Development of a Pointing, Acquisition, and
Tracking System for a Nanosatellite Laser
Communications Module
by
Kathleen Michelle Riesing
B.S.E., Princeton University (2013)
Submitted to the Department of Aeronautics and Astronautics
in partial fulfillment of the requirements for the degree of
Master of Science in Aeronautics and Astronautics
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
September 2015
c Massachusetts Institute of Technology 2015. All rights reserved.
○
Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Department of Aeronautics and Astronautics
August 20, 2015
Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Kerri L. Cahoy
Assistant Professor of Aeronautics and Astronautics
Thesis Supervisor
Accepted by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Paulo C. Lozano
Associate Professor of Aeronautics and Astronautics
Graduate Committee Chair
2
Development of a Pointing, Acquisition, and Tracking System
for a Nanosatellite Laser Communications Module
by
Kathleen Michelle Riesing
Submitted to the Department of Aeronautics and Astronautics
on August 20, 2015, in partial fulfillment of the
requirements for the degree of
Master of Science in Aeronautics and Astronautics
Abstract
Launch opportunities for small satellites are rapidly growing and their technical capabilities are improving. Several commercial constellations of small satellites for Earth
imaging and scientific observation are making their way onto orbit, increasing the need
for high bandwidth data downlink. Obtaining regulatory licensing for current radio
frequency (RF) communications systems is difficult, and state of the art nanosatellite RF systems struggle to keep up with the higher demand. Laser communications
(lasercom) has the potential to achieve high bandwidth with a reduction in power and
size compared to RF, while simultaneously avoiding the significant regulatory burden
of RF spectrum allocation.
Due to narrow beamwidths, the primary challenge of lasercom is the high-precision
pointing required to align the transmitter and receiver. While lasercom has been successfully demonstrated on multiple spacecraft platforms, it has not yet been demonstrated on a scale small enough to meet the size, weight, and power constraints for
nanosatellites. The Nanosatellite Optical Downlink Experiment (NODE) developed
at MIT is designed to achieve a lasercom downlink of 10 to 100 Mbps within the
constraints of a typical 3-U CubeSat.
This thesis focuses on the development of the pointing, acquisition, and tracking
system for NODE. The key to achieving a high bandwidth downlink is to bridge the
gap between existing CubeSat attitude determination and control capabilities and the
narrow beamwidths of lasercom. We present a two-stage pointing control system to
achieve this. An uplink beacon and detector provide fine attitude feedback to enable
precision pointing, and CubeSat body pointing is augmented with a fine steering
mechanism.
The architecture of the pointing, acquisition, and tracking system is presented,
followed by the in-depth design and hardware selection. A detailed simulation of
the ground tracking performance is developed, including novel on-orbit calibration
algorithms to eliminate misalignment between the transmitter and receiver. A testbed
is developed to characterize the selected fine steering mechanism for performance
and thermal stability. The proposed system is capable of achieving at least two
3
orders of magnitude better pointing than existing CubeSats to enable high bandwidth
nanosatellite downlinks.
Thesis Supervisor: Kerri L. Cahoy
Title: Assistant Professor of Aeronautics and Astronautics
4
Acknowledgments
I would first like to thank my advisor Kerri Cahoy. Beyond technical guidance, she
is an excellent role model and has provided me incredible opportunities in my time
at MIT. I look forward to continuing on for my PhD.
A special thank you to my parents: to my dad, for inspiring me to be an engineer
and fostering my intellectual curiosity, and to my mom for providing the support and
continual encouragement to make it through to the other side. To my brother, whom
I always strive to surpass and will not allow to be the only doctor in the family.
Thank you to all the friends who have helped me along the way. In particular, Britta
Kelley, David Sternberg, and Margaret Tam have kept me smiling through many
rough patches.
This project would not have been possible without the contributions of graduate
students Ryan Kingsbury and Tam Nguyen. Thank you for motivating discussions
and filling in the gaps in my knowledge. I would also like to thank undergraduates
Hang Woon Lee and Derek Barnes for their work on the project.
This project was supported by a JPL Strategic University Research Partnership
(SURP). This work was also supported by a NASA Space Technology Research Fellowship under grant #NNX14AL61H.
5
6
Contents
1 Introduction
21
1.1
Motivation for a Nanosatellite Laser Communications System . . . .
21
1.2
Laser Communications Background & Challenges . . . . . . . . . . .
24
1.2.1
Pointing, Acquisition & Tracking Subsystem . . . . . . . . . .
25
1.2.2
Overview of Prior Missions . . . . . . . . . . . . . . . . . . . .
29
Nanosatellite Attitude Determination & Control Background . . . . .
33
1.3.1
Three-axis-stabilized CubeSat Missions . . . . . . . . . . . . .
33
1.3.2
Commercial-Off-The-Shelf Hardware . . . . . . . . . . . . . .
35
Nanosatellite Laser Communications . . . . . . . . . . . . . . . . . .
37
1.4.1
Key Challenges & Existing Efforts . . . . . . . . . . . . . . . .
37
1.4.2
NODE Concept of Operations . . . . . . . . . . . . . . . . . .
39
Thesis Objective & Roadmap . . . . . . . . . . . . . . . . . . . . . .
40
1.3
1.4
1.5
2 Pointing, Acquisition & Tracking Approach
2.1
2.2
2.3
43
NODE System Overview . . . . . . . . . . . . . . . . . . . . . . . . .
43
2.1.1
Design Approach & Key Requirements . . . . . . . . . . . . .
43
2.1.2
Summary of Key Parameters . . . . . . . . . . . . . . . . . . .
46
Pointing, Acquisition, & Tracking Architecture . . . . . . . . . . . . .
47
2.2.1
Concept of Operations . . . . . . . . . . . . . . . . . . . . . .
48
2.2.2
Single-Stage vs. Two-Stage Design . . . . . . . . . . . . . . .
49
2.2.3
Monostatic vs. Bistatic Design . . . . . . . . . . . . . . . . . .
53
2.2.4
Hybrid Laser & Radio Calibration Method . . . . . . . . . . .
55
Derivation of Requirements . . . . . . . . . . . . . . . . . . . . . . .
56
7
2.4
2.3.1
Host Spacecraft Performance . . . . . . . . . . . . . . . . . . .
57
2.3.2
Fine Steering Requirements . . . . . . . . . . . . . . . . . . .
57
2.3.3
Beacon Detector Requirements . . . . . . . . . . . . . . . . .
58
2.3.4
On-orbit Calibration Requirements . . . . . . . . . . . . . . .
59
Fine Stage Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
2.4.1
Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
2.4.2
Beacon Detector . . . . . . . . . . . . . . . . . . . . . . . . .
61
2.4.3
Fast Steering Mirror . . . . . . . . . . . . . . . . . . . . . . .
61
3 Simulation Analysis & Results
3.1
3.2
65
Ground Tracking Simulation . . . . . . . . . . . . . . . . . . . . . . .
65
3.1.1
Motivation & Overview . . . . . . . . . . . . . . . . . . . . . .
66
3.1.2
Dynamic Models . . . . . . . . . . . . . . . . . . . . . . . . .
69
3.1.3
Sensor Models . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
3.1.4
Actuator Models . . . . . . . . . . . . . . . . . . . . . . . . .
75
3.1.5
Control & Estimation Models . . . . . . . . . . . . . . . . . .
77
3.1.6
Pointing & Tracking Results . . . . . . . . . . . . . . . . . . .
82
Post-Acquisition Calibration Simulation
. . . . . . . . . . . . . . . .
85
3.2.1
Motivation & Overview . . . . . . . . . . . . . . . . . . . . . .
86
3.2.2
Description of Algorithms . . . . . . . . . . . . . . . . . . . .
87
3.2.3
Noise & Error Models . . . . . . . . . . . . . . . . . . . . . .
89
3.2.4
Calibration Results . . . . . . . . . . . . . . . . . . . . . . . .
93
4 Fast Steering Mirror Characterization & Results
4.1
4.2
97
Fast-Steering Mirror Testbed . . . . . . . . . . . . . . . . . . . . . . .
97
4.1.1
Components & Layout . . . . . . . . . . . . . . . . . . . . . .
98
4.1.2
Thermal Test Environment . . . . . . . . . . . . . . . . . . . .
99
Description of Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.2.1
Comparison to Fixed Mirror . . . . . . . . . . . . . . . . . . . 101
4.2.2
Response to High Voltage Enable . . . . . . . . . . . . . . . . 101
4.2.3
Voltage Sweeps . . . . . . . . . . . . . . . . . . . . . . . . . . 101
8
4.3
4.2.4
Position Repeatability . . . . . . . . . . . . . . . . . . . . . . 102
4.2.5
Thermal Conditions
. . . . . . . . . . . . . . . . . . . . . . . 103
Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.3.1
Device Hysteresis . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.3.2
Zero Position . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.3.3
Device Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.3.4
Position Repeatability . . . . . . . . . . . . . . . . . . . . . . 110
4.3.5
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5 Conclusion
115
5.1
Thesis Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.2
Thesis Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.3
Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
9
10
List of Figures
1-1 Nanosatellite market projection [1]. . . . . . . . . . . . . . . . . . . .
22
1-2 Absorption of the electromagnetic spectrum in the Earth’s atmosphere
[2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
1-3 Typical lasercom pointing, acquisition, and tracking sequence. . . . .
26
1-4 Point-ahead angle as a function of relative velocity. . . . . . . . . . .
27
1-5 Generic block diagram for PAT subsystem [3]. . . . . . . . . . . . . .
29
1-6 LCT 2nd generation, the backbone of the EDRS [4]. . . . . . . . . . .
31
1-7 Rendering of LLCD inertially stabilized telescope [5]. . . . . . . . . .
32
1-8 Reaction wheels developed by Sinclair Interplanetary for CanX-2 [6].
34
1-9 Rendering of OCSD [7].
. . . . . . . . . . . . . . . . . . . . . . . . .
38
1-10 NODE hybrid RF and optical architecture. . . . . . . . . . . . . . . .
40
2-1 NODE requirements flowdown. . . . . . . . . . . . . . . . . . . . . .
44
2-2 Functional block diagram of NODE. . . . . . . . . . . . . . . . . . . .
46
2-3 Histogram of CubeSat orbital altitudes from 2010-2014. . . . . . . . .
47
2-4 Concept of operations for pointing, acquisition, and tracking on NODE. 49
2-5 Pointing loss as a function of pointing error (requirement shown in gray). 50
2-6 Block diagram of monostatic and bistatic architectures. . . . . . . . .
53
2-7 Angular magnification with beam reduction. Off-axis incoming light
(green) as compared to on-axis light (red) for reference. . . . . . . . .
55
2-8 Hybrid laser downlink and radio uplink calibration concept. . . . . .
56
2-9 NODE hardware layout. . . . . . . . . . . . . . . . . . . . . . . . . .
60
2-10 NODE beacon detector prototype. . . . . . . . . . . . . . . . . . . . .
62
11
2-11 NODE fine stage MEMS fast-steering mirror.
. . . . . . . . . . . . .
63
3-1 RSW satellite reference frame [8]. . . . . . . . . . . . . . . . . . . . .
66
3-2 Pitch maneuver for ground tracking. . . . . . . . . . . . . . . . . . .
67
3-3 Atmospheric density as a function of altitude. . . . . . . . . . . . . .
68
3-4 Block diagram of tracking simulation. . . . . . . . . . . . . . . . . . .
69
3-5 MiRaTA 3-U CubeSat used for modeling the host spacecraft [9]. . . .
70
3-6 Geometry of pitch angle and angle of elevation with ground station in
orbit plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
3-7 Bode plot of FSM response data and transfer function model. . . . .
77
3-8 Environmental disturbance torques for ground tracking maneuvers at
400 km. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
83
3-9 Coarse and fine stage pointing error with beacon feedback and compensation for environmental disturbances. . . . . . . . . . . . . . . .
3-10 Receiver power as a function of slant range, normalized to peak power.
84
90
3-11 Probability density function of effect of atmospheric scintillation on
downlink power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
91
3-12 Mitigation of atmospheric scintillation with time-averaged power measurements (𝑡𝑎𝑣𝑔 = 100𝑡𝑑 ). . . . . . . . . . . . . . . . . . . . . . . . . .
93
3-13 Example of calibration performance for uncertain search and compass
search. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
94
3-14 Normalized histogram of Monte Carlo (N=1000) calibration results for
compass search and uncertain search. . . . . . . . . . . . . . . . . . .
95
4-1 Testbed used for FSM characterization. . . . . . . . . . . . . . . . . .
98
4-2 Geometry of FSM testbed. . . . . . . . . . . . . . . . . . . . . . . . .
99
4-3 Thermal chamber setup for FSM characterization. . . . . . . . . . . . 100
4-4 Commanded FSM voltages for X axis sweep. . . . . . . . . . . . . . . 102
4-5 Commanded voltages for 5-sided die repeatability pattern. . . . . . . 103
4-6 Ramp and soak profile #1 used for testing FSM response. . . . . . . 104
4-7 Ramp and soak profile #2 used for testing FSM thermal deformation. 105
12
4-8 X-axis response hysteresis in FSM device S4045. . . . . . . . . . . . . 106
4-9 No hysteresis in response of FSM devices S4044 and S4043. . . . . . . 106
4-10 Thermally-induced angular shift of testbed setup with fixed mirror. . 107
4-11 Thermally-induced angular shift of FSM devices calibrated against
fixed mirror. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4-12 Angular shift of FSM devices on HV enable. . . . . . . . . . . . . . . 110
4-13 Error in 5th order polynomial fit to voltage sweep data at 20 ∘ C for
S4044, showing an increase in device sensitivity at low temperature. . 111
4-14 Tip/tilt repeatability of S4044 in random dice pattern. . . . . . . . . 112
13
14
List of Tables
1.1
Summary of major free-space lasercom missions. . . . . . . . . . . . .
30
1.2
Key design parameters for LCT and LLCD systems. . . . . . . . . . .
31
1.3
Summary of key three-axis-stabilized nanosatellite missions. . . . . .
34
1.4
Control modes for the OCSD mission. . . . . . . . . . . . . . . . . . .
39
2.1
Summary of key parameters of NODE. . . . . . . . . . . . . . . . . .
48
2.2
Comparison of key parameters for OCSD and NODE. . . . . . . . . .
52
2.3
Host spacecraft performance requirements for compatibility with NODE. 57
2.4
NODE fine steering requirements. . . . . . . . . . . . . . . . . . . . .
58
2.5
NODE beacon detector requirements. . . . . . . . . . . . . . . . . . .
59
2.6
NODE on-orbit calibration requirements. . . . . . . . . . . . . . . . .
59
2.7
Commercial focal plane array options for beacon detector. . . . . . .
61
2.8
Commercial fast-steering mirror performance and operational characteristics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
3.1
Simulation parameters for beacon detector. . . . . . . . . . . . . . . .
74
3.2
Simulation parameters for gyroscope. . . . . . . . . . . . . . . . . . .
75
3.3
Simulation parameters for reaction wheel.
. . . . . . . . . . . . . . .
76
3.4
Simulation parameters for FSM. . . . . . . . . . . . . . . . . . . . . .
76
3.5
Simulation results of tracking performance of fine and coarse stages. .
84
3.6
Effect of sources of error (added incrementally) on ground tracking
performance.
4.1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
Summary of FSM thermal testing and sources of pointing error. . . . 113
15
16
Nomenclature
ADCS
Attitude determination and control subsystem
ALEX
Airborne Lasercom Experiment
APD
Avalanche photodiode
BCT
Blue Canyon Technologies
BRITE
Bright Target Explorer
CanX
Canadian Advanced Nanospace Experiment
CMOS
Complementary metal-oxide-semiconductor
COTS
Commercial-off-the-shelf
DIP
Dual in-line package
DOF
Degree of freedom
EDRS
European Data Relay Satellite System
ESA
European Space Agency
FOV
Field of view
FPA
Focal plane array
FWHM
Full width at half maximum
Gbps
Gigabits per second
17
GEO
Geosynchronous Earth orbit
GeoLITE
Geosynchronous Lightweight Technology Experiment
GPS
Global Positioning System
HV
High voltage
IMU
Inertial measurement unit
IR
Infrared
ISL
Intersatellite link
ISS
International Space Station
JAXA
Japanese Aerospace Exploration Agency
JPL
Jet Propulsion Laboratory
LCT
Laser Communication Terminal
LEO
Low Earth orbit
LLCD
Lunar Laser Communication Demonstration
LOS
Line of sight
LUCE
Laser Utilizing Communications Experiment
MAI
Maryland Aerospace, Inc.
Mbps
Megabits per second
MEMS
Microelectromechanical systems
MIT
Massachusetts Institute of Technology
MPE
Maximum permitted exposure
MTI
Mirrorcle Technologies Inc.
18
NASA
National Aeronautics and Space Administration
NODE
Nanosatellite Optical Downlink Experiment
NRL
Naval Research Laboratory
19
20
Chapter 1
Introduction
Space-based laser communications (lasercom) has the potential to transform scientific, defense, and commercial spacecraft communications platforms. Compared with
traditional radio frequency (RF) communications, lasercom offers higher bandwidth,
reduced size and mass of transceivers, lower power consumption, and also avoids the
significant regulatory hurdles of radio frequency allocation. Nanosatellites in particular have great potential to benefit from lasercom as they are heavily constrained
in size, weight, and power (SWaP). The Nanosatellite Optical Downlink Experiment
(NODE) is a 10 × 10 × 5 cm3 module targeting a >10 Mbps downlink that is being
developed at the MIT Space Telecommunications, Astronomy, and Radiation Laboratory (STAR Lab) [10]. This thesis focuses on the pointing, acquisition, and tracking
(PAT) subsystem design for NODE.
1.1
Motivation for a Nanosatellite Laser Communications System
Nanosatellites are a class of small satellites with a mass between 1-10 km. The most
common type of nanosatellite is the CubeSat. The CubeSat first emerged in 1999 as
an academic exercise to design a very small satellite [11]. A CubeSat is a miniaturized
satellite that is measured in segments called “U”s. Each U measures 10 × 10 × 10 cm3
21
and weighs no more than 1.33 kg. The CubeSat was ideal for academic use since it
allowed students to work with space-bound hardware without the long timelines of
large satellite projects. Since 1999, the CubeSat has become a popular standard for
rideshare opportunities. When a large satellite is launched, extra space in the launch
vehicle can be filled with deployers designed to match CubeSat standards.
The CubeSat market is currently experiencing a period of rapid growth. While
CubeSats were designed for primarily academic use, a significant increase in commercial activity has led to the expansion of the CubeSat market shown in Figure 1-1.
Thousands of nanosatellites are predicted to launch before 2020, with Earth observation and remote sensing satellites leading this trend [1]. Two Earth observation
start-ups, Planet Labs and Spire, have led the commercial trend and plan to deploy
major constellations. Spire has launched four CubeSats to date, with plans to deploy
20 by the end of 2015 and 100 by the end of 2017 [12]. Planet Labs has successfully
launched 101 satellites despite the loss of 26 satellites in the Antares rocket failure in
2014, and has plans to launch hundreds more [13, 14].
Figure 1-1: Nanosatellite market projection [1].
As the number of satellites in orbit grows, the rate of data generation puts pressure
on existing RF communications infrastructure, particularly as low latency downlink
22
is a priority for many commercial companies. The communications subsystem has
long been a limitation for CubeSats. The time required to license a portion of the RF
spectrum often takes longer than the entire time to design, build, and test the satellite [15]. The amateur band is becoming overcrowded with CubeSats and licensing
organizations such as the Federal Communications Commission (FCC) are straining
to keep up with increased demand [16].
Operators requiring high-speed data rates must use higher frequency bands for
which there is little available commercial hardware. Commercial options offer data
rates up to 5 megabits per second (Mbps), and other academic and commercial operators have developed custom solutions [17, 18]. The existing communications bottleneck will continue to worsen as more nanosatellites enter into orbit. Development
of commercial high-rate RF radios can provide the hardware to support high-rate
communications. However, this will present even more of a challenge for the licensing
of the overcrowded RF spectrum. A high-rate, scalable communications solution for
CubeSats is needed.
The near-infrared spectrum utilized in lasercom has few regulations.
Unlike
RF, lasercom spectrum does not require official allocation to use because the small
beamwidths present little risk of interference. The only restrictions for lasercom frequencies are focused on safety. The American National Standards Institute (ANSI)
provides a metric for the maximum permitted exposure (MPE), which limits the
power flux (in W/cm2 ) of the signal and is dependent on wavelength [19]. For lasercom downlinks, transmitted power is spread out over a large area and does not approach the MPE limit. Safety limits must be considered on uplink since the power is
concentrated on the ground, but careful design can avoid the MPE without too much
difficulty.
Given the fundamental limitation of available RF bandwidth, a lasercom solution
for nanosatellites is an attractive option. High-gain apertures allow reductions in
SWaP while supporting high-rate communication. More importantly, the lasercom
spectrum is nearly unregulated and enough bandwidth is available to meet communications needs well into the future.
23
1.2
Laser Communications Background & Challenges
There are two major bands of the electromagnetic spectrum that pass through the
Earth’s atmosphere with very little attenuation. One of these bands is located in the
radio frequency spectrum and the other includes wavelengths near the visible portion
of the spectrum, as shown in Figure 1-2. Laser communications utilize wavelengths
in the near-infrared (near-IR) region of the spectrum.
Figure 1-2: Absorption of the electromagnetic spectrum in the Earth’s atmosphere [2].
The high carrier frequency of lasercom offers a significant advantage in link efficiency [20]. This can be seen in a simplified version of the link equation:
𝑃𝑅𝑥 ∝
𝑃𝑇 𝑥 𝐴𝑇 𝑥 𝐴𝑅𝑥
𝜆2 𝑅 2
(1.1)
where 𝑃𝑅𝑥 is received power (W), 𝑃𝑇 𝑥 is transmitted power (W), 𝐴𝑇 𝑥 is transmitter
area (m2 ), 𝐴𝑅𝑥 is receiver area (m2 ), 𝜆 is wavelength (m), and 𝑅 is distance between
transmitter and receiver (m). Received power scales with the inverse square of the
wavelength. RF wavelengths range from 1 m in the UHF band down to 7.5 mm in the
24
K𝑎 -band. In contrast, lasercom wavelengths are typically between 0.8-1.6 microns.
The result is that lasercom can achieve higher bandwidth communications with reduced volume, mass, and power. In fact, the entire bandwidth of the RF spectrum
could fit into just a small window in the near-IR portion utilized for lasercom.
However, the benefits of lasercom also come with a unique set of challenges. The
first major challenge of lasercom is atmospheric loss. Lasercom frequencies are very
susceptible to atmospheric effects. Absorption and scattering cause attenuation losses,
and atmospheric turbulence produces variations in signal phase, intensity, and direction [21]. Atmospheric effects can be mitigated by ground station diversity, and
optimization studies have focused on site selection [22–24]. While single-site availability ranges from 60-80%, a combination of three or more sites can achieve over
90% availability [25].
The second major challenge of lasercom is the pointing, acquisition, and tracking
(PAT) subsystem. While narrow transmit beamwidths increase lasercom link efficiency, the tradeoff is the need for very precise PAT. This topic is covered in detail in
section 1.2.1. The primary aim of this thesis is developing a lasercom PAT subsystem
that addresses this challenge and is compatible with current nanosatellite technology.
1.2.1
Pointing, Acquisition & Tracking Subsystem
Lasercom systems must align the optical line-of-sight (LOS) very precisely, with typical systems requiring error as small as submicroradians [3]. Usually this cannot be
achieved by the spacecraft bus alone, so multiple stages of sensors and actuators are
required. The coarse sensors have a wider field of view (FOV) to acquire the uplink
beacon and the coarse actuators have a large range at the expense of resolution. The
fine sensors have a narrow FOV to enable precision pointing by the fine actuators.
The stages of control must be coordinated for handoff such that the range of one
stage overlaps with the resolution of the stage that precedes it. The most capable
lasercom systems may have four or more stages of actuation to achieve the pointing
accuracy required for communications [5, 26].
The pointing, acquisition, and tracking steps for a typical lasercom system are
25
shown in Figure 1-3. The vast majority of lasercom systems use beacon tracking to
locate the ground station. In this approach, the ground station sends up a wide beam
at a predetermined wavelength towards the spacecraft. The spacecraft, expecting this
signal, can then reorient towards the beacon to improve its pointing. While beaconless tracking reduces system complexity and is particularly appealing for deep space
lasercom, it is extremely challenging to implement in practice [27]. The PAT sequence
described here is specific to beacon tracking. Step 1 describes initial pointing, steps
2-3 follow the acquisition of the ground beacon, and steps 4-5 describe ground station
tracking. Together these make up the pointing, acquisition, and tracking segments.
Figure 1-3: Typical lasercom pointing, acquisition, and tracking sequence.
Initial conditions for the spacecraft consist of orbital and pointing knowledge. The
sequence begins with initial pointing towards the expected location of the ground
station. Orbital knowledge usually comes from GPS, radar tracking, or two-line
element sets (TLEs), and any error in the spacecraft’s position is translated into
mispointing. The mispointing induced by position error gets worse the closer the
spacecraft is to the ground station. Pointing knowledge also induces error as the
spacecraft relies on a combination of gyroscopes, magnetometers, accelerometers, sun
sensors, Earth horizon sensors, or star trackers to determine its orientation with
26
limited accuracy.
The spacecraft then enters steps 2 and 3, the acquisition sequence. After the
spacecraft points at the predicted location of the ground station, it uses wide FOV
sensors and coarse actuators to scan for the ground station beacon. Once the beacon
has been detected, the spacecraft can close its tracking loop around the beacon and
reduce pointing error. The spacecraft transitions from open-loop tracking to closedloop tracking. The spacecraft maintains the beacon within the fine sensor FOV which
enables high bandwidth feedback control. Handoff occurs from the coarse to the fine
stage to achieve the accuracy required for communications.
After acquisition, steps 4-5 describe the tracking segment. The spacecraft has
closed its tracking loop around fine sensors and fine actuators, but one additional
step is needed for downlink. The spacecraft has a relative velocity with respect to
the ground station, which means that its position changes during the time-of-flight
of the signal between the two terminals. Therefore, a point-ahead/look-behind angle
is needed to correct for the expected location of the terminal as shown in Figure 1-4.
Figure 1-4: Point-ahead angle as a function of relative velocity.
The point-ahead angle depends only on the relative velocity between the terminals
and can be derived geometrically from Figure 1-4. Using a small angle approximation
and simple geometry, the point ahead angle becomes:
27
𝜃≈
2𝑉𝑟𝑒𝑙
𝑐
(1.2)
where 𝑉𝑟𝑒𝑙 is the relative velocity between the terminals and 𝑐 is the speed of light.
For the ground station, this correction points ahead in the spacecraft trajectory. For
the spacecraft terminal, the correction has the same magnitude but looks behind in
its trajectory.
The final step is link maintenance which is conducted throughout communications. The purpose of link maintenance is to ensure transmit/receive (Tx/Rx) path
alignment. This can be done by slightly nutating pointing angle and applying a correction based on received power at the opposing terminal. Alternatively, the system
can be designed with self-test capabilities through the use optical elements to redirect
transmitted signal into the receive path for periodic alignment.
Figure 1-5 shows a generic block diagram for a PAT subsystem [3]. The most common coarse actuators are gimbals since they have a large range. Typical fine pointing
actuators are tip/tilt fast-steering mirrors (FSM) and linear stages to adjust position
on the receive and transmit fibers. Adjusting the position of the fiber adjusts the
Tx/Rx angle, which is a technique known as nutation tracking. Another fine steering
technique is the use of an inertially stabilized platform, which has linear actuators
to adjust the orientation of a telescope/optical assembly and actively dampen vibrational disturbances [5]. To implement the point-ahead angle described by Equation
1.2, a point-ahead mirror or nutation of the Tx fiber is commonly used.
Lasercom links from low Earth orbit (LEO) to ground present several unique
challenges for PAT. The satellite will have to slew rapidly to track the ground station,
placing stress on the attitude determination and control subsystem. The point-ahead
angle given in Equation 1.2 will be relatively large due to high orbital velocities.
Finally, ground station passes will last less than 10 minutes, so the PAT subsystem
must quickly acquire and track the ground station to maximize data transmission.
28
Figure 1-5: Generic block diagram for PAT subsystem [3].
1.2.2
Overview of Prior Missions
While early lasercom missions demonstrated feasibility, recent missions have focused
on developing optimal, high bandwidth systems with low SWaP. Table 1.1 summarizes
some key historical and recent missions [5, 20, 26, 28–30], highlighting the increase in
system capabilities as well as the diversity of global participants. Links have been
successfully demonstrated between terminals in geosynchronous orbit (GEO), low
Earth orbit (LEO), airplanes, ground, and the moon.
In particular, two state-of-the-art missions highlight the current capabilities of
lasercom systems and also provide insight into PAT subsystem design. The first is
the Laser Communication Terminal (LCT) developed by Tesat Spacecom of Germany,
and the second is the Lunar Laser Communication Demonstration (LLCD) developed
jointly by NASA and MIT Lincoln Laboratory. Key design parameters for these
missions are summarized in Table 1.2.
LCT is a lasercom terminal design that has been reused on multiple missions. The
first LCT was demonstrated on the Semiconductor-laser Inter-satellite Link Experiment (SILEX) in 2001 between satellites in LEO and GEO. Additional LCTs were
developed for LEO satellites NFIRE and TerraSAR-X, launched in 2007, as well as
29
Table 1.1: Summary of major free-space lasercom missions.
Year
Mission
Organization
Link Type
Data Rate
(Gbps)
2001
GeoLITE/
ALEX
SILEX
LUCE
MIT Lincoln
Laboratory
ESA
JAXA
>1
Tesat Spacecom
2013
NFIRE/
TerraSAR-X
LLCD
GEO-ground/
GEO-air
LEO-GEO
LEO-GEO
LEO-ground
LEO-LEO
LEO-ground
Moon-ground
2014
2014
OPALS
EDRS
ISS-ground
LEO-GEO
GEO-ground
0.05
1.8
2001
2005
2008
MIT Lincoln
Laboratory/NASA
JPL
Tesat Spacecom/
ESA
0.05
0.05
5.65
0.622
for an accompanying optical ground station. NFIRE and TerraSAR-X conducted an
intersatellite link (ISL) and LEO-ground link at 5.65 Gbps, the highest rate published
as yet [26].
Based on these successes, European Space Agency (ESA) has embarked on developing the European Data Relay Satellite System (EDRS). EDRS will consist of
a constellation of GEO satellites to relay data between LEO satellites and ground
stations that relies on the 2nd generation LCT as the backbone [31]. LCT 2nd generation, shown in Figure 1-6, successfully demonstrated a 1.8 Gbps link between
Alphasat in GEO and Sentinel-1 in LEO in late 2014 [32].
The PAT subsystem of LCT consists of 4 stages (i.e. 4 independent actuators for
pointing). The coarse stage consists of a two-axis gimbal assembly with hemispherical
coverage [4, 33]. The next stage is a coarse steering mirror immediately following the
aperture. There is an additional fine pointing mirror, and finally a mirror dedicated
to point-ahead implementation on the downlink. Altogether, the actuators consist of
a two-axis gimbal assembly and three tip/tilt mirrors which enable an RMS pointing
accuracy of 100 𝜇rad [34].
30
Table 1.2: Key design parameters for LCT and LLCD systems.
LCT (2nd Gen.) LLCD
Link type
Tx wavelength (nm)
Data rate (Gbps)
Range (km)
Tx power (W)
Aperture (cm)
Mass (kg)
Power consumption (W)
# of PAT stages
RMS pointing accuracy (𝜇rad)
LEO-GEO-ground
1064
1.8
>45000
2.2
13.5
56
160
4
100
Moon-ground
1550
0.622
>380000
0.5
10.8
30
100
4
2.5
Figure 1-6: LCT 2nd generation, the backbone of the EDRS [4].
The second state-of-the-art mission highlighted here is the Lunar Laser Communication System (LLCD) developed jointly by MIT Lincoln Laboratory and NASA.
LLCD was launched in September 2013 as a technology demonstration on the Lunar
Atmosphere and Dust Environment Explorer (LADEE). LLCD successfully demonstrated a 622 Mbps lasercom link from lunar orbit, which is the furthest link range
demonstrated to date. LLCD’s data rate was six times faster than prior lunar RF
communications at half the weight and one quarter the power consumption [7].
LLCD’s PAT system contains 5 stages. The coarse stage consists of the spacecraft
31
body pointing. While this is not strictly part of the LLCD system, the host spacecraft has a pointing requirement of 100 𝜇rad RMS in each axis to support LLCD [5].
Whereas LCT had a hemispherical gimbal assembly enabling some degree of autonomy from the host spacecraft, LLCD relies on LADEE’s body pointing for initial
alignment. LLCD also includes a two-axis gimbal assembly to execute coarse adjustments. Both the Tx and Rx fibers have two-axis linear stages. For the Rx fiber, the
stage enables nutation tracking of the uplink signal, and the Tx stage implements
the point-ahead angle for the downlink. This entire assembly rests on a two-axis
inertially stabilized platform used for fine positioning, pictured in Figure 1-7. The
overall pointing accuracy is within 2.5 𝜇rad [5].
Figure 1-7: Rendering of LLCD inertially stabilized telescope [5].
Future missions are planned with involvement from both the public and private
sector [31, 35]. The successful demonstrations thus far have targeted a much larger
class of satellites than CubeSats, with the existing terminals ranging from 30-150 kg
and consuming >100 W of power. A 3-U CubeSat measuring 10 × 10 × 34 cm3 weighs
no more than 4 kg and typically consumes only 10-20 W. While lasercom technology
is advancing greatly, the challenge of developing a lasercom terminal to meet the
needs of nanosatellites has not yet been addressed.
32
1.3
Nanosatellite Attitude Determination & Control
Background
The attitude determination and control subsystem (ADCS) for nanosatellites has
improved tremendously in recent years. Early CubeSats had no attitude control and
simply tumbled or relied on spin or gravity gradient stabilization [11]. Three-axis
stabilized CubeSats have been made possible by the development of commercial-offthe-shelf (COTS) ADCS components, particularly the miniaturization of reaction
wheels [36]. Attitude knowledge has long been a limiting factor for nanosatellite
ADCS but the development and integration of small sensors, particularly star trackers,
is rapidly improving capabilities.
1.3.1
Three-axis-stabilized CubeSat Missions
Nanosatellites, which range between 1-10 kg, are the smallest satellites currently capable of three-axis-stabilized pointing. Table 1.3 summarizes key missions advancing
the state of the art in nanosatellite ADCS [6, 37–43].
The first nanosatellite to achieve three-axis stabilization was SNAP-1, developed
at the University of Surrey and launched in 2010. SNAP-1 ADCS consisted of a
magnetometer, three-axis magnetorquers, and a single momentum wheel. With only
a magnetometer, orientation around the B-field vector cannot be resolved, so a large
momentum bias was used to compensate for the absence of full three-axis attitude
knowledge. The satellite experienced a 1.5∘ bias in both roll and yaw but maintained
pointing within 3∘ (1-𝜎) in these axis, resulting in an overall pointing accuracy within
about 15∘ (3-𝜎) [37]. SNAP-1 was a major milestone in demonstrating nanosatellite
three-axis stabilization, particularly given the limited ADCS hardware.
Two major players emerged in the development of three-axis-stabilized nanosatellites. The Space Flight Laboratory at the University of Toronto Institute for Aerospace
Studies (UTIAS-SFL) developed CanX-2, an early three-axis-stabilized CubeSat [6].
For CanX-2, UTIAS-SFL developed a custom suite of six sun sensors and a three-axis
33
Table 1.3: Summary of key three-axis-stabilized nanosatellite missions.
Year
Mission
2001
SNAP-1
2008
2010
2011
2012
2013
Organization
Size
Surrey Space
6.5 kg *
Centre
CanX-2
UTIAS-SFL
10 × 10 × 34
QbX
NRL
10 × 10 × 34
PSSCT-2
The Aerospace 13 × 13 × 26
Corporation
AeroCube-4 The Aerospace 10 × 10 × 10
Corporation
BRITE
UTIAS-SFL
20 × 20 × 20
*Dimensions not available.
Bus Pointing
Accuracy
15∘ (3-𝜎)
cm3
cm3
cm3
2∘ (1-𝜎)
5∘ (3-𝜎)
15∘ (3-𝜎)
cm3
3∘ (3-𝜎)
cm3
0.015∘ (1-𝜎)
magnetometer. A reaction wheel developed jointly with Sinclair Interplanetary was
used for momentum bias in a similar approach to SNAP-1. The reaction wheels,
shown in Figure 1-8, were a major step forward in the development of COTS components for CubeSat ADCS. CanX-2 achieved attitude determination accuracy to
around 1.5∘ (1-𝜎), allowing control to approximately 2∘ (1-𝜎).
Figure 1-8: Reaction wheels developed by Sinclair Interplanetary for CanX-2 [6].
UTIAS-SFL went on to develop the Bright Target Explorer (BRITE) constellation
mission, which consists of six 20 × 20 × 20 cm3 nanosatellites dedicated to astronomy.
BRITE attitude sensors include sun sensors, a three-axis magnetometer, a three34
axis gyroscope, and a star tracker. The addition of a gyroscope is an important
development that greatly improves attitude determination during eclipse. However,
it is the star tracker that is critical to achieving high accuracy. The actuators are
a full three-axis set of reaction wheels and magnetorquers. These additions to the
ADCS suite have enabled BRITE to achieve the best nanosatellite pointing accuracy
to date of 0.015∘ (1-𝜎) [43].
The second major player in the development of three-axis-stabilized CubeSats is
The Aerospace Corporation, which first demonstrated attitude control on PSSCT-2
in 2011 [39]. For this program, The Aerospace Corporation developed sun and Earth
nadir sensors and also included COTS magnetometers and an inertial measurement
unit (IMU) with three-axis rate gyroscopes and accelerometers. With a three-axis set
of reaction wheels and magnetorquers, PSSCT-2 achieved an accuracy of 15∘ (3-𝜎).
The Aerospace Corporation followed this mission with AeroCube-4 in 2012 [39,41].
The IMU was eliminated and a camera was added for sensor calibration and as a potential star tracker. AeroCube-4 demonstrated 3∘ (3-𝜎) of pointing accuracy and
demonstrated camera technology for their upcoming mission, the Optical Communication and Sensor Demonstration (OCSD) program [7]. This is the first proposed
mission to conduct lasercom on a CubeSat and is discussed in detail in Section 1.4.1.
While other missions have included three-axis stabilization, on-orbit results are
currently not available [44–47]. Notably, the start-up company Planet Labs has deployed 75 satellites since January 2014. This constellation conducts Earth imaging,
and therefore three-axis stabilization is necessary, but published results do not include
information on pointing accuracy [14].
1.3.2
Commercial-Off-The-Shelf Hardware
While sub-degree pointing accuracy on nanosatellites has only been demonstrated by
the BRITE mission so far, it is definitely on the horizon as ADCS hardware continues
to improve. Several companies have emerged specifically to provide nanosatellite
ADCS hardware, although there is currently limited flight heritage.
Nanosatellites typically utilize a combination of five sensor types: magnetome35
ters, sun sensors, Earth sensors, star trackers, and gyroscopes/IMUs. Magnetometers
measure the local magnetic field, which provides an attitude reference in two axes
when combined with knowledge of orbital position. Sun sensors similarly provide an
attitude reference to the sun, while Earth sensors provide a reference nadir vector.
Gyroscopes and IMUs utilize spacecraft angular rates to provide additional attitude
knowledge which can be integrated to determine attitude. These components are
readily available and have many commercial suppliers (e.g. GomSpace, Analog Devices, Honeywell, etc.). A combination of magnetometers, sun sensors, earth sensors,
and gyroscopes can generally resolve attitude to 0.1∘ -1∘ of accuracy.
Unlike the other sensor types, star trackers provide full three-axis attitude knowledge in each measurement. Since multiple stars are identified rather than a single
target, the attitude can be resolved in all axes. This property, combined with the fact
that star tracker measurements are not affected by errors in orbital knowledge due
to the relative distances, allows star trackers to provide substantially better pointing
knowledge than prior sensors. Several commercial vendors have developed star trackers targeting nanosatellites (e.g. Sinclair Interplanetary, Blue Canyon Technologies,
and Berlin Space Technologies) with accuracy on the order of 0.001∘ RMS. While
star trackers are still expensive in terms of both cost and SWaP requirements, they
will be a disruptive technology once they are more widely adopted, allowing greatly
enhanced pointing accuracy as in the case of BRITE.
Maryland Aerospace, Inc. (MAI) and Blue Canyon Technologies (BCT) now offer
“plug and play” solutions for CubeSat ADCS. MAI’s newest ADCS module, the MAI400, is slightly larger than a 1/2-U form factor and contains a magnetometer, sun
sensor, IMU, optional Earth horizon sensor, three-axis reaction wheel set, and threeaxis magnetorquer set [48]. BCT’s ADCS module, XACT, contains a star tracker,
magnetometer, sun sensor, IMU, three-axis reaction wheel set, and a three-axis magnetorquer set [49]. While not yet demonstrated on orbit, BCT claims RMS pointing
performance of 0.003∘ in cross-boresight axes and 0.007∘ in boresight. Given the
growing market of COTS hardware, nanosatellite ADCS capabilities should continue
to improve in the upcoming years.
36
1.4
Nanosatellite Laser Communications
Existing lasercom systems for larger satellites typically rely on multiple stages of actuators and use gimbals for coarse pointing, as described in Section 1.2.2. In considering
a lasercom system for nanosatellites, constraints on SWaP rule out many approaches
used for larger systems. A different design approach is required for implementation
of lasercom on a nanosatellite.
1.4.1
Key Challenges & Existing Efforts
NODE aims to be compatible with a 3-U CubeSat platform. Several aspects of the
CubeSat platform make lasercom particularly challenging. The major limitations are
size, power, and pointing capabilities. The size of the CubeSat constrains the volume
of the optics and optical path, which makes some techniques, such as an optical
relay, challenging to implement. Pointing actuators commonly used on large systems,
such as gimbals or an inertial stabilization platform, will not fit within the CubeSat
volume. The ramifications of the size constraint on system architecture are discussed
in more detail in Section 2.2.2.
CubeSat power generally does not exceed 20 W and there is limited space for batteries. The available bus power limits the transmitted power, which creates tradeoffs
in the link budget. Link efficiency must be improved either by transferring capabilities to the ground station or improving the satellite pointing to reduce Tx beamwidth.
However, CubeSats are just beginning to achieve sub-degree pointing, which is still
substantially worse than the pointing capabilities of larger systems. A major challenge
for the CubeSat ADCS is the need for ground station tracking. In LEO, slew rates
can exceed 1∘ /s for ground tracking, and the CubeSat must achieve pointing accuracy
while executing the slew maneuver. Of the existing missions discussed in Section 1.3,
only the AeroCube-4 mission presented results of a ground track maneuver.
The first proposed mission to conduct lasercom on a CubeSat is the Optical Communication and Sensor Demonstration (OCSD) program, led by the Aerospace Corporation. OCSD is a 1.5-U CubeSat set to launch in 2015 that will demonstrate a 5-50
37
Mbps optical downlink to a ground station with 30 cm diameter [7]. As described in
Section 1.3.1, the Aerospace Corporation is a leader in CubeSat pointing capability,
and OCSD contains a large attitude sensor suite as pictured in Figure 1-9.
Figure 1-9: Rendering of OCSD [7].
OCSD is a single-stage control design that relies entirely on the body pointing of
the CubeSat. OCSD coarse attitude sensors include six two-axis sun sensors, four
Earth horizon sensors, a two-axis Earth nadir sensor, two sets of three-axis magnetometers, and two three-axis gyroscopes. Fine attitude sensors include a quad photodiode to track an uplink beacon and dual star trackers. Actuators are a three-axis
magnetorquer set and a three-axis reaction wheel set. Given all the attitude sensors
available, OCSD has a number of control modes that utilize different combinations of
sensors, which are summarized in Table 1.4. It is useful to examine these modes to
better understand the state of the art CubeSat pointing capabilities. The best attitude control mode is achieved using the star tracker and The Aerospace Corporation
expects OCSD to become actuation-limited at around 0.1∘ RMS [41].
Given that the pointing accuracy is estimated to be around 0.1∘ RMS, the downlink beamwidth must be large enough to accommodate this pointing error. The
38
Table 1.4: Control modes for the OCSD mission.
Control Mode
Sensors
RMS Pointing
Accuracy
Sunlit open loop
Eclipsed open loop
Sun and Earth horizon
Earth horizon, magnetometers
and gyros
Star tracker open loop Magnetometers and star trackers
Beacon closed loop
Uplink receiver
and magnetometers
0.6∘
0.7∘
0.7∘
0.1∘
0.2∘
pointing error should stay within the full width at half maximum (FWHM) downlink
beamwidth to keep pointing losses within 3 dB. As a result, the downlink beamwidth
is set at 0.35∘ FWHM. To close the link at this beamwidth, 10 W of transmitted
power is required, and this puts the electrical input power at 50 W. This is a significant amount of power for a CubeSat and motivates the two-stage PAT approach of
this thesis, which accepts harsher pointing requirements for a reduction in power.
1.4.2
NODE Concept of Operations
The primary aim of NODE is to provide a high bandwidth downlink that targets a
typical CubeSat. NODE is designed to fit within a 1/2-U form factor without requiring more power or host pointing capabilities than have been demonstrated on current
CubeSat missions. To meet this objective, NODE introduces a fine steering mechanism to improve pointing performance. Providing an affordable lasercom solution is
also a priority, which means that COTS components are used wherever possible.
The communications architecture for NODE is shown in Figure 1-10. NODE will
utilize an uplink beacon to locate and track the ground station. NODE provides a
high rate optical downlink of 10-100 Mbps. A low-rate RF link is utilized for uplink
as well as command and control when the optical link is unavailable. The RF link
will also be utilized to perform calibration as needed for Tx/Rx alignment on NODE.
The concept of operations is as follows: at the start of a communications over-
39
pass, the host spacecraft will point at the ground station. As the spacecraft reaches
approximately 30∘ above the horizon, NODE will detect the ground station beacon
and lock on to the signal. Once NODE is tracking the uplink beacon, a fine steering
mechanism will improve pointing accuracy to enable a 10-100 Mbps downlink.
Figure 1-10: NODE hybrid RF and optical architecture.
1.5
Thesis Objective & Roadmap
With the growth of the nanosatellite market, nanosatellites are generating an unprecedented amount of data. The RF spectrum is quickly becoming overcrowded,
and lasercom holds the potential for a high bandwidth, scalable solution. Existing
lasercom systems have targeted a much larger and more capable class of satellites and
do not meet the size, weight, and power constraints of a standard CubeSat.
40
The Nanosatellite Optical Downlink Experiment (NODE) project under development at MIT aims to provide a >10 Mbps downlink for a typical 3-U CubeSat
with COTS components [10]. The key challenge of lasercom is the need for precision
pointing. While CubeSat ADCS capabilities have improved substantially in the past
decade, they are still orders of magnitude below the pointing accuracy required for
lasercom.
This thesis addresses the challenge of achieving the pointing, acquisition, and
tracking accuracy required to enable lasercom on a nanosatellite platform. Chapter
1 presents the motivation for a lasercom solution for CubeSats along with the PAT
performance of existing lasercom systems and current CubeSat ADCS capabilities.
Chapter 2 describes the design methodology and introduces the key approach of twostage control, followed by the detailed requirements derivation and hardware selection. Chapter 3 details the simulations developed to evaluate pointing performance,
including novel algorithms for on-orbit pointing calibration. Chapter 4 presents hardware characterization of the fast-steering mirror for fine pointing. Finally, Chapter
5 summarizes the key contributions of this thesis and discusses the path forward to
flight.
41
42
Chapter 2
Pointing, Acquisition & Tracking
Approach
While existing lasercom systems have weighed between 30-150 kg, NODE is limited to
1 kg based on the mass constraints of the CubeSat platform. The PAT architectures
used for these larger systems do not scale well to the CubeSat platform. This chapter
describes the design of a PAT system compatible with the CubeSat form factor. After
describing the design flow and requirements of the NODE system as a whole, the PAT
architectural decisions and detailed design are presented.
2.1
NODE System Overview
Before addressing the pointing, acquisition, and tracking design and analysis that is
the focus of this thesis, it is necessary to provide a background on the key design
aspects of NODE. The overall system architecture and requirements derivation is
discussed in this section before delving in-depth into the PAT subsystem.
2.1.1
Design Approach & Key Requirements
The primary objective of NODE is to provide a high bandwidth downlink for CubeSats
that is competitive with existing commercial RF options in size, weight, power, and
43
cost. System design for NODE is driven by three external factors:
1. NODE must be compatible with the size, weight, and power usage of a 3-U
CubeSat
2. NODE must be competitive with existing commercial RF communications
systems for nanosatellites
3. NODE must function within demonstrated CubeSat ADCS capabilities
The requirements flowdown based on these goals is shown in Figure 2-1.
Figure 2-1: NODE requirements flowdown.
Requirements for NODE were derived from these external factors, referred to as
Items 1, 2, and 3. This process involved substantial iteration to optimize the system
and determine feasible requirements, and only the results are summarized here. For
a more detailed treatment, refer to [50]. The key parameter in the design of NODE is
the selection of the downlink beamwidth, described in Section 2.1.2. The beamwidth
dictates the fine pointing accuracy of the system, which becomes the key design
requirement for the PAT subsystem.
Item 1 states that NODE must be compatible with the SWaP constraints of a
3-U CubeSat. NODE is therefore constrained to a 1/2-U volume (10 × 10 × 5 cm3 )
44
to minimize size while still providing enough room for necessary hardware. CubeSat
weight is limited to 4 kg, and therefore NODE is limited to 0.5 kg, which lies below
the average density of the satellite based on this requirement. Finally, power usage
of NODE is limited to 10 W while transmitting, which can be supported by a typical
CubeSat power system. This is also the power usage of comparable RF systems [18].
Item 2 states that NODE must be competitive with commercial nanosatellite
radios. Based on link rates achieved by commercial systems as discussed in Section
1.1, the baseline performance of NODE was set at 10 Mbps with a stretch goal of
100 Mbps. Item 2 also has implications for the acquisition process. The beacontracking approach requires an acquisition process to lock onto the ground station.
The acquisition time limits overall throughput, so we designed the system to acquire
instantaneously. This places a requirement on the FOV of the beacon detector, as
described in Section 2.3.3.
Item 3 states that NODE must function within current CubeSat ADCS capabilities. Since the aim of the project is to be compatible with a standard CubeSat,
NODE does not assume pointing ability above what has already been demonstrated
on multiple missions. The key effects of this requirement are that the range of the
fine pointing stage and the beacon FOV must encompass expected host spacecraft
pointing error.
The functional block diagram of NODE is pictured in Figure 2-2. The host spacecraft interfaces with the NODE processor to share telemetry and control the NODE
module. While tracking, NODE shares the fine attitude knowledge it receives from
the beacon detector to its host so that the host can improve its body pointing. Based
on the feedback received from the beacon detector, the PAT processor in NODE centroids the image and computes the boresight offset to control the fast-steering mirror
(FSM). The FSM corrects the transmit beam. A calibration loop provides feedback
from the ground to correct Tx/Rx path misalignment, which is described in detail in
Section 2.3.4.
45
Figure 2-2: Functional block diagram of NODE.
2.1.2
Summary of Key Parameters
A radiometric analysis was conducted to specify the downlink beamwidth, which is
the key parameter of the system [50]. Several assumptions and design choices led
to the final beamwidth of 2.1 mrad, which are briefly discussed here. A downlink
wavelength of 1550 nm was selected due to the wide availability of COTS components from the telecommunications industry. Similarly, the wavelength for the uplink
beacon was selected to be 850 nm, which enables the use of CMOS or CCD sensors.
These detectors are low power and do not require cooling as is the case with InGaAs
detectors.
The link range was set at 1000 km, since CubeSats are typically launched into
400 to 700 km orbits, shown in Figure 2-3. The target orbit for which the system is
designed is just above 400 km, which is the orbit of the International Space Station
(ISS). The company NanoRacks added a CubeSat deployer to the ISS in early 2014,
and since then it has deployed 61 CubeSats [51]. This has led to the ISS-orbit becoming one of the most common orbits for CubeSats. Lower altitudes place greater stress
46
on the PAT subsystem since the satellite must slew rapidly (up to around 1 degree per
second) to track the ground station and the aerodynamic drag environment produces
much greater disturbances.
Figure 2-3: Histogram of CubeSat orbital altitudes from 2010-2014.
Modest performance assumptions were made for the ground station. It is assumed
to be 30 cm in diameter with a receiver sensitivity of 1000 photons/bit. Taking
into account atmospheric and path losses, the beamwidth was adjusted to achieve a
performance of 10 Mbps, resulting in a FWHM beamwidth of 2.1 mrad. The key
system parameters for NODE are summarized in Table 2.1.
2.2
Pointing, Acquisition, & Tracking Architecture
The key decisions in the design of the PAT system are described in this section. As
compared to The Aerospace Corporation’s OCSD mission, the architecture of NODE
is quite different, particularly in the addition of a fine pointing stage. NODE is also
unique in having a bistatic architecture as compared to most lasercom missions which
have a monostatic design. The motivation and implications of these design decisions
are discussed, followed by layout and hardware selection.
47
Table 2.1: Summary of key parameters of NODE.
Link rate
Wavelength
Bit error rate
Link range
Beamwidth
Downlink Parameters
10 Mbps (baseline, uncoded)
100 Mbps (stretch, uncoded)
1550 nm
1 × 10−4 (uncoded)
≤ 1000 km
2.1 mrad (FWHM)
Space Segment Parameters
Size
Mass
Power consumption
Fine pointing range
Fine pointing accuracy
Beacon detector type
Beacon detector FOV
Receive aperture
10 × 10 × 5 cm3
0.5 kg
10 W (max. during Tx)
± 1.0∘
±1.05 mrad (3-𝜎)
CMOS focal plane array
6.6∘
2.54 cm
Ground Segment Parameters
Beacon wavelength
Beacon power
Acquisition detector type
Comm. receiver type
Receive aperture
2.2.1
850 nm
10 W
InGaAs focal plane array
APD/TIA
30 cm
Concept of Operations
The pointing, acquisition, and tracking approach for NODE follows the same flow
that was introduced in Section 1.2.1. The concept of operations for PAT on NODE
is shown in Figure 2-4 with three major steps. In addition to these steps, an optional
Tx/Rx path calibration procedure can be performed during tracking.
The host CubeSat points towards the expected location of the ground station and
looks for an uplink beacon. The beacon detector on NODE is large enough that the
host should not need to scan for the beacon. Once the beacon is seen, the detector
48
Figure 2-4: Concept of operations for pointing, acquisition, and tracking on NODE.
centroid provides a direct measurement of the pointing error in the body frame. This
measurement is fed back to the host satellite to improve its pointing.
At this point, the satellite undergoes a transition from being primarily sensinglimited to primarily actuation-limited as it attempts to center the beacon on the
detector. As discussed in Section 1.3, attitude determination is a major limitation
in current CubeSat pointing performance. Once the beacon is acquired, attitude
knowledge is no longer the major source of pointing error. This allows the host
satellite to improve pointing performance to overlap with the fine stage.
The fast steering mirror provides a final correction to the downlink to achieve
fine pointing. The host satellite and fine stage continue to track the beacon for the
duration of the pass. As the final step, a calibration procedure can be executed to
correct Tx/Rx path alignment if necessary.
2.2.2
Single-Stage vs. Two-Stage Design
The decision to pursue a two-stage PAT design was the result of the requirements
flowdown shown in Section 2.1.1. To be compatible with a typical CubeSat, NODE
was constrained to use no more than 10 W of power during communications. With
less power, a tighter beamwidth is required, and 2.1 mrad was the largest beamwidth
49
that could support a 10 Mbps downlink.
For a FWHM beamwidth of 2.1 mrad, constraining the pointing error to be within
±1.05 mrad (3-𝜎) will limit pointing losses to 3 dB, given that the transmitted laser
signal has a Gaussian profile. Figure 2-5 shows pointing loss as a function of pointing
error, with the pointing requirement highlighted in gray. For diffraction-limited lasercom systems the pointing accuracy can be as tight as 1/10th of the diffraction-limited
beamwidth, and the optimal ratio of pointing accuracy to beamwidth is around 4 for
these systems [52]. However, for systems that are not diffraction limited, the requirement can be relaxed. The pointing requirement for NODE is set at the half-power
point, beyond which the losses grow rapidly.
Figure 2-5: Pointing loss as a function of pointing error (requirement shown in gray).
With a pointing requirement of ±1.05 mrad (3-𝜎), a single-stage design is beyond
existing nanosatellite capabilities. The current pointing capabilities of CubeSats, as
discussed in Section 1.3, are just at the cusp of achieving sub-degree RMS error (i.e.
error less than 17 mrad on average). Given the constraint of 10 W maximum power
consumption, it is not possible to close the link with just body pointing unless an
extremely capable ADCS is pursued. A fine pointing stage must be introduced to
50
provide a 10 Mbps downlink for a CubeSat with standard pointing capabilities.
While staged control is a common technique in lasercom systems, it is a novel
concept for CubeSats. The only proposed two-stage pointing system on a CubeSat
is the ExoplanetSat mission developed jointly at the MIT SSL and Draper Laboratory [53]. ExoplanetSat is a 3-U CubeSat designed to detect exoplanets via the transit
method. Due to the high photometric precision required of the imager, very precise
pointing within 20 arcseconds (97 𝜇rad) is necessary. Fine stage control on ExoplanetSat consists of a piezoelectric linear stage that translates the imager in two axes,
and the imager is used for star tracking to provide fine attitude knowledge. While the
two-stage control approach has not been demonstrated on orbit, simulation results
predict a 3-𝜎 pointing precision of 2.3 arcseconds (11 𝜇rad).
NODE takes a different approach to two-stage control. ExoplanetSat is concerned
with maintaining star position very precisely on the imager, which it achieves by
directly actuating the imager on a stage. For lasercom, the primary concern is the
outgoing signal. A design similar to ExoplanetSat is possible if the beacon receiver is
collocated with the transmitter on the piezoelectric stage. Fine steering could then be
conducted with the two-axis stage, but this has several drawbacks. The piezoelectric
stage utilized in ExoplanetSat is about 1/4-U in size, which is too large to meet the
overall 1/2-U requirement of NODE. Additionally, the range of the stage is 100 𝜇m,
which in angular space is well under a degree for reasonable focal lengths of the beacon
receiver. This is not sufficient to overlap with standard CubeSat body pointing.
NODE uses a static beacon receiver for fine attitude knowledge and a tip/tilt
FSM to point the downlink. To motivate the two-stage control approach, it is useful
to compare key parameters of NODE to key parameters of OCSD (introduced in
Section 1.4.1) which takes a single-stage body pointing approach. Table 2.2 shows a
side-by-side comparison of NODE and OCSD.
OCSD and NODE are comparable in size, link range, and ground station size.
To close the link budget, NODE introduces a fine-pointing stage and reduces the
beamwidth. OCSD approaches this problem by increasing optical output power and
consequently the consumed power. To provide the required power, OCSD uses two
51
Table 2.2: Comparison of key parameters for OCSD and NODE.
OCSD
NODE
Link range
Size
900 km
10 × 10 × 15 cm3
Data rate
Pointing requirement
5-50 Mbps
±0.1∘ (1-𝜎)
±1.7 mrad (1-𝜎)
0.35∘
6.1 mrad
50 W
30 cm
1000 km
10 × 10 × 5 cm3 (NODE module)
10 × 10 × 34 cm3 (target host satellite)
10-100 Mbps
±0.06∘ (3-𝜎)
±1.05 mrad (3-𝜎)
0.12∘
2.1 mrad
10 W
30 cm
FWHM Beamwidth
Peak power consumption
Ground station aperture
18650 lithium ion batteries [7].
Referring to the basic link equation (see Equation 1.1), increasing transmitted
power is linearly proportional to received power. Improving pointing accuracy allows a reduction in beamwidth, which increases the gain of the transmitted signal
quadratically. The gain is directly related to directivity, which is given by:
𝐷=
4𝜋
Ω𝐴
(2.1)
where Ω𝐴 is the solid angle subtended by the beam. This is simply the ratio of the
surface area of a sphere to the solid angle of the beam. The solid angle of a cone with
apex 𝜃 is:
Ω𝐴 = 2𝜋(1 − cos 𝜃)
(2.2)
With a small angle approximation, this becomes:
Ω𝐴 ≈ 𝜋𝜃2
52
(2.3)
This gives directivity as a function of beamwidth 𝜃:
𝐷≈
4
𝜃2
(2.4)
Improving the pointing of the lasercom terminal allows a reduction in beamwidth
with a quadratic gain, whereas increasing power is only linear. Based on this logic,
NODE addresses the challenge of pointing rather than increasing power directly. This
allows similar performance capability within typical power usage for a CubeSat.
2.2.3
Monostatic vs. Bistatic Design
The choice between a monostatic and bistatic architecture was an important decision
in the early design process. A monostatic design has a shared Tx/Rx path with a
single aperture, whereas a bistatic design has split Tx and Rx paths with independent
apertures as shown in Figure 2-6. While some systems may have a separate aperture
to acquire the uplink beacon, the uplink signal path during tracking is almost always
shared with the downlink path in a monostatic architecture (refer to Figure 1-5).
Figure 2-6: Block diagram of monostatic and bistatic architectures.
The advantage of the monostatic architecture is that it provides closed loop feed53
back for the fine stage. The tip/tilt of the FSM acts on both the Tx and Rx signals,
ensuring that a well-designed controller can eliminate steady state pointing error.
With the bistatic design, closed loop feedback is lost. The FSM acts only on the
downlink, so if the Tx and Rx paths are misaligned it cannot be detected. This could
occur due to mechanical misalignment during launch, thermal variations on orbit, or
a change in the response characteristics of the FSM.
The justification for a monostatic design was based primarily on size constraints.
A link budget was conducted on the uplink beacon and a 25 mm diameter on the Rx
aperture is necessary to collect enough signal to identify the beacon [50]. The FSM
is constrained to a size less than 5 mm due to limited COTS actuators that fit within
NODE. These parameters were not flexible and made a monostatic design extremely
challenging, as described below.
The incoming signal from the receive aperture may either be collimated or left
uncollimated and focused directly onto the beacon detector. Each of these cases
presents significant challenges. If the beam is collimated, it must be resized by a
factor of 1/5 to fit on the FSM. However, by reducing the size of the collimated
beam, the off-axis angle is magnified by the resize factor. This concept is shown in
Figure 2-7 and described by:
𝐷𝐼𝑛𝑝𝑢𝑡
𝛼𝑂𝑢𝑡𝑝𝑢𝑡
=
𝛼𝐼𝑛𝑝𝑢𝑡
𝐷𝑂𝑢𝑡𝑝𝑢𝑡
(2.5)
If the incoming angle is 1∘ off-axis due to body pointing error, the resized beam
will have an error of 5∘ that the FSM must correct. This exceeds the capabilities
of COTS actuators to meet the range and resolution required for fine steering, and
also presents the issue of beam walk-off. Coarse stage body pointing errors are on
the order of a degree based on CubeSat body pointing capabilities, so the incoming
signal may be off-axis as much as several degrees which is then magnified by beam
resizing.
If the beam is not collimated, then the aperture size is limited by the FSM, and the
link cannot be closed. More power could be put into the beacon, but the design begins
54
Figure 2-7: Angular magnification with beam reduction. Off-axis incoming light
(green) as compared to on-axis light (red) for reference.
to encroach upon laser safety regulations [19]. Based on these concerns, a bistatic
design was pursued, and a semi-closed loop calibration method was developed to
compensate for Tx/Rx path misalignment.
2.2.4
Hybrid Laser & Radio Calibration Method
Since NODE has a bistatic configuration, the FSM tracks the ground station in an
open loop manner. Pointing bias may occur due to a variety of factors, such as
mechanical or thermally-induced misalignment of optical components or a shift in
response characteristics of the FSM. A means of calibrating out this bias is needed
to ensure that fine steering requirements can be met.
While there is no closed loop feedback on NODE, power measurements from the
ground can be sent back to NODE through the low-rate RF link. This concept is
shown in Figure 2-8. The laser beam profile is a two-dimensional Gaussian. While
the FSM tracks the beacon, the tip/tilt angles can be modified slightly. The ground
station will take a time-averaged power measurement, which will be relayed to the
RF ground station and transmitted back to the satellite. By repeating this pattern,
NODE can calibrate out the mispointing until the ground is receiving at the peak of
the signal.
This approach presents several challenges, which are addressed in detail in Section
3.2. The primary challenge is the atmospheric channel. This will cause time-varying
55
Figure 2-8: Hybrid laser downlink and radio uplink calibration concept.
intensity on the ground that will inject noise into the power measurements. An
additional challenge is the time-shifting power curve over the duration of the pass.
As the orbital trajectory approaches the ground station, received power will increase
as the link range decreases. Likewise, as the satellite recedes from the ground station
received power will decrease. This time-shifting power makes relative comparisons
between measurements a challenge. Finally, the calibration approach may be applied
during communications (i.e. while transmitting data) so the pointing adjustments
must be small enough to avoid compromising the link.
2.3
Derivation of Requirements
From the high level system requirement of providing a >10 Mbps downlink for a
typical SWaP-constrained CubeSat, requirements are levied on PAT system perfor-
56
mance. The key challenge for the PAT subsystem is to bridge the gap between current
CubeSat pointing capabilities and the required pointing for high bandwidth lasercom.
2.3.1
Host Spacecraft Performance
Three requirements are placed on the host spacecraft’s ADCS to be compatible with
NODE. CubeSat pointing capabilities are just beginning to achieve sub-degree error,
as described in Section 1.3. With this figure in mind, NODE is designed to support
CubeSats with an initial pointing accuracy of ± 3∘ (3-𝜎). The beacon receiver requires
this accuracy to see the beacon within its FOV.
The second constraint comes after beacon acquisition. The host satellite will
correct its pointing in response to the beacon receiver feedback, with the aim of
centering the beacon on the camera. At this point, the satellite is receiving very fine
attitude feedback and with this it must be able to point within ±1∘ (3-𝜎). This allows
an overlap with the fine steering stage range so that fine corrections can be applied.
The final requirement is that the CubeSat must support slew rates of up to 1∘ /sec
to enable ground tracking from a 400 km orbit. These requirements are summarized
in Table 2.3.
Table 2.3: Host spacecraft performance requirements for compatibility with NODE.
Parameter
Pre-acq. pointing
(no beacon)
Post-acq. pointing
(beacon feedback)
Slew rate
2.3.2
Performance Req. Reason
±3∘ (3-𝜎) Beacon must be within camera FOV.
52 mrad (3-𝜎)
±1∘ (3-𝜎) Must overlap with fine stage range.
17 mrad (3-𝜎)
1∘ /sec Max. slew to track ground station
at 400 km.
Fine Steering Requirements
The fine steering must bridge the gap between coarse stage body pointing and the
accuracy required to close the link. There are two major requirements placed on the
57
fine stage, which are the range and accuracy. The fine stage range must be larger
than ±1∘ to overlap with the coarse stage. The optical beam deflection will be up
to twice as much as the range depending on the optical configuration, so this ensures
that the fine steering mechanism will not be operating near saturation.
The second requirement of the fine stage is that it provide steering accuracy to
±1.05 mrad (3-𝜎), which limits pointing loss to 3 dB or less. This requirement
is intentionally conservative, and if pointing performance significantly exceeds the
requirement higher data rates can be achieved. The requirements for fine steering are
summarized in Table 2.4.
Table 2.4: NODE fine steering requirements.
Parameter
>1∘
Range
Pointing accuracy
2.3.3
Performance Req. Reason
Must overlap with coarse stage postacquisition pointing.
∘
±0.06 (3-𝜎) Max. pointing loss of 3 dB.
1.05 mrad (3-𝜎)
Beacon Detector Requirements
The beacon from the ground provides fine attitude knowledge to NODE and its host
CubeSat. Two requirements are placed on the detector, shown in Table 2.5. The
FOV of the detector must be large enough to acquire the beacon with the expected
host body pointing error. This error is limited to ±3∘ based on CubeSat pointing
capabilities, so the detector FOV must be at least 6∘ . The attitude knowledge must
be sufficient to support the pointing requirement of ±1.05 mrad, so a requirement is
placed on the beacon detector to achieve a centroid measurement accurate to better
than ±0.1 mrad, a factor of ten better than the required pointing.
58
Table 2.5: NODE beacon detector requirements.
Parameter
Performance Req. Reason
>6∘
Field of view
Centroid accuracy
2.3.4
Must overlap with coarse stage preacquisition pointing.
∘
±0.006 (3-𝜎) 1/10th of fine pointing requirement.
0.1 mrad (3-𝜎)
On-orbit Calibration Requirements
On-orbit calibration is needed to ensure that the transmit and receive paths are
aligned. If they become misaligned, the FSM is in an open loop configuration and will
not receive feedback that there is a pointing bias. To calibrate out this bias, a hybrid
lasercom/RF procedure is conducted that utilizes received power measurements from
the ground to eliminate pointing bias. The requirements on this calibration regard
the calibration time and its accuracy, summarized in Table 2.6.
Given that a communications pass in LEO lasts less than 10 minutes, we require
that the calibration be performed within 120 seconds. The calibration must also
eliminate pointing bias to within 1/2 of the required pointing error (i.e. in the worst
case, half of the pointing error budget is given up to an open loop misalignment term).
Table 2.6: NODE on-orbit calibration requirements.
Parameter
Time to converge
Post-calibration bias
2.4
Performance Req. Reason
120 s
<0.03∘
Can occur during LEO pass.
1/2 of fine pointing requirement.
Fine Stage Hardware
A major challenge of designing NODE was the selection of COTS hardware that could
meet both pointing requirements and SWaP constraints. The two key components of
the PAT system are the beacon detector and the FSM. While the beacon detector is
59
a CMOS camera with many COTS options, FSM technology is very limited in the
form factor required for NODE. The design layout is presented followed by selected
hardware.
2.4.1
Layout
The key hardware components of NODE consist of a seed laser, fiber amplifier, beacon
detector, FSM and supporting electronics. The general layout of NODE hardware is
shown in Figure 2-9. The largest components are the erbium-doped fiber amplifier
(EDFA) that provides the power needed for transmission and the beacon detector
with filters for background rejection.
Figure 2-9: NODE hardware layout.
The top portion of the assembly is dedicated to the PAT subsystem, while the
bottom portion encases the seed laser and fiber amplifier. The FSM and beacon detector are collocated on an optics bench to maintain alignment. The uplink aperture
is sized at 2.5 cm and the downlink aperture is 1 cm. High-speed electronics to implement PAT control as well as forward error correction, interleaving, and modulation
for downlink data are located adjacent to the PAT hardware.
60
2.4.2
Beacon Detector
Early in the design process the beacon uplink was selected at 850 nm to be able to
utilize standard CCD and CMOS sensors. These cameras have common commercial
applications and as a result the technology is well-developed.
Several focal plane arrays (FPAs) were examined with properties shown in Table
2.7. The Aptina FPA was selected due to the small pixel size. This enables a shorter
focal length with improved resolution. The Aptina was paired with a lens of focal
length 35 mm, which gives it a 6.6∘ full-angle FOV, placing a lenient requirement on
CubeSat body pointing to acquire the beacon.
Table 2.7: Commercial focal plane array options for beacon detector.
Read noise (RMS 𝑒− )
Dark current (𝑒− /pixel/sec)
Quantum efficiency
Full well capacity (𝑒− )
Pixel pitch (𝜇m)
Focal length for
6∘ FOV (mm)
CMOSIS
Fairchild
CMV4000-3E12 CIS1910F
Aptina
MT9P031
13
125
0.3
13500
5.5
108
21.3
60
0.15
10000
2.2
41
1.2
30
0.22
30000
6.5
67
The beacon detector consists of the CMOS FPA, a 25.4 mm aperture with a 35
mm focal length, and two optical filters for background rejection [54]. The two filters
consist of a 10 nm bandpass filter at 850 nm as well as a UV/Vis cut-filter at 700
nm to limit solar radiation. The prototype that has been used for testing is shown in
Figure 2-10.
2.4.3
Fast Steering Mirror
While there were many options for the beacon detector, there are very few commercial
FSM options that fit within the form factor of NODE. Common optical steering
solutions use galvanometers, piezoelectric devices or voice coils, but these devices
61
Figure 2-10: NODE beacon detector prototype.
have high power consumption and large controllers that in themselves exceed the
size of NODE. An alternative to these types of actuators are microelectromechanical
systems (MEMS). These actuators usually rely on electrostatic forces that are not
strong enough for large actuators but can be utilized on small scales. An advantage
of these devices is that they consume very little power, although they require a high
voltage to operate.
The MEMS fast-steering mirror selected for NODE, produced by Mirrorcle Technologies Inc., utilizes four electrostatic comb-drive rotators to achieve tip/tilt actuation [55]. The device is capable of large angular deflections with relatively little power,
and the device driver is about the size of a credit card. To highlight the reduced size
of the MEMS device, its performance and operational characteristics are compared
to state of the art FSM devices with different actuator types in Table 2.8.
The comparison of FSM actuators in Table 2.8 highlights the benefits of using a
MEMS device for NODE fine steering. Standard drivers for other types of actuators
often exceed the entire volume of a CubeSat and draw more power than a CubeSat
bus could provide.
The tradeoff in using a MEMS device is a very small mirror diameter, but it is
sufficient for downlink beam steering and is the only feasible option for meeting size,
weight, and power constraints. A ramification of the small MEMS mirror, however,
is the monostatic design discussed in section 2.2.3. Closed loop feedback in which
62
Table 2.8: Commercial fast-steering mirror performance and operational characteristics.
Thorlabs
GVS001
OIM
OIM101
PI
S-334
MTI
13L2.2
Type
Galvo
Voice coil
Piezo
MEMS
Mirror size (mm) 5
25
10
3
Mechanical range ±12.5
±1.5
±2.9
±1.25
(deg)
Resolution (𝜇rad) 15
<2
0.5
<3
Bandwidth (Hz)
250
>850
>100
>650
Device dimensions 19 × 34 × 40 56 × 58 × 58
25 × 33 × 47
5 × 20 × 20
(mm3 )
Driver dimensions 44 × 74 × 85 51 × 102 × 155 51 × 128 × 186 12 × 40 × 60
(mm3 )
Peak power (W)
90
30
10
<0.5
OIM = Optics In Motion, PI = Physik Instrumente, MTI = Mirrorcle Tech. Inc.
the FSM steers both the Tx/Rx signals becomes very challenging, since the receive
aperture is limited by the mirror diameter. This drawback was accepted in exchange
for very low power consumption and small driver size. The MEMS FSM selected is
pictured in Figure 2-11.
Figure 2-11: NODE fine stage MEMS fast-steering mirror.
63
64
Chapter 3
Simulation Analysis & Results
Two simulations were developed to assess the pointing performance of NODE. The
first simulation, presented in Section 3.1, models the post-acquisition tracking performance of the system. If the host satellite achieves initial pointing within the required
±3∘ of the ground station, the beacon can be acquired instantaneously. This simulation begins at the moment of acquisition of the ground station and models the
pointing performance of a representative CubeSat bus as well as the performance of
the fine stage. Without Tx/Rx path misalignment, predicted pointing performance
of NODE is 0.18 mrad (3−𝜎).
The second simulation, presented in Section 3.2, focuses on calibration of the
Tx/Rx alignment. Algorithms for the elimination of pointing bias are assessed to
ensure that any on-orbit misalignment can be corrected. Results of this simulation
indicate that Tx/Rx path misalignment can be reduced to 0.11 mrad or less.
Combining results from both simulations, the predicted performance of NODE is
±0.3 mrad (3-𝜎) which meets the ±1.05 mrad fine pointing requirement with a large
margin.
3.1
Ground Tracking Simulation
A single-axis simulation is developed to model the coarse and fine stage beacon tracking. NODE is designed to operate within the constraints of a standard CubeSat with
65
modest pointing capabilities. A CubeSat bus is modeled with representative hardware to assess expected pointing performance and ensure that NODE can meet the
±1.05 mrad pointing requirement.
3.1.1
Motivation & Overview
The simulation models an overhead pass of a satellite at 400 km. The overhead
pass produces the highest slew rate, which peaks at 1.1∘ /sec. A single-axis model is
developed to assess pointing performance and determine the major contributions to
pointing error.
The satellite executes a pitch maneuver to track the ground station. To understand
the single-axis model, we must first define the relevant reference frames. We utilize
the RSW reference frame, as defined by D. Vallado [8] (refer to Figure 3-1). This
frame defines the local vertical and local horizontal directions. The radial component,
ˆ extends from the center of mass of Earth to the center of mass of the satellite.
𝑅,
ˆ , is perpendicular to the orbit plane. The along-track
The cross-track component, 𝑊
ˆ completes a right-handed set. If the satellite is in a circular orbit, 𝑆ˆ
component, 𝑆,
will be aligned with the velocity vector of the satellite.
Figure 3-1: RSW satellite reference frame [8].
66
If the RSW set is rotated 180∘ about the 𝑆ˆ axis, a roll-pitch-yaw configuration
ˆ axis, which is the axis
results. The pitch corresponds with a rotation about the 𝑊
modeled in this simulation. It is assumed that one of the satellite body axes is
ˆ vector, resulting in the pitch maneuver occurring about one body
aligned with the 𝑊
axis. This results in the most simple configuration for a slew maneuver. The pitch
maneuver is shown in Figure 3-2. The roll and yaw axes are much less exercised than
the pitch axis, so the greatest errors are expected in pitch.
Figure 3-2: Pitch maneuver for ground tracking.
While the discussion in Section 1.3 indicated that nanosatellites are approaching
sub-degree pointing precision, these satellites were inertially pointing rather than
slewing. The ground track maneuver is more challenging. Additionally, the LEO
environment has very different drag conditions depending on altitude and NODE is
designed for a low orbit. Most precision pointing missions occur at altitudes above
600 km, where the effect of atmospheric drag is relatively small. NODE is designed
for a 400 km orbit where atmospheric density is an order of magnitude larger than at
600 km [56], as seen in Figure 3-3.
In the single-axis simulation, several assumptions are made. First, the momentum
control of the satellite is not considered. The host satellite is expected to perform
momentum control with magnetorquers to avoid reaction wheel saturation. Additionally, the effects of gyroscopic coupling are ignored. Gyroscopic terms should be
measured prior to flight and compensated for in the host control system. If the gyroscopic coupling terms are not well understood, they can adversely affect pointing
performance on orbit. However, the simulation models the pitch maneuver, and the
67
Figure 3-3: Atmospheric density as a function of altitude.
gyroscopic effects on the other axes will contribute relatively little to overall error.
The vast majority of pointing error will be in the pitch axis as it must achieve both
precision pointing and rate control.
The simulation consists of sensors, actuators, and software for estimation and
control for the fine and coarse stages. The block diagram of the simulation is shown
in Figure 3-4. The coarse stage models a CubeSat bus with a reaction wheel actuator
and gyroscope sensor. Precise position feedback is provided by the beacon detector
on NODE. The fine stage FSM actuator is modeled to augment coarse pointing. The
outer loop in Figure 3-4 is the coarse pointing, which occurs at a rate of 4 Hz, while
the inner fine pointing loop occurs at a rate of 10 Hz.
Sources of error are included from sensors, actuators, and dynamics (which includes environmental disturbances, orbital knowledge, and knowledge of inertial attributes). The dynamic, sensor, and actuator models and errors are presented, and
the contributions of various error sources are quantified in Section 3.1.6.
Parameters for the host spacecraft are modeled after the Microwave Radiometer Technology Acceleration Mission (MiRaTA) [9], a 3-U CubeSat developed by the
MIT Space Telecommunications, Astronomy, and Radiation (STAR) Lab and MIT
Lincoln Laboratory. MiRaTA, pictured in Figure 3-5, is a remote sensing mission that
takes atmospheric measurements and could benefit from a high-rate lasercom down68
Figure 3-4: Block diagram of tracking simulation.
link. Physical parameters modeling the host CubeSat are generated from MiRaTA
specifications.
3.1.2
Dynamic Models
While only the pitch axis of the satellite is explicitly tracked in the single-axis simulation, environmental disturbances from a six degree of freedom (DOF) simulation
are incorporated into the single-axis simulation. The pitch maneuver is modeled in
the six-DOF simulation to generate a timeseries of environmental disturbances that
include atmospheric drag, gravity gradient, solar radiation pressure, and magnetic
disturbances.
Attitude Dynamics
The attitude dynamics of a spacecraft are given by Euler’s equations, which describe
the rotation of a rigid body about its center of mass. The spacecraft’s equations of
motion are:
69
Figure 3-5: MiRaTA 3-U CubeSat used for modeling the host spacecraft [9].
𝐽𝜔
⃗˙ = −⃗𝜔 × (𝐽⃗𝜔 ) + ⃗𝜏
(3.1)
where 𝐽3×3 is the inertia matrix, 𝜔
⃗ 3×1 is the angular velocity vector, and ⃗𝜏3×1 is the
torque vector acting on the spacecraft.
For the purposes of the single-axis simulation, it is assumed that the first term on
the right side of Equation 3.1, the gyroscopic coupling, is negligible. This is justified
because the angular rates about the yaw and roll axes are small (ideally they are
controlled to zero) and the gyroscopic term can be accounted for in the control law
of the spacecraft. For small changes in angle, the resulting single-axis equation can
be linearized as:
⎡
⎤
⎡ ⎤
⎡ ⎤
0 1
0
0
⎦ ⃗𝑥 + ⎣ ⎦ 𝜏𝑐𝑚𝑑 + ⎣ ⎦ 𝜏𝑑𝑖𝑠𝑡
⃗𝑥˙ = ⎣
1
1
0 0
𝐽
𝐽
(3.2)
[︁
]︁T
where ⃗𝑥 = 𝜃 𝜃˙ is the state composed of angle and angular rate, 𝐽 is the moment
of inertia, 𝜏𝑐𝑚𝑑 is the commanded torque, and 𝜏𝑑𝑖𝑠𝑡 is the disturbance torque acting
on the system.
70
Orbital Dynamics
In the single-axis simulation, the orbital position is not modeled explicitly. However,
a six-DOF simulation that draws on prior work from the MIT Space Systems Lab
is used to generate disturbances [47, 57]. The orbital dynamics are derived from
Newton’s second law and the law of gravity. The effect of external forces on the orbit
are not modeled, so the dynamics follow the restricted two-body problem:
𝜇
⃗𝑟¨ + 3 ⃗𝑟 = 0
𝑟
(3.3)
Using the Keplerian orbital dynamics, the angle of elevation and pitch of the
satellite can be determined as a function of time. For the simulation, the ground
station is assumed to be in the orbit plane, since this will produce the highest slew
rates. The geometry of the setup is shown in Figure 3-6.
Figure 3-6: Geometry of pitch angle and angle of elevation with ground station in
orbit plane.
The angle of elevation 𝜀 can be determined as a function of the orbital altitude
and the angle between the ground station and the satellite from the center of the
Earth, 𝜑. Using the law of sines, an implicit equation for the angle of elevation can
be determined:
71
cos 𝜀
cos (𝜀 + 𝜑)
=
𝑅𝐸
𝑅𝐸 + ℎ
(3.4)
where 𝑅𝐸 is the radius of the Earth and ℎ is the altitude of the orbit. The rate of
change of 𝜑 is assumed constant based on the period of the orbit (the ground station is
treated as stationary for the duration of the pass, which is ∼10 minutes from horizon
to horizon).
Differentiating Equation 3.4 gives the rate of change of angle of elevation:
𝜀˙ =
(𝑅𝐸 + ℎ) sin (𝜀 + 𝜑) 𝜑˙
𝑅𝐸 sin 𝜀 − (𝑅𝐸 + ℎ) sin (𝜀 + 𝜑)
(3.5)
Using Equations 3.4 and 3.5, a series of angle and angular rate commands can be
generated for the single-axis simulation. For each timestep, 𝜑 is propagated forward
and 𝜀 is calculated using Equation 3.4, followed by 𝜀˙ using Equation 3.5.
For generating disturbances, angle of elevation can be converted to a pitch angle
𝜃 by once again using the law of sines:
−1
𝜃 = sin
(︂
𝑅𝐸
cos 𝜀
𝑅𝐸 + ℎ
)︂
(3.6)
With this trajectory, atmospheric disturbances are generated by treating roll and
yaw as zero while pitch follows from Equation 3.6.
Atmospheric Drag
Atmospheric drag is the largest environmental disturbance torque in a 400 km orbit.
The atmospheric density is modeled using the 1976 U.S. Standard Atmosphere [56],
and is equal to about 2.8×10−12 kg/m3 at 400 km. To calculate the aerodynamic
torque, the satellite is modeled as a collection of planar surfaces, each of which experience aerodynamic effects. The overall atmospheric drag torque is given by [58]:
𝑛
∑︁
1
⃗ 𝑐𝑝,𝑖 × [𝐴𝑖 (ˆ
⃗𝜏𝑑𝑟𝑎𝑔 = − 𝐶𝐷 𝜌𝑉 2
𝑅
𝑛𝑖 · 𝑣ˆ)ˆ
𝑣]
2
𝑖=1
72
(3.7)
where 𝐶𝐷 is the drag coefficient (2.5 is used), 𝜌 is the atmospheric density, 𝑉 is the
⃗ 𝑐𝑝,𝑖 is the vector from the center of mass to the center of
velocity of the spacecraft, 𝑅
pressure of the 𝑖𝑡ℎ surface, 𝐴𝑖 is the surface area of the 𝑖𝑡ℎ face, 𝑛
ˆ 𝑖 is the unit normal
of the 𝑖𝑡ℎ surface, and 𝑣ˆ is the unit vector velocity direction.
Magnetic Disturbances
Torques arise from the Earth’s magnetic field acting on the spacecraft’s residual magnetic field. The torque is given simply by [58]:
⃗
⃗𝜏𝑚𝑎𝑔 = 𝑚
⃗ ×𝐵
(3.8)
where 𝑚
⃗ is the residual magnetic dipole in the body frame (0.001 A/m2 in roll axis
⃗ is the geocentric local magnetic field (T) in the body frame. The
is used) and 𝐵
local magnetic field is calculated with the IGRF-11 model [59] following the approach
outlined in [60] using terms up to 6th order.
Gravity Gradient
The gravity gradient torque results from the variation in the earth’s gravity field
across the body of the spacecraft. The torque in the body frame due to the gravity
gradient is given by [58]:
⃗𝜏𝐺𝐺
)︁
3𝜇 (︁ ⃗
⃗
= 3 𝑅𝑠 × (𝐽 · 𝑅𝑠 )
𝑅𝑠
(3.9)
⃗ 𝑆 is the position of the satellite
where 𝜇 is the gravitational constant of the earth, 𝑅
in the body reference frame, and 𝐽3×3 is the inertia matrix of the satellite.
Solar Radiation Pressure
A torque is produced from the sun’s rays incident on the spacecraft. The sun’s rays
may either be absorbed, specularly reflected, or diffusely reflected. The satellite is
modeled as a collection of plane surfaces and the torque on each surface with incident
sunlight is calculated. The overall torque is given by the sum of these surfaces [58]:
73
⃗𝜏𝑆𝑅𝑃
)︂ ]︂
[︂
(︂
𝑛
𝐹𝑆 ∑︁
1
⃗ 𝑐𝑝,𝑖 × (1 − 𝐶𝑠 )ˆ
ˆ
=−
𝐴𝑖 (ˆ
𝑠·𝑛
ˆ 𝑖 )𝑅
𝑠 + 2 𝐶𝑠 (ˆ
𝑠·𝑛
ˆ 𝑖 ) + 𝐶𝑑 𝑛
𝑐 𝑖=1
3
(3.10)
where 𝐹𝑆 is the solar constant taken to be 1367 W/m2 at 1 AU, 𝑐 is the speed of
light, 𝐴𝑖 is the area of the 𝑖𝑡ℎ surface, 𝑠ˆ is the unit vector from the spacecraft to the
⃗ 𝑐𝑝,𝑖 is the
sun in the body frame, 𝑛
ˆ 𝑖 is the 𝑖𝑡ℎ surface normal in the body frame, 𝑅
vector from the spacecraft center of mass to the center of pressure of the 𝑖𝑡ℎ surface
in the body frame, 𝐶𝑠 is the specular reflection coefficient (0.4 is used), and 𝐶𝑑 is the
diffuse reflection coefficient (0.2 is used).
3.1.3
Sensor Models
Two sensors are modeled. The beacon detector on NODE, described in Section 2.4.2,
provides fine attitude knowledge. A coarse stage gyroscope is modeled to provide rate
feedback, as this is a common element of CubeSat attitude determination.
Beacon Detector
The detector model is based on a detailed analysis of the uplink beacon signal, which
includes a laser link radiometry model, hardware model, atmospheric scintillation
model, and sky radiance model [54]. The resulting parameters included in the pointing
simulation are summarized in Table 3.1.
Table 3.1: Simulation parameters for beacon detector.
Parameter
Value
Focal length
Centroid noise
Pixel size
Probability of fade
35 mm
0.5 pixel (1-𝜎)
2.2 micron
0.05
Centroiding error is modeled as zero-mean Gaussian white noise. Occasional fades
74
result in a failure to detect the beacon, and a probabilistic fade is injected into the
simulation. In the event of a fade, the previous beacon position is used.
Gyroscope
The gyroscope modeled is the Analog Devices ADIS16334 inertial measurement unit
(IMU) [61]. Parameters included in the simulation are listed in Table 3.2. Modeled
sources of noise and error from the gyroscope include limited resolution, angular
random walk and rate random walk. The simulation does not directly estimate gyro
bias but it assumes that it has been compensated for and is treated as zero at the
start of the simulation.
Table 3.2: Simulation parameters for gyroscope.
3.1.4
Parameter
Value
Resolution
Range
Angular random walk
In-run bias stability
0.0125∘ /s
±75∘ /s
√
2∘ / hr
0.0072∘ /s
Actuator Models
Two actuators are modeled, which include the coarse stage reaction wheel and fine
stage FSM. Magnetorquers and momentum control are not modeled for the host
spacecraft. The FSM is modeled based on response data.
Reaction Wheel
The coarse stage reaction wheel is based on the MAI-400, which is actuated at a
4 Hz rate. The parameters included in the simulation are summarized in Table 3.3.
Reaction wheel noise is modeled as sinusoids. The amplitude of the disturbance scales
with the square of the reaction wheel speed and the frequency matches the harmonics
of the reaction wheel speed. Parameters for this noise are based off of data from
75
MAI-200 testing. A description of the testing and fitting of these parameters can be
found in [57].
Table 3.3: Simulation parameters for reaction wheel.
Parameter
Value
Wheel inertia
Maximum torque
Maximum speed
Quantization
8.93 × 10−6 kg·m2
6.25×10−4 N·m
10000 rpm
8 bit
Fast Steering Mirror
The fast steering mirror is modeled by fitting a transfer function of commanded angle
to output angle based on response data. The response data and model are shown in
Figure 3-7. The model is given by the second order transfer function:
𝜃𝐹 𝑆𝑀 (𝑠)
𝜔𝑛2
= 2
𝜃𝑐𝑚𝑑 (𝑠)
𝑠 + 2𝜁𝜔𝑛 𝑠 + 𝜔𝑛2
(3.11)
where 𝜃𝐹 𝑆𝑀 is the FSM response angle, 𝜃𝑐𝑚𝑑 is the commanded FSM angle, 𝜔𝑛 is the
first resonance of the FSM at 1764 Hz, and 𝜁 is the damping ratio fit to 0.005.
The FSM is also quantized into 8-bit commands and noise is added based on results
from device testing, described in Section 4.3.4. FSM parameters are summarized in
Table 3.4.
Table 3.4: Simulation parameters for FSM.
Parameter
Value
Range
±1.25∘
Noise
0.02 mrad (1-𝜎)
Quantization 14 bit
76
Figure 3-7: Bode plot of FSM response data and transfer function model.
3.1.5
Control & Estimation Models
The coarse stage is modeled to represent a typical CubeSat. A Kalman filter is implemented for the coarse stage which estimates attitude, rate, and disturbance. A
standard PD controller is implemented with non-constant rate and attitude commands and feedforward compensation. The fine stage is driven open loop with a
low-pass filter to protect the FSM from resonance.
Coarse Stage
It is important to note an atypical feature of the coarse estimation and control loop
architecture (refer to Figure 3-4). The beacon detector and gyroscope measurements
are fed into a Kalman filter to estimate attitude and angular rate. However, only the
angular rate is used for attitude control. The reason for this is that errors in position
knowledge introduce attitude errors, as explained below.
The centroid provides a direct measure of pointing error in the body frame of the
satellite to an accuracy of about 30 𝜇rad RMS [54]. To convert this measurement
into an inertial pointing vector so that it can be incorporated into a Kalman filter,
77
the location of the satellite and ground station must be known. Unfortunately, this
position knowledge is often not very precise for CubeSats in LEO. The errors in
position knowledge will greatly degrade the measurement accuracy. For example,
a 1 km in-track error at a range of 400 km will introduce an angular error of 2.5
mrad to the measurement. If the host satellite has a GPS receiver, precision position
knowledge is possible, but the majority of CubeSats rely on two-line element (TLE)
sets for orbit determination which have errors of several kilometers or more [62].
Therefore, the attitude error measured by the beacon detector is fed directly into the
controller, bypassing the Kalman filter attitude estimate but still using the estimated
angular rate.
Estimation for the coarse stage utilizes a discrete Kalman filter. Given the large
environmental (particularly aerodynamic) disturbances at 400 km, coarse pointing
performance is significantly improved with estimation of disturbances. This formulation is presented (for a detailed treatment of Kalman filtering with an augmented
state vector, refer to [63]).
The augmented state in continuous time is given by:
]︁𝑇
[︁
˙
⃗𝑥 = 𝜃 𝜃 𝜏𝑑
(3.12)
where 𝜃 is the angle, 𝜃˙ is the angular rate, and 𝜏𝑑 is the disturbance torque. The
continuous process is modeled as:
⃗𝑥˙ = 𝐴⃗𝑥 + 𝐵𝜏 + 𝑤
⃗
(3.13)
or,
⎡
⎤
⎡ ⎤
⎡ ⎤
⎢0 1 0 ⎥
⎢0⎥
⎢0⎥
⎢
⎥
⎢ ⎥
⎢ ⎥
⎢1⎥
⎢ ⎥
1⎥
⃗𝑥˙ = ⎢
⎢0 0 𝐽 ⎥ ⃗𝑥 + ⎢ 𝐽 ⎥ 𝜏 + ⎢0⎥ 𝑤(𝑡)
⎣
⎦
⎣ ⎦
⎣ ⎦
0 0 0
0
1
(3.14)
where 𝜏 is the commanded torque, 𝐽 is the moment of inertia, and 𝜔(𝑡) is white
noise with specified power. The process noise power scales with the magnitude of the
disturbance torques and can be tuned based on performance.
78
The continuous process is converted to discrete time using the Van Loan method
[63] with discrete time steps at 4 Hz. This method yields the discrete time formulation:
⃗𝑥𝑘+1 = 𝐴𝑘 ⃗𝑥𝑘 + 𝐵𝑘 𝜏𝑘 + 𝑤
⃗𝑘
(3.15)
where 𝑤
⃗ 𝑘 is a white noise sequence with covariance matrix 𝑅𝑤 .
Process observations, consisting of the beacon detector and gyroscope measurements, are modeled as:
⃗𝑧𝑘 = 𝐶𝑘 ⃗𝑥𝑘 + ⃗𝑣𝑘
(3.16)
⎡
⎤
1 0 0
⎦ ⃗𝑥𝑘 + ⃗𝑣𝑘
⃗𝑧𝑘 = ⎣
0 1 0
(3.17)
or,
where ⃗𝑣𝑘 is the sensor noise modeled as a white noise sequence with covariance matrix
𝑅𝑣 .
Note that the beacon detector measurements do not directly measure attitude, but
rather attitude error relative to the ground station. This measurement is converted to
attitude by treating it as a deviation from the commanded attitude. As discussed at
the beginning of the section, this introduces additional error to the measurement, but
the centroid measurement is still more precise than typical CubeSat attitude sensors.
At each iteration, the Kalman filter loop goes through a sequence of projecting
the state and covariance, computing the Kalman gain, and updating the state and
covariance estimates. The state and covariance projections are given by:
ˆ𝑘−1 + 𝐵𝑘−1 𝜏𝑘−1
𝑥ˆ−
𝑘 = 𝐴𝑘−1 𝑥
(3.18)
𝑃𝑘− = 𝐴𝑘−1 𝑃𝑘−1 𝐴𝑇𝑘−1 + 𝑅𝑤
(3.19)
The Kalman gain is calculated as:
)︀−1
(︀
𝐿𝑘 = 𝑃𝑘− 𝐶𝑘𝑇 𝐶𝑘 𝑃𝑘− 𝐶𝑘𝑇 + 𝑅𝑣
79
(3.20)
The state is then updated by the new measurement:
(︀
)︀
𝑥ˆ𝑘 = 𝑥ˆ−
𝑧𝑘 − 𝐶𝑘 𝑥ˆ−
𝑘 + 𝐿𝑘 ⃗
𝑘
(3.21)
And finally the covariance is updated:
𝑃𝑘 = (𝐼 − 𝐿𝑘 𝐶𝑘 ) 𝑃𝑘−
(3.22)
The covariance is initialized to its steady-state value, which can be determined by
solving the discrete algebraic Ricatti equation:
]︁
[︁
(︀
)︀−1
𝐶𝑘 𝑃𝑆𝑆 𝐴𝑇𝑘 + 𝑅𝑤
𝑃𝑆𝑆 = 𝐴𝑘 𝑃𝑆𝑆 − 𝑃𝑆𝑆 𝐶𝑘𝑇 𝐶𝑘 𝑃𝑆𝑆 𝐶𝑘𝑇 + 𝑅𝑣
(3.23)
With the estimation algorithm in place, the angular rate estimate is subtracted
from the rate command to produce rate error. The rate error is paired with the
beacon detector measurement of angular error. These signals are then fed into a PD
controller.
The controller design follows a very standard approach. The PD controller is
based on the work of Wie et al. [64], who first developed a quaternion feedback
regulator for eigenaxis rotations. The proposed controller was intended for large-angle
rest-to-rest maneuvers, and includes linear quaternion and quaternion rate terms as
well as a nonlinear gyroscopic coupling cancellation. This approach was extended to
include rate tracking [65] as well as feedforward compensation for non-constant rate
tracking [66, 67]. Additional disturbance cancellation terms have been proposed for
ground-target tracking [66].
The control law formulated in the simulation is as follows:
(︁
)︁
𝜏𝑐𝑚𝑑 = 𝐾𝑝 𝜃𝑟 − 𝜃ˆ + 𝐾𝑑 (𝜔𝑟 − 𝜔
ˆ ) + 𝐽 𝜔˙ 𝑟 − 𝑑ˆ
(3.24)
where 𝜏𝑐𝑚𝑑 is the commanded torque, 𝜃𝑟 is the reference angle, 𝜔𝑟 is the reference
angular rate, 𝐾𝑝 and 𝐾𝑑 are the proportional and derivative controller gains, and
𝑑ˆ is the estimated environmental disturbance torque. The first two terms are the
80
proportional and derivative terms, the third term is a feedforward term, and the final
term is disturbance cancellation.
The selection of control gains follows the analysis of Wie et al. [64]. It is shown
that the gains can be chosen via a linear second-order approximation for small angles,
which yields:
𝐾𝑝 = 𝐽𝜔𝑛2
(3.25)
𝐾𝑑 = 2𝐽𝜁𝜔𝑛2
(3.26)
The controller gains are defined by the closed loop damping ratio 𝜁 and natural
frequency 𝜔𝑛 . These terms are selected to be 0.7 for 𝜁 for good system response and
𝜔𝑛 set at 0.04 Hz to avoid any structural excitations or instabilities.
Fine Stage
The FSM is driven open loop from the beacon detector centroid, so the control is
fairly simple. The location of the centroid is converted from pixels to angles based on
the focal length of the detector setup. The correction is scaled by an optical factor
of 2 for the reflected beam. It should be noted that if the tip or tilt axis of rotation
is not perpendicular to the incoming beam, this scale factor will reduce and must be
calculated accordingly. The scale factor varies between 1 to 2 and is accounted for in
design, so it should not affect performance.
The centroid readout rate is 10 Hz, and these measurements are low-pass filtered
to protect the mirror from resonance. The manufacturer recommends a 6th order
Bessel filter at 460 Hz, which is implemented. The point-ahead angle is ignored since
it is at most 0.05 mrad and the orbital position knowledge is not good enough to
determine point-ahead accurately.
Knowledge Errors
Several additional sources of error are present in the simulation which can be grouped
together as knowledge errors.
81
The first is an error in the moment of inertia of the satellite. It is challenging to
measure this with high precision on the ground, so in the simulation a 5% underestimate of the moment of inertia is injected (a value of 0.035 kg·𝑚2 is used for 𝐽). This
introduces errors in the Kalman filter estimation, the gain selection of the controller,
and also the feedforward compensation.
The second source of knowledge error is the orbital position of the satellite. An
in-track lag of 1 km is included, which results in the rate commands and feedforward
being slightly delayed. Position errors of several kilometers are common in published
TLEs of small satellites in LEO [62], but can be reduced with GPS.
The final source of knowledge error is the point-ahead angle. Since the orbital
position is not well known, the point-ahead angle cannot be known accurately, so it
is ignored in software. The simulation includes the correct point-ahead angle (see
Figure 1-4 and Equation 1.2) which contributes directly to pointing error.
3.1.6
Pointing & Tracking Results
Simulation results indicate that with the addition of a fast steering mirror, pointing
improves by an order of magnitude. The environmental disturbance torques place
significant strain on the host ADCS, even with estimation and compensation of disturbances.
Disturbance torques are generated from the 6-DOF simulation while executing
ground track maneuvers. Figure 3-8 shows the disturbances for repeated ground
track maneuvers over the course of two orbits. The aerodynamic disturbances are
approximately two orders of magnitude larger than the other environmental disturbances. The next largest disturbance is the Earth’s magnetic field, followed by gravity
gradient and solar radiation pressure.
The pointing performance of the coarse and fine stages is shown in Figure 3-9
and summarized in Table 3.5. With estimation and compensation for environmental
disturbances, the coarse stage can achieve 0.82 mrad RMS, and the fine stage can
achieve 0.06 mrad RMS.
To understand the contribution of various error sources to the coarse tracking
82
Figure 3-8: Environmental disturbance torques for ground tracking maneuvers at 400
km.
performance, error sources in the time-domain simulation were turned on and off. For
a more analytic understanding of contributions to error a frequency domain analysis
can be conducted, but time-domain analysis is sufficient to provide some insight. The
effect of adding error sources is summarized in Table 3.6. The errors are separated into
three major categories: errors in knowledge, errors in sensors, and errors in actuators.
It should be noted that Table 3.6 does not provide the individual contribution
of each source, as they cannot be fully decoupled in a discrete-time simulation. For
example, the effect of gyroscope noise becomes much more pronounced when trying
to execute a slew maneuver and counteract significant disturbances. However, it does
83
Figure 3-9: Coarse and fine stage pointing error with beacon feedback and compensation for environmental disturbances.
Table 3.5: Simulation results of tracking performance of fine and coarse stages.
RMS Error 3𝜎 Error
Coarse stage
Fine stage
0.82 mrad
(0.044∘ )
0.060 mrad
2.32 mrad
(0.13∘ )
0.18 mrad
help highlight major error contributions.
The environmental disturbances and slew maneuver are challenging to the CubeSat ADCS. The discrete control already provides some baseline error because the
satellite bus cannot execute the slew maneuver perfectly. Environmental disturbances
increase the coarse stage RMS error to nearly 0.4 mrad with no knowledge, sensor,
or actuator errors. Imperfect knowledge in inertial properties also adds a nontrivial
amount of error, since imperfect torques are applied. The final significant contribution is the gyroscope noise, which makes estimation of angular rate and execution of
the slew challenging.
For the fine stage, the major contributions to the error are the FSM noise, beacon
84
Actuators
Sensors
Knowledge
Table 3.6: Effect of sources of error (added incrementally) on ground tracking performance.
Baseline simulation
Coarse Stage
Fine Stage
RMSE (mrad) RMSE (mrad)
+ discretization
+ environmental disturbances
+ inertial knowledge error
+ orbital knowledge error
+ point-ahead error
+ sensor feedback delay
+ gyroscope quantization
+ gyroscope noise
+ detector noise
+ reaction wheel quantization
+ reaction wheel noise
+ FSM quantization
+ FSM noise
Overall performance
0.013
0.39
0.51
0.51
0.52
0.52
0.52
0.81
0.82
0.82
0.82
0.82
0.82
0.82
0.00077
0.0028
0.0039
0.0046
0.023
0.024
0.024
0.030
0.044
0.044
0.044
0.044
0.060
0.060
detector noise, and point-ahead error. However, this simulation has ignored pointing
bias due to Tx/Rx misalignment or due to a shift in FSM response characteristics.
Based on the results of FSM testing (see Chapter 4), it is expected that Tx/Rx path
misalignment induced by the FSM will be the dominant factor in pointing error.
To compensate for this effect, calibration algorithms were developed which are the
subject of Section 3.2.
3.2
Post-Acquisition Calibration Simulation
After acquisition, the ability to calibrate the alignment of the downlink beam is necessary to mitigate the effects of Tx/Rx misalignment. The motivation and approach
for this procedure are discussed, followed by the algorithms developed. Models of
atmospheric turbulence, receiver noise, and time-shifting power due to range are presented. Results indicate that calibration to within 0.11 mrad can be achieved in a
85
few minutes at most.
3.2.1
Motivation & Overview
Calibration of the Tx/Rx alignment is necessary because the transmit and receive
paths are decoupled, as described in Section 2.2.3. Currently there is no direct feedback mechanism for the position of the FSM. While precision alignment may be
achieved on the ground, there is the potential for mechanical misalignment postlaunch, thermally-induced misalignment on-orbit, or a change in FSM response characteristics that induces open loop bias. As a result, a procedure needed to be developed to eliminate this bias on-orbit.
The strategy for calibration relies on a low-rate radio frequency (RF) link on the
satellite. The RF link can be utilized to send received power measurements on the
ground back to the satellite. Using this feedback mechanism, the satellite can slowly
adjust its pointing until the ground receives at peak power. This procedure could
utilize the beacon uplink instead of RF to encode this information, but for simplicity
the RF link is used since an analysis of using the beacon as an uplink has not been
conducted.
The laser beam profile is Gaussian, so the calibration simply aims to locate the
Gaussian peak. However, there are several factors that make this calibration procedure difficult. First, the atmospheric channel produces large fades/surges that can
overwhelm differences seen in received power. Second, the range to the satellite
changes over the duration of the pass, and with it the free space loss, so the Gaussian power curve is shifting during the pass. For practical purposes, this means that
prior measurements rapidly become inaccurate. Third, this procedure may be run
during a downlink (e.g. in the event of a slow, thermally-induced bias over the pass).
Therefore the procedure must be conservative in its angular adjustments so as not to
cause loss of signal. Finally, the number of iterations must be minimized given that
there is a large latency associated with this approach. The latency is primarily due
to atmospheric effects that require long averaging times to overcome.
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3.2.2
Description of Algorithms
The calibration procedure is a convex optimization problem where gradient information cannot be evaluated directly and where there is significant measurement noise.
The objective function is this application is the received power measured on the
ground, which we want to maximize. Direct search algorithms are examined for this
application, which have a long history of development and have been categorized into
several main areas [68–70].
The first major category of direct search algorithms are simplex methods. A
simplex is a set of 𝑛 + 1 points in a search space of 𝑛 dimensions. The simplex
should be nondegenerate so that the edges connecting each vertex form a basis of
the space. Then, if any vertex is reflected across the centroid of the other vertices,
a modified simplex results. The general approach is to order vertices based on the
objective function and then apply a reflection to the worst vertex. Nelder and Mead
produced the most widely used version of this method by adding expansion and
contraction features in addition to reflections [71]. This method is still widely used
today, although it has been shown to fail in specific instances on smooth, convex
functions [72].
Simplex methods are not pursued for this calibration. The primary reason for this
is that the simplex method holds on to “old” points for multiple function evaluations.
This is problematic for calibration of NODE because the power curve shifts with
time as the range changes. If the satellite is moving towards the ground station, older
points will tend to be rejected in place of more recent evaluations, and if the satellite
is moving away from the ground station, newer points will appear worse in trying to
maximize power. Another concern of contracting/expanding simplex methods with
noisy measurements is that they can contract below the noise floor. While simplex
methods for noisy function evaluations have been developed [73], these are somewhat
complex and require more knowledge of the noise source and function evaluation than
we have available.
The second category of search algorithms are adaptive search direction methods.
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These approaches try to determine the optical direction for search based on information accumulated from prior function evaluations. This may include modeling of the
function based on evaluations (e.g. quadratic models [68]). However, this approach
is even more problematic for our calibration application. These methods tend to respond very poorly to noisy measurements [73] and the time-shifting power once again
makes older measurements inaccurate in representing the function.
The last category of algorithms are pattern search methods, which were actually
the first methods to appear as direct search algorithms [70]. These methods involve
a series of exploratory moves in a predefined pattern. This pattern is repeated sequentially and the algorithm moves in a direction of improvement at each iteration.
Pattern search methods are well-suited for our problem because they require very
little information about the function and are more robust to noisy measurements and
time-shifting power.
Two methods of pattern search were examined. The first method is a standard
compass search, which simply checks each cardinal direction and moves to the first
point that shows an improved objective function [74]. A threshold term was introduced for robustness to noise [69], such that the algorithm does not select a point
unless the objective function improves beyond the threshold value. While this method
is very robust, it tends to be sluggish and require many function evaluations.
The second method is one that has not been presented in the literature although
it draws on many existing techniques [69]. This algorithm, which is referred to here
as “uncertain search,” continues in one direction as long as it sees improvement over
the threshold. The novel aspect is the concept of “uncertainty”: the algorithm scans
along a line until the change in the objective function does not meet the threshold,
so it cannot be declared better or worse with certainty. In this case, the algorithm
changes direction by some angle 𝜃 and begins again. If the algorithm sees the objective function worsen beyond the threshold, it turns 180∘ . An advantage of this
algorithm is that it always commits to a direction, and therefore only ever compares
two chronological function evaluations. The pseudo-code for uncertain search is shown
as Algorithm 1.
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Algorithm 1 Uncertain search
1: 𝑥𝑐𝑢𝑟 ← 𝑥𝑖𝑛𝑖𝑡
2: 𝐹𝑐𝑢𝑟 ← 𝑓 (𝑥𝑐𝑢𝑟 )
◁ Evaluate objective function 𝑓 (𝑥)
3: 𝜃 ← 0
4: while true do
5:
𝑥𝑠𝑡𝑒𝑝 ← step ∆𝑥 in direction 𝜃 from 𝑥𝑐𝑢𝑟
6:
𝐹𝑠𝑡𝑒𝑝 ← 𝑓 (𝑥𝑠𝑡𝑒𝑝 )
7:
if (𝐹𝑠𝑡𝑒𝑝 − 𝐹𝑐𝑢𝑟 )/𝐹𝑐𝑢𝑟 > 𝛼𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 then
◁ Step is better
8:
do nothing
9:
else if (𝐹𝑠𝑡𝑒𝑝 − 𝐹𝑐𝑢𝑟 )/𝐹𝑐𝑢𝑟 < −𝛼𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 then
◁ Step is worse
10:
𝜃 ← −𝜃
◁ Turn around
11:
else
◁ Step is uncertain
12:
𝜃 ←𝜃+𝛽
◁ Change direction by 𝛽
13:
end if
14:
𝑥𝑐𝑢𝑟 ← 𝑥𝑠𝑡𝑒𝑝
15:
𝐹𝑐𝑢𝑟 ← 𝐹𝑠𝑡𝑒𝑝
16: end while
3.2.3
Noise & Error Models
The two algorithms chosen for testing were implemented in simulation with a timeshifting power curve, atmospheric effects, and receiver noise based on satellite range.
The power and atmospheric models are used to scale the received power and the
receiver noise is added onto the result. These noise sources and simulation conditions
are described.
Time-shifting Power
The time-shifting power curve is caused by the varying range of the satellite. Referring
to the basic link equation (see Equation 1.1), the received power scales with 1/𝑅2 .
The slant range between the ground station and satellite (refer to Figure 3-6) is given
by:
2
2
𝑟𝑠𝑙𝑎𝑛𝑡
= 𝑅𝐸
+ (𝑅𝐸 + ℎ)2 − 2𝑅𝐸 (𝑅𝐸 + ℎ) cos 𝜑
(3.27)
where 𝑅𝐸 is the radius of the Earth, ℎ is the orbital altitude, and 𝜑 is the angle
between the ground station and the satellite from the center of the Earth. The range
changes most rapidly when the ground station is in-plane with the satellite orbit. In
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this case, the rate of change of 𝜑 is known from the period of the orbit (rotation rate
of Earth is ignored), and the receiver power is shown as a function of slant range in
Figure 3-10.
Figure 3-10: Receiver power as a function of slant range, normalized to peak power.
Given that the pass is less than 10 minutes, the received power varies considerably
as the range changes, emphasizing the need for an algorithm that is robust to a shifting
power curve.
Atmospheric Model
The atmosphere is modeled as a log-normal distribution that depends on scintillation
index [75]. The atmospheric loss is described by:
(︀
)︀
𝐿𝑎𝑡𝑚 = 1 − ln 𝒩 𝜇, 𝜎 2
(3.28)
where the parameters 𝜇 and 𝜎 are functions of the scintillation index 𝑖𝑠𝑐 , as follows:
𝜇=−
90
𝑖𝑠𝑐
2
(3.29)
𝜎 2 = 𝑖𝑠𝑐
(3.30)
The value for scintillation index is taken to be 0.08 based on [75] for a 30 cm
ground aperture, which is the planned size of the ground station for NODE. The
probability density function for this lognormal distribution is shown in Figure 3-11.
Figure 3-11: Probability density function of effect of atmospheric scintillation on
downlink power.
The log normal distribution model can be used to generate a timeseries of atmospheric fades sampled at the decorrelation time 𝑡𝑑 of the atmospheric measurements.
The decorrelation time is related to the isoplanatic angle 𝜃0 , which is the angle beyond
which phase is uncorrelated. This typically ranges from 5 to 20 𝜇rad in the visible
and scales by a power of 6/5 with the wavelength [76], giving about 20 to 80 𝜇 rad
in the near-IR.
For statistical purposes, the atmospheric loss can be treated as constant for the
decorrelation time. For our application the decorrelation time is not easily described.
Usually this parameter is a function of effective windspeed, and for stationary ground
telescopes this parameter has been characterized. However, due to the fact that the
satellite is in LEO, the ground station must slew to track it. This increases the
effective windspeed and reduces the decorrelation time.
To mitigate the effects of atmospheric scintillation, power measurements on the
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ground should be averaged over a period of time. This allows comparison between
measurements to perform the calibration procedure. Ideally, we want to average for
as short a time as possible so we would hope that the decorrelation time is short. The
decorrelation time can be estimated based on the isoplanatic angle and the slew rate
of the ground station. At 1550 nm, the maximum isoplanatic angle is approximately
80 𝜇rad and at 1000 km the slew rate is 0.2 ∘ /sec. The decorrelation time is therefore
bounded by approximately 20 ms and a more likely estimate is on the order of ∼5
ms or less based on a few published results from satellites in LEO [34, 77].
Due to the uncertainty in atmospheric decorrelation time, the simulation time is
non-dimensionalized as a function of the decorrelation time. Each timestep is one
interval of the decorrelation time, so the resulting calibration time is a multiple of 𝑡𝑑 .
The averaging period can then be adjusted depending on atmospheric conditions.
The central limit theorem states that as the number of samples of random variable
𝑋 increases the mean will tend towards a Gaussian distribution. For a random variable 𝑋 with mean 𝜇 and variance 𝜎 2 , the variance of the sample mean will approach
𝜎 2 /𝑛, where 𝑛 is the number of samples. This provides some insight into how long to
average received power measurements. To reduce the standard deviation by a factor
of two, we must spend four times as long averaging on the ground. If the power
curve were stationary, we could in theory estimate the mean to any accuracy desired.
However, the power curve is shifting as the satellite range varies, and we must keep
these timescales separate to calibrate properly.
By selecting an averaging time a factor of one hundred over the correlation time,
the standard deviation is less than 3% of the mean power, shown in Figure 3-12. For
a decorrelation time of 5 ms, this results in an averaging time of 0.5 s. The overall
calibration rate is set at 3 s per iteration to accommodate worst-case atmospheric
conditions.
Receiver Noise
The leading term in the receiver error is the APD electronics noise which can be
modeled as a Gaussian distribution. The receiver noise figure is taken from the final
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Figure 3-12: Mitigation of atmospheric scintillation with time-averaged power measurements (𝑡𝑎𝑣𝑔 = 100𝑡𝑑 ).
signal-to-noise ratio (SNR) a detailed link budget analysis [50]. This resulting SNR
value is 15, which provides the variance used in the simulation.
3.2.4
Calibration Results
An example calibration for both algorithms is shown in Figure 3-13. The step size is
non-dimensionalized as a function of the Gaussian beamwidth, which is set to 𝜎/4 in
the simulation.
A Monte Carlo simulation was conducted (N=1000) for various calibration scenarios with different starting locations in the region of convergence. For both calibration
algorithms, a threshold of 5% was used, and it was found that beyond ±2.5-𝜎 of
the Gaussian beamwidth, the algorithm fails to converge. For NODE, the FWHM
beamwidth is 0.12∘ and 1-𝜎 is related to FWHM by:
FWHM
𝜎= √
2 2 ln 2
(3.31)
This results in a region of convergence of ±0.13∘ initial error for NODE. If the
pointing bias is worse than 0.13∘ , the averaging time on the ground will need to
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Figure 3-13: Example of calibration performance for uncertain search and compass
search.
increase to determine the direction of improvement. This may be possible as long as
the time-shifting power curve does not begin to interfere based on the timescale.
The results of the Monte Carlo simulation are shown in Figure 3-14. The number
of iterations was limited to 50, beyond which the calibration procedure is considered
to have failed to converge during the pass (i.e. the algorithm has not converged in
about two minutes).
As shown in Figure 3-14, compass search has a high failure rate of 70%, whereas
uncertain search performs robustly without failure. The cause of the poor performance of compass search is that it does not adapt well to the time-varying power. It
tends to compare measurements that are several iterations old to the most recent measurement, which can result in an inaccurate comparison. Uncertain search only ever
compares two consecutive points, and therefore performs much better under these
conditions. Additionally, uncertain search continues in a direction of improvement
until it is exhausted, whereas compass search has a predetermined evaluation pattern
that results in extra iterations.
With uncertain search, the number of iterations required for calibration was at
most 45, and with an iteration time of at most 3 seconds, the expected calibration time
is up to 135 seconds. The calibration can reduce pointing bias to within 0.11 mrad
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Figure 3-14: Normalized histogram of Monte Carlo (N=1000) calibration results for
compass search and uncertain search.
(or 0.0065∘ ), as compared to the pointing requirement of ±1.05 mrad. If more time
is spent on the calibration procedure, a more precise correction is possible through
longer time-averaging on the ground.
95
96
Chapter 4
Fast Steering Mirror Characterization
& Results
NODE relies on a MEMS fast steering mirror (FSM) for fine steering of the downlink.
To ensure that the selected FSM can meet performance requirements, the response
and repeatability of three devices were tested. After initial benchtop testing, the
devices were tested in a thermal chamber to assess sensitivity to a wide range of
thermal conditions. While one of the FSM devices exhibited some hysteresis and a
temperature dependence was observed in responsivity, overall the devices performed
reliably over the range of temperatures tested. The tip/tilt accuracy of the FSM is
within the desired capability to meet NODE’s ±1.05 mrad (3-𝜎) pointing requirement,
with a worst-case error of 0.38 mrad if no correction is applied.
4.1
Fast-Steering Mirror Testbed
The FSM testbed was developed to precisely measure the tip/tilt of the FSM. This
testbed was used first for testing in a lab environment [78], and then the setup was
transported to a thermal chamber for thermal testing. The physical components and
layout are described, followed by a description of the thermal chamber.
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4.1.1
Components & Layout
The testbed consists of a laser, focusing lens, FSM, focal plane array (FPA), and
supporting electronics. A 650 nm red laser is attached to a collimator that produces
a 1 mm beam. This beam is directed through a converging lens with a focal length
of 100 mm, which then reflects off of the FSM onto the focal plane of the camera. The
FPA measures 1024×1280 pixels with a pixel pitch of 5.2 𝜇m and takes a monochrome
image.
Figure 4-1: Testbed used for FSM characterization.
Based on the location of the spot on the focal plane and the geometry of the setup,
the angle of the FSM can be determined. The geometry is shown in Figure 4-2 and
the angle of the FSM is given by:
𝜃𝐹 𝑆𝑀 =
tan−1 (𝑟𝑐 /𝑑)
2
(4.1)
where 𝑟𝑐 is the distance of the centroid from the center of the FPA and 𝑑 is the
distance between the FSM and FPA. The FSM and focal plane are separated by 65
mm, resulting in a pixel FOV of 80 𝜇rad. The centroid is accurate to a fraction of a
pixel which provides sufficient resolution for measuring FSM angles. The focal plane
array measures 5.32×6 mm, which results in a total FOV of 82×92 mrad (4.7∘ ×5.3∘ ).
98
FSM tip/tilt angles of ±1∘ were tested which result in optical deflections of up to ±2∘ ,
nearly filling the FPA.
Figure 4-2: Geometry of FSM testbed.
The FSM is differentially driven with four high voltage (HV) inputs from an MTI
PicoAmp board. This board accepts commands over an SPI interface, low-pass filters
them to protect the FSM from resonances and then converts them to HV analog
output. A Raspberry Pi is used to interface with the HV driver board and tests are
executed from a Linux terminal.
4.1.2
Thermal Test Environment
NODE will experience temperature shifts on orbit as the host satellite enters and
exits eclipse. The FSM testbed was placed in a thermal chamber to ensure that the
FSM performs reliably over a range of temperatures. The thermal chamber utilized
is produced by Envirotronics and the test space dimensions measure 450 × 580 × 750
mm3 . The chamber utilizes an air-cooled condenser and supports heating and cooling
rates of several degrees per minute. Temperatures over the range of −20∘ C to 60∘ C
were tested. Nitrogen gas can be fed in to purge the chamber, and liquid nitrogen
can also be used to achieve very low temperatures.
For environmental testing, the optical breadboard containing the FSM, camera,
99
focusing lens and fiber launch were placed in the thermal chamber. The laser and
supporting electronics were placed external to the chamber. The thermal chamber
setup is shown in Figure 4-3. To avoid condensation that could damage testbed
hardware, the chamber was purged with nitrogen gas prior to testing.
Figure 4-3: Thermal chamber setup for FSM characterization.
4.2
Description of Tests
The FSM was characterized for response and repeatability at temperatures spanning
−20∘ C to 60∘ C. We identified four possible sources of thermally-induced misalignment:
1. Physical deformation due to temperature shift
2. Zero position shift on enabling high voltage
3. Shift in sensitivity and responsiveness of device
4. Reduction in tip/tilt repeatability
Tests were designed to assess these sources of deformation, which are described below.
100
4.2.1
Comparison to Fixed Mirror
The first test is designed to assess the first source of thermally-induced misalignment,
which is physical deformation of the device. High voltage to the FSM is disabled
for the duration of the test so that the device remains in its resting position. This
position is measured over a range of temperatures to detect any shift that occurs.
Due to the vibration of the thermal chamber and the fact that the camera, lenses,
and fiber launch are included within the thermal chamber rather than external to it,
the setup is not perfectly stationary across the temperature range. To calibrate out
the deformation of the setup and assess the physical deformation of the device itself,
a fixed mirror is used for comparison. The fixed mirror is 3×3 mm2 and is epoxied to
a DIP chip. It can then be interchanged with the FSM mounted in the DIP socket.
The tip/tilt position of the fixed mirror and FSM devices are then compared across
the temperature range to determine if the FSM undergoes any shift.
4.2.2
Response to High Voltage Enable
This test addresses the second source of error noted at the beginning of Section
4.2. When high voltage (HV) is enabled to the FSM, it enters into its nominal zero
tip/tilt position. A large angular shift of about 0.75 mrad occurs between the nominal
position when HV is disabled and enabled. Since the FSM will be powered up on orbit,
it is important that the HV enable shift is highly repeatable. To test repeatability,
the device is toggled between HV enable and disable and the position is measured.
The test cycles through enable/disable ten times each, with ten measurements taken
per iteration.
4.2.3
Voltage Sweeps
Voltage sweeps measure the response of the device over temperature, which addresses
the third potential source of thermally-induced error noted at the beginning of Section
4.2. For each axis, voltage sweeps are conducted between ±110 V, near the maximum
voltage of the device. Each sweep starts at maximum negative voltage, ramps up to
101
max positive voltage, and then returns to max negative. This pattern is repeated five
times for each axis. The sweep is discretized into 100 segments, resulting in step sizes
of 2.2 V. To illustrate the pattern, the commanded voltages are shown for an X axis
sweep in Figure 4-4.
Figure 4-4: Commanded FSM voltages for X axis sweep.
4.2.4
Position Repeatability
This test addresses the fourth source of identified error to ensure the desired repeatability is met across the temperature range. The repeatability test ensures that the
FSM returns to the commanded tip/tilt position with high precision. This test utilizes a 5-sided die pattern, as shown in Figure 4-5. The five positions span the range
of the device. In each iteration, the five positions are visited in a random order to
account for possible hysteresis. This randomized trial is repeated 100 times per test
to produce a spread of points at each location.
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Figure 4-5: Commanded voltages for 5-sided die repeatability pattern.
4.2.5
Thermal Conditions
Two ramp and soak profiles were used for testing the FSMs. The first profile was used
for the response to high voltage enable, voltage sweeps, and position repeatability described in Sections 4.2.2-4.2.4. These tests were aimed at measuring device response,
so temperatures across the full range were revisited to measure any thermal hysteresis. The ramp and soak profile is shown in Figure 4-6 with increments of 20∘ C. Tests
are run during the nine “soak” intervals of the profile, so the measurement sequence
is 20∘ C, 0∘ C, −20∘ C, 0∘ C, 20∘ C, 40∘ C, 60∘ C, 40∘ C, 20∘ C.
As noted in Section 4.2.1, the FSM testbed itself exhibits thermal deformation
during testing, causing the nominal tip/tilt position of the mirror to shift over the
duration of the test. For the tests measuring device response, the bias can be removed
by accounting for the new zero position and measuring the FSM tip/tilt angle relative
to the zero position at a given temperature. However, to understand if the FSM itself
is deforming or whether the cause lies within the testbed, the fixed mirror calibration
procedure described in Section 4.2.1 was developed. A second ramp/soak profile,
shown in Figure 4-7, was utilized for this test with smaller increments of 10∘ C. This
103
allowed more precise temperature control and longer soak periods prior to each test
run. The measurement sequence for this profile is −20∘ C, −10∘ C, 0∘ C, 10∘ C, 20∘ C,
30∘ C, 40∘ C, 50∘ C, 60∘ C.
Figure 4-6: Ramp and soak profile #1 used for testing FSM response.
4.3
Test Results
The three devices tested are identified by the manufacturer labels as S4043, S4044, and
S4045. Devices S4043 and S4044 followed similar trends and both met desired pointing
performance, whereas device S4045 exhibited hysteresis across all temperatures and
was less reliable. All devices exhibited a change in responsivity with temperature, with
colder temperatures increasing the sensitivity of the device and warmer temperatures
decreasing sensitivity. First, the device hysteresis of S4045 is discussed, followed by
a discussion of the four sources of error identified at the beginning of Section 4.2.
104
Figure 4-7: Ramp and soak profile #2 used for testing FSM thermal deformation.
4.3.1
Device Hysteresis
Hysteresis was noted in the manufacturer’s characterization data [78]. It was first
observed in the response of device S4045 in testing at room temperature and persisted
across the temperature range. The voltage sweep test revealed this effect following the
voltage profile of Figure 4-4. The output of the test consists of commanded voltages
paired with camera centroids measured in pixels. The centroid values are scaled by
subtraction of the zero tip/tilt value, and the pixel values are converted to angles
using Equation 4.1. With the input voltage commands and output tip/tilt angles of
the FSM, a 5th order polynomial is fit to the data using the least-squares method.
Examining the polynomial fit error as a function of commanded voltage, shown
in Figure 4-8, reveals the hysteresis in device S4045. For the portion of the inputs
from 20 V to −110 V, the device tends to lag behind the direction in which it is
commanded. This results in the fork seen in the fit error. Devices S4043 and S4044
did not exhibit hysteresis and are shown in Figure 4-9.
The hysteresis in device S4045 is about 50 𝜇rad, which is still small compared to
the pointing requirement of ±1.05 mrad. However, the voltage sweep test allows us
105
to identify hysteresis and select the best devices for flight to minimize pointing error.
Figure 4-8: X-axis response hysteresis in FSM device S4045.
Figure 4-9: No hysteresis in response of FSM devices S4044 and S4043.
4.3.2
Zero Position
The FSM has a resting position when high voltage is disabled, and moves to its
zero tip/tilt position when HV is enabled. Examining the resting position with HV
disabled over temperature allows us to determine if the device is thermally deforming.
106
It is also important to ensure that on HV enable, the FSM moves to a predictable
zero position. For the three devices tested, the zero position on HV enable was very
predictable across temperature. The question of thermal deformation is still being
addressed due to challenges with the test setup, but initial results indicate that any
thermal deformation is within desired performance.
High Voltage Disabled
To measure the thermal deformation of the FSM with HV disabled, its position
shift was calibrated against a fixed mirror as described in Section 4.2.1. Absolute
measurements of tip/tilt were challenging due to the deformation of the testbed,
which induced angular shifts. The camera, fiber launch, optics or mounts may be the
source of the shifts seen, and ongoing work is focused on resolving this issue. However,
the fixed mirror position was used to calibrate the setup for initial measurements.
The shift of the angular position in the focal plane is shown in Figure 4-10, with
a maximum of about 0.25 mrad. These tip/tilt positions are subtracted from the
measurements of the HV-disabled FSM devices to measure thermal deformation.
Figure 4-10: Thermally-induced angular shift of testbed setup with fixed mirror.
107
The angular shifts of the HV disabled devices across the temperature range are
shown in Figure 4-11 relative to the tip/tilt position at 20∘ C. The angular shift of each
device is unique and must be measured individually for flight. Given the magnitude
of the testbed deformation, much of the observed angular shift could be due to the
testbed itself. The shifts observed in Figure 4-11 are bounded within 0.15 mrad,
which can be viewed as the upper bound on thermal deformation in the HV disabled
position. Ongoing modifications to the testbed will enable more precise thermal
characterization, as the setup does not currently measure absolute position.
Figure 4-11: Thermally-induced angular shift of FSM devices calibrated against fixed
mirror.
108
High Voltage Enabled
When HV is enabled on the FSM, it moves to its zero tip/tilt position. This position
must be precisely aligned with the receive path to avoid pointing bias. As a result, it
is very important that the device’s response to enabling high voltage is predictable.
Section 4.2.2 describes the test used to measure the relative shift between the HV
disabled and HV enabled position, which is measured across all temperatures to ensure
it is stable.
The angular shift on HV enable was different for each device, but the shifts for each
device were stable across temperature. These are shown in Figure 4-12. All devices
tend to move in the same direction but with different magnitudes. The position does
not appear to be strongly affected by temperature, and maximum deviation was 25
𝜇rad across all devices, with the best device (S4044) within 15 𝜇rad. For the flight
device, the zero tip/tilt position on HV enable should be well characterized.
4.3.3
Device Sensitivity
The device response was measured by the voltage sweeps described in Section 4.2.3
from −20∘ C to 60∘ C. The data at 20∘ C was fit to a 5th order polynomial using
the least-squares method. To understand the change in device response, the voltage
sweeps at each temperature were compared to the 20∘ C polynomial. The resulting
errors in fit are shown as a function of commanded voltage in Figure 4-13 for device
S4044.
In Figure 4-13, the device sensitivity appears to increase at lower temperatures.
The fit error is positively correlated with the commanded direction. At temperatures
above 20∘ C the device sensitivity is for the most part unchanged. Across the three
devices that were tested the same pattern was noted. The fit error does not exceed
0.1 mrad and is the largest near the edges of the FSM range, whereas we should be
operating near the center of the range.
For on-orbit operations, an FSM HV driver is being designed which will have
a temperature sensor to allow compensation for thermal effects. To mitigate the
109
Figure 4-12: Angular shift of FSM devices on HV enable.
effect of variable device sensitivity, flight control software will include multiple lookup
tables depending on temperature. Additionally, the calibration procedure described
in Section 3.2 is capable of eliminating this thermal bias.
4.3.4
Position Repeatability
FSM tip/tilt repeatability was assessed using the random dice pattern described in
Section 4.2.4. The resulting tip/tilt angles give a statistical measure of the repeatability of the device at its corners. The spread of points from the test of device S4044
is shown in Figure 4-14. The repeatability results are very positive and repeatability
does not appear to be dependent on temperature. Across all temperatures and positions, the 3-𝜎 error is 0.06 mrad, which is well within desired performance. Given
110
Figure 4-13: Error in 5th order polynomial fit to voltage sweep data at 20 ∘ C for
S4044, showing an increase in device sensitivity at low temperature.
the strong repeatability of the devices, the potential for pointing bias due to thermal
effects are of much greater concern than the repeatability.
4.3.5
Summary
The FSM devices performed robustly under temperatures ranging from −20∘ C to
60∘ C, but several areas of concern must be addressed to ensure performance. Four
sources of potential misalignment were highlighted at the beginning of this section,
and are repeated here:
1. Physical deformation due to temperature shift
2. Zero position shift on enabling high voltage
3. Shift in sensitivity and responsiveness of device
111
Figure 4-14: Tip/tilt repeatability of S4044 in random dice pattern.
4. Reduction in tip/tilt repeatability
The first two sources focus on the nominal “zero” position of the device, and the
second two sources focus on device response characteristics.
The HV disabled tip/tilt position of the device is important in characterizing
thermally-induced physical deformation. Thermal deformation was measured with
comparison to a fixed mirror. The testbed exhibited thermal shifts that made measurement of the device challenging, and the testbed is in the process of being modified
to improve measurement fidelity. However, initial measurements with the existing
testbed indicate that FSM thermal deformation is bounded within 0.15 mrad. Much
of this deviation may be due to testbed errors, and further characterization is required.
Upon HV enable the device enters into its zero tip/tilt position. The zero position
was measured across temperature for consistency. The spread of points was repeatable
to within 0.02 mrad and is not a factor of concern in causing pointing bias.
112
The final two tests for sensitivity and repeatability focused on device response. It
was noted that one of the three devices tested exhibited hysteresis in one axis across
all temperatures, with 5th order polynomial fit errors of about 0.05 mrad. This error
is still well within the ±1.05 mrad budget, but it highlighted the need to test each
device for hysteresis to ensure the flight FSM shows good performance. The device
sensitivity was found to be dependent on temperature, with increased sensitivity at
low temperatures. With no additional compensation for temperature, response errors
were bounded by 0.15 mrad at the edges of the device range. Tip/tilt repeatability
across all temperatures and all devices was within 0.06 mrad (3-𝜎) error, and is not
a major source of pointing error.
Table 4.1 summarizes these results. If no effort is made to compensate for temperature effects or pointing bias, worst-case error is estimated to be 0.38 mrad of the
1.05 mrad pointing budget. However, simple software modifications can be utilized to
reduce the thermal sensitivity shift . Since device sensitivity is dependent on temperature, a lookup table can be used to select input voltage based on desired response.
The HV driver being designed for flight will have a temperature sensor to enable
this correction. Additional mitigation of thermal effects will rely on the calibration
procedure to close the pointing loop.
Table 4.1: Summary of FSM thermal testing and sources of pointing error.
Error Source
Worst-case Magnitude (mrad)
Thermally-induced deformation
Zero position repeatability
Thermal sensitivity shift
Tip/tilt command repeatability
<0.15*
0.02
0.15**
0.06
Total error
0.38
*Further characterization required
**With no compensation in software
113
114
Chapter 5
Conclusion
The thesis is summarized, followed by the specific contributions of this work. This
thesis complements additional work on NODE that has focused on the laser transmitter and beacon receiver [50, 54]. A flight demonstration of NODE is planned in
2016, and ongoing and future work for this effort is discussed.
5.1
Thesis Summary
This thesis presents a novel design of a pointing, acquisition, and tracking system for a
nanosatellite laser communications module. This work supports the MIT Nanosatellite Optical Downlink Experiment (NODE), which aims to provide a 10-100 Mbps
downlink within the size, weight, and power constraints of a typical CubeSat.
As the number of nanosatellites on orbit grows, there is an increasing demand for
high bandwidth downlink. NODE is designed to achieve a 10-100 Mbps downlink,
whereas commercial state of the art RF solutions for nanosatellites can only provide
a few Mbps. NODE is compatible with a 3-U CubeSat and fits in a 0.5-U form factor.
The major challenge in achieving lasercom on a nanosatellite is the precision pointing
needed to close the link with the ground station. This is particularly challenging
for nanosatellites given that the state of the art in pointing capability is orders of
magnitude less accurate than typical lasercom beamwidths. We have presented a
novel two-stage control design that overcomes this limitation.
115
Chapter 1 motivates the need for a nanosatellite lasercom module. The growth
of the nanosatellite market and increasing need for high bandwidth downlink is presented. The fundamental differences between radio frequency communications and
laser communications are discussed, including the need for precision pointing of lasercom links. The standard pointing, acquisition, and tracking approach for lasercom
systems is considered, including a detailed look at relevant existing missions. The
state of the art in CubeSat pointing, acquisition, and tracking is documented and
compared to the needs of a lasercom mission. Existing efforts at achieving lasercom
on a CubeSat are discussed and the concept of operations of NODE is presented.
Chapter 2 presents the high level approach for the pointing, acquisition, and
tracking system of NODE. First, some background is provided on the NODE system
to provide an understanding of the derivation of requirements and how they relate to
the PAT design. The key design goals are presented, followed by the development of
the PAT architecture. Major design decisions that are addressed include the singlestage vs. two-stage design, monostatic vs. bistatic design, and hybrid calibration
approach. The PAT requirements are derived and the selection of fine stage hardware
is discussed. NODE employs a two-stage design with a fine pointing requirement of
±1.05 mrad, and a MEMS FSM is selected to provide fine steering.
In Chapter 3, the simulations developed to analyze NODE performance are presented. The first simulation examines the ground tracking performance during downlink. The single-axis simulation models are presented, which include the models of
dynamics, sensors, and actuators. The estimation and control approaches are developed. Results indicate that the fine stage can achieve a pointing accuracy of 0.18
mrad (3-𝜎) which improves the coarse stage pointing by an order of magnitude. This
performance assumes that the Tx/Rx paths are aligned, and to ensure that this is
the case a novel on-orbit calibration approach is developed. The calibration problem
is presented, followed by the algorithms pursued to perform the calibration. A simulation of the calibration procedure is explored, including the models of time-shifting
power, atmospherics, and receiver noise. Results indicate that the calibration procedure can reduce the misalignment to less than 0.11 mrad within a few minutes at
116
most. Combining the results of these two simulations, overall pointing accuracy is
0.3 mrad (3-𝜎) with calibration.
Chapter 4 discusses the characterization of the fast steering mirror. The testbed
developed for measuring FSM response and the thermal chamber used for environmental characterization are presented. The primary sources of FSM error are discussed
and specific tests are designed to assess these error sources. The results of thermal
testing are presented and contributions to FSM error are enumerated. The discovery of device hysteresis and thermal sensitivity is discussed, followed by mitigation
strategies. Overall pointing error is found to be 0.38 mrad in the worst case, within
the pointing budget of ±1.05 mrad.
5.2
Thesis Contributions
Contributions of this thesis include:
∙ Increased understanding of the differences between the pointing, acquisition,
and tracking architecture of lasercom terminals on large spacecraft vs. small
spacecraft
∙ Development and simulation of novel two-stage pointing approach to enable
high bandwidth lasercom
∙ Simulation analysis that examines the ground tracking performance of a CubeSat and contributions to pointing error
∙ Novel on-orbit calibration approach to ensure Tx/Rx alignment that is robust
to time-shifting power and atmospheric effects
∙ Thermal characterization of MEMS fast steering mirror device
5.3
Future Work
Required areas of work for the path to flight:
117
∙ Flight FSMs in an LCC rather than DIP package must be acquired from the
manufacturer and characterized with the testbed setup.
∙ FSM testing was conducted with the manufacturer’s HV driver board, but a
custom version of this board is being developed for flight with more efficient
packaging. This board will also have a temperature sensor so that thermal
effects can be compensated for in software. Once this board is fabricated, commanded angles to FSM angles must be measured using the testbed setup.
∙ Beacon detection software must be further developed to ensure robustness against
fades and false detections (e.g. “hot pixels”). This will include a threshold term
for detection and background subtraction.
∙ Flight FSMs must be thermally characterized and thermal compensation incorporated into control software.
∙ Flight software must be ported and tested on the flight processor.
∙ Flight packaging must be developed to couple the transmit fiber launch to the
FSM, with careful consideration of thermal and mechanical misalignment. This
will consist of an optics board to which the FSM, Tx fiber launch, and beacon
detector are rigidly connected.
∙ An approach for pre-flight check and calibration of Tx/Rx path alignment must
be developed. This will provide final characterization of device alignment in its
flight configuration.
Areas that would benefit from further study:
∙ It would be beneficial to revisit the bistatic configuration. While the challenges
of a monostatic design discussed in Section 2.2.3 still apply, pointing precision
could improve significantly with closed loop feedback. Some possibilities to
achieve this include tightening the pointing requirement on the host satellite,
increasing beacon power from the ground, or selecting a more sensitive beacon
receiver.
118
∙ Development of a full 6 degree of freedom simulation to increase overall fidelity.
This will help characterize the pointing precision expected in the roll/yaw axes
that are not performing the slew maneuver. Additionally, this will provide
more insight into the contribution of reaction wheel noise, which cannot be
fully modeled in a single axis. Overall performance is not expected to change
significantly, but will be relevant in developing host satellite ground tracking
software.
∙ Thermal vacuum testing of the FSM can provide more information on expected
flight performance. The manufacturer has designed a hermetically sealed package, and we can evaluate if hermetic packaging is necessary. Without any damping from the air the FSM may experience additional “ringing” and the effects of
this should be characterized.
∙ The work on NODE has focused on the space terminal, but the development
of the ground station is equally important to providing a low-cost downlink
solution. While the space terminal may be demonstrated with existing ground
stations, the design of a compatible ground station using primarily COTS components should be pursued.
119
120
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