plane. We explore techniques for achieving high frequency actuator control,
which also allow the compensation of motor defects, specifically cogging torque.
We combine passive stability with the motion control into two vehicles, UNO and Piccolissimo. UNO, the
Underactuated-propeller Naturally-stabilized One-motor vehicle, demonstrates the capabilities of simple
vehicles by performing maneuvers like conventional quadrotors. Piccolissimo, Italian for “very little”,
demonstrates the merits of passive stability and single actuator control by being the smallest, self-
powered, controllable MAV.
DDeeggrreeee TTyyppee
Dissertation
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Doctor of Philosophy (PhD)
GGrraadduuaattee GGrroouupp
Mechanical Engineering & Applied Mechanics
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Mark Yim
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Micro Aerial Vehicles, Motor Control, Unmanned Aerial Vehicles
SSuubbjjeecctt CCaatteeggoorriieess
Aerospace Engineering | Mechanical Engineering | Robotics
This dissertation is available at ScholarlyCommons: https://repository.upenn.edu/edissertations/2529
PASSIVE STABILITY AND ACTUATION OF
MICRO AERIAL VEHICLES
Matthew Piccoli
A DISSERTATION
in
Mechanical Engineering and Applied Mechanics
Presented to the Faculties of the University of Pennsylvania
in
Partial Fulfillment of the Requirements for the
Degree of Doctor of Philosophy
2016
Mark Yim, Ph.D., Supervisor of Dissertation
Professor of Mechanical Engineering and Applied Mechanics, Univ. of Pennsylvania
Kevin Turner, Ph.D., Graduate Group Chairperson
Professor of Mechanical Engineering and Applied Mechanics, Univ. of Pennsylvania
Dissertation Committee:
Vijay Kumar, Ph.D., The Nemirovsky Family Dean of Penn Engineering; Professor
of Mechanical Engineering and Applied Mechanics, Univ. of Pennsylvania
Mark Yim, Ph.D., Professor of Mechanical Engineering and Applied Mechanics,
Univ. of Pennsylvania
Raffaello D’Andrea, Ph.D., Professor of Mechanical and Process Engineering, Eid-
geno¨ssische Technische Hochschule Zu¨rich
Daniel Koditschek, Ph.D., Alfred Fitler Moore Professor of Electrical and Systems
Engineering, Univ. of Pennsylvania
Bruce Kothmann, Ph.D., Lecturer of Mechanical Engineering and Applied Mechan-
ics, Univ. of Pennsylvania
ABSTRACT
PASSIVE STABILITY AND ACTUATION OF
MICRO AERIAL VEHICLES
Matthew Piccoli
Mark Yim
Micro Aerial Vehicles (MAVs) have increased in popularity in recent years. The most
common platform, the quadrotor, has surpassed other MAVs like traditional helicopters
and ornithopters in popularity mainly due to their simplicity. Yet the quadrotor design
is a century old and was intended to carry people. We set out to design a MAV that
is designed specifically to be a MAV, i.e. a vehicle not intended to carry humans as a
payload. With this constraint lifted the vehicle can continuously rotate, which would
dizzy a human, can sustain larger forces, which would damage a human, or can take
advantage of scaling properties, where it may not work at human scale. Furthermore, we
aim for simplicity by removing vehicle controllers and reducing the number of actuators,
such that the vehicle can be made cost effective, if not disposable.
We begin by studying general equations of motion for hovering MAVs. We search for
vehicle configurations that exhibit passive stability, allowing the MAV to operate without
a controller or actuators to apply control, ideally a single actuator. The analysis suggests
two distinct types of passively stabilized MAVs and we create test vehicles for both.
Withsimplehoveringachieved, weconcentrateoncontrolledmotionwithanemphasis
on doing so without adding actuators. We find we can attain three degree of freedom
ii
control using separation of time scales with our actuator via low frequency for control
in the vertical direction and high frequency for control in the horizontal plane. We
explore techniques for achieving high frequency actuator control, which also allow the
compensation of motor defects, specifically cogging torque.
We combine passive stability with the motion control into two vehicles, UNO and
Piccolissimo. UNO, the Underactuated-propeller Naturally-stabilized One-motor vehicle,
demonstrates the capabilities of simple vehicles by performing maneuvers like conven-
tional quadrotors. Piccolissimo, Italian for very little, demonstrates the merits of passive
stabilityandsingleactuatorcontrolbybeingthesmallest,self-powered,controllableMAV.
iii
Contents
Abstract ii
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Low Reynolds Number . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Proposed Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Passive Stability 11
2.1 Vehicle Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 Simple Stability Simulation . . . . . . . . . . . . . . . . . . . . . . 15
2.1.2 COP Vs. COM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.3 Differential Lift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 Linearized Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.1 Routh-Hurwitz Stability Criterion . . . . . . . . . . . . . . . . . . 21
2.2.2 Aerodynamic With Angular Momentum . . . . . . . . . . . . . . . 22
2.2.3 Aerodynamic Without Angular Momentum . . . . . . . . . . . . . 32
3 Passive Stability Experiments 36
3.1 COP Vs. COM Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.1.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.1.2 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.1.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2 Differential Lift Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.2.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2.2 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4 Actuation Methods 61
4.1 Control Using Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2 Control Using Torques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.3 Actuator Authority . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5 Motor Control 72
5.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.2 Anticogging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.2.1 Anticogging Proposed Approach . . . . . . . . . . . . . . . . . . . 87
5.2.2 Waveform Collection . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.2.3 Waveform Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
iv
5.2.4 Waveform Suppression . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.2.5 Ripple Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.2.6 Design and Experimental Results . . . . . . . . . . . . . . . . . . . 101
5.2.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6 Three DOF Experimental Vehicles 118
6.1 UNO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.1.1 Design and Manufacturing . . . . . . . . . . . . . . . . . . . . . . . 119
6.1.2 Experimental Results and Analysis . . . . . . . . . . . . . . . . . . 127
6.2 Piccolissimo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.2.1 Design and Manufacturing . . . . . . . . . . . . . . . . . . . . . . . 131
6.2.2 Experiments and Analysis . . . . . . . . . . . . . . . . . . . . . . . 138
7 Conclusion 143
7.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
Bibliography 144
v
List of Tables
3.1 Tested vehicle configurations . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2 Predicted and actual stability. Those that do not follow predictions are
highlighted in red. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3 Vehicle costs for a run of 1000 in USD . . . . . . . . . . . . . . . . . . . . 49
3.4 Stability results of various vehicle configurations . . . . . . . . . . . . . . 58
5.1 Anticogging Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.1 Speeds of UNO’s body and propeller. All units are rad/sec. . . . . . . . . 128
6.2 Mass distribution of both versions of Piccolissimo in grams. . . . . . . . . 134
6.3 Comparison of Mini and Maneuverable Piccolissimo with commercial mul-
ticopters. TheFY805andFY804aremadebyFayee, whiletheCX-STARS
is made by Cheerson, and is the source of Mini Piccolissimo’s motor and
propeller. The FY804 and the CX-STARS are the current smallest com-
mercial self powered MAVs. . . . . . . . . . . . . . . . . . . . . . . . . . . 139
vi
List of Figures
1.1 Yim’s Tracking Device with passive stability fins (125) and offset mass for
steering (126). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2 Ahighlevelmapofthetopicsdiscussedinthisthesis. Greenisthemotiva-
tion, partially done by Mark Yim. Blue is theory. Orange is experimental
hardware not designed by the author. Yellow is experimental hardware
created by the author. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1 FT-Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 Varying the linear drag term, a, from a simulated vehicle with differential
lift and angular momentum. The top plot shows all six eigenvalues, while
the bottom plot focuses on the two closest to the imaginary axis with
positive imaginary values. . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3 Varying the differential lift term, b, from a simulated vehicle with differ-
ential lift and angular momentum. The top plot shows all six eigenvalues,
while the bottom plot focuses on the two closest to the imaginary axis with
positive imaginary values. . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4 Varying the COP vs. COM term, c, from a simulated vehicle with differ-
ential lift and angular momentum. The top plot shows all six eigenvalues,
while the bottom plot focuses on the two closest to the imaginary axis with
positive imaginary values. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.5 Varyingtheangulardragterm, d, fromasimulatedvehiclewithdifferential
lift and angular momentum. The top plot shows all six eigenvalues, while
the bottom plot focuses on the two closest to the imaginary axis with
positive imaginary values. . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.6 Varying the angular momentum term, e, from a simulated vehicle with
differential lift and angular momentum. The top plot shows all six eigen-
values, while the bottom plot focuses on the two closest to the imaginary
axis with positive imaginary values.. . . . . . . . . . . . . . . . . . . . . . 31
2.7 Varying assumptions used in Section 2.2.2, from a simulated vehicle with
differential lift and angular momentum. The top plot shows all six eigen-
values, while the bottom plot focuses on the two closest to the imaginary
axis with positive imaginary values.. . . . . . . . . . . . . . . . . . . . . . 33
3.1 COP Vs. COM Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2 Side-by-side comparison of the nine tested configurations . . . . . . . . . . 40
3.3 Root locus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.4 Configuration a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.5 Configuration b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.6 Configuration c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
vii
3.7 Configuration d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.8 Coordinate systems used while computing the equations of motion. . . . 51
3.9 Propeller 1 FT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.10 Wide (left) and tall (right) variants and motor module (center) . . . . . . 55
3.11 Variable replaceable elements . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.1 Coordinate systems: I for inertial, F for flyer, B for body. F and B
are located at COM. The forces and torques generated by the motor and
propeller are f and τ. The offset between the COM at the body frame and
the propeller’s force is o. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.1 Possible driven states of a brushed motor. Asynchronous configurations
are on the left and synchronous configurations are on the right. . . . . . 74
◦ ◦
5.2 Possible driven states of a three phase motor with 120 on the left, 180 on
the right, and null or motor braking in the center. Arrows represent motor
lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.3 Sinusoidal PWM values and the resulting phase voltages with respect to
neutral. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.4 Trapezoidal PWM values and the resulting phase voltages with respect to
neutral. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.5 RectangularPWMvaluesandtheresultingnormalizedphasevoltageswith
respect to neutral. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.6 Quadrature PWM values and the resulting normalized phase voltages with
respect to the shared line. . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
◦
5.7 Space vector patterns for three phase drivers with 180 vectors drawn as
black arrows and quadrature vectors drawn in yellow . . . . . . . . . . . . 81
5.8 Nominal and compensated torque ripple ratio vs. price for a set of motors
of nominally same size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.9 Diagram of a single half H-bridge inverter connected to one of three phases
of a sectioned motor. δ is the high time duty cycle, δ is the time it takes
dt
for the FETs to switch, and f is the PWM frequency. . . . . . . . . . 89
pwm
5.10 Positionmethodcollecteddatashowingdutycyclerequiredtoholdposition
from motor M4 in Table 5.1. This process is described in Section 5.2.6. (a)
◦
A full 360 dataset with forward and backward trials and (b) a magnified
section showing difference between forward and reverse. . . . . . . . . . . 91
5.11 Top view of the robotic arm. . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.12 Trajectory of robotic arm with and without anticogging. Cmd is the com-
mandedtrajectory, Cogistheactualtrajectorywithoutcompensation, and
Anti is the actual trajectory with anticogging enabled. . . . . . . . . . . . 104
5.13 Torque ripple after anticogging versus torque ripple before anticogging for
eleven tested motors. Fit line is y = 0.3139x with an R2 = 0.8922. . . . . 108
5.14 Motor M4 RMS torque versus PWM frequency with anticogging disabled.
(+) is τ , ( ) is τ , (*) is τ , (.) is τ , (x) is τ , ((cid:3)) is τ , ( ) is
res frq cog fr dt cog
◦ ⋄
τ , ( ) is τ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
nom,est nom,act
△
viii