Development of a Pointing, Acquisition, and Tracking System for a Nanosatellite Laser Communications Module

Transcription

1 Development of a Pointing, Acquisition, and Tracking System for a Nanosatellite Laser Communications Module Kathleen Riesing, Kerri Cahoy September 2015 SSL # 19-15

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3 Development of a Pointing, Acquisition, and Tracking System for a Nanosatellite Laser Communications Module Kathleen Riesing, Kerri Cahoy September 2015 SSL # This work is based on the unaltered text of the thesis by Kathleen Riesing submitted to the Department of Aeronautics and Astronautics in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology. 1

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5 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

6 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

7 Acknowledgements This work was performed primarily under contract #NNX14AL61H with NASA as part of the NASA Space Technology Research Fellowship (NSTRF) program.

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9 Contents 1 Introduction Motivation for a Nanosatellite Laser Communications System Laser Communications Background & Challenges Pointing, Acquisition & Tracking Subsystem Overview of Prior Missions Nanosatellite Attitude Determination & Control Background Three-axis-stabilized CubeSat Missions Commercial-Off-The-Shelf Hardware Nanosatellite Laser Communications Key Challenges & Existing Efforts NODE Concept of Operations Thesis Objective & Roadmap Pointing, Acquisition & Tracking Approach NODE System Overview Design Approach & Key Requirements Summary of Key Parameters Pointing, Acquisition, & Tracking Architecture Concept of Operations Single-Stage vs. Two-Stage Design Monostatic vs. Bistatic Design Hybrid Laser & Radio Calibration Method Derivation of Requirements

10 2.3.1 Host Spacecraft Performance Fine Steering Requirements Beacon Detector Requirements On-orbit Calibration Requirements Fine Stage Hardware Layout Beacon Detector Fast Steering Mirror Simulation Analysis & Results Ground Tracking Simulation Motivation & Overview Dynamic Models Sensor Models Actuator Models Control & Estimation Models Pointing & Tracking Results Post-Acquisition Calibration Simulation Motivation & Overview Description of Algorithms Noise & Error Models Calibration Results Fast Steering Mirror Characterization & Results Fast-Steering Mirror Testbed Components & Layout Thermal Test Environment Description of Tests Comparison to Fixed Mirror Response to High Voltage Enable Voltage Sweeps

11 4.2.4 Position Repeatability Thermal Conditions Test Results Device Hysteresis Zero Position Device Sensitivity Position Repeatability Summary Conclusion Thesis Summary Thesis Contributions Future Work

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13 List of Figures 1-1 Nanosatellite market projection [1] Absorption of the electromagnetic spectrum in the Earth s atmosphere [2] Typical lasercom pointing, acquisition, and tracking sequence Point-ahead angle as a function of relative velocity Generic block diagram for PAT subsystem [3] LCT 2nd generation, the backbone of the EDRS [4] Rendering of LLCD inertially stabilized telescope [5] Reaction wheels developed by Sinclair Interplanetary for CanX-2 [6] Rendering of OCSD [7] NODE hybrid RF and optical architecture NODE requirements flowdown Functional block diagram of NODE Histogram of CubeSat orbital altitudes from Concept of operations for pointing, acquisition, and tracking on NODE Pointing loss as a function of pointing error (requirement shown in gray) Block diagram of monostatic and bistatic architectures Angular magnification with beam reduction. Off-axis incoming light (green) as compared to on-axis light (red) for reference Hybrid laser downlink and radio uplink calibration concept NODE hardware layout NODE beacon detector prototype

14 2-11 NODE fine stage MEMS fast-steering mirror RSW satellite reference frame [8] Pitch maneuver for ground tracking Atmospheric density as a function of altitude Block diagram of tracking simulation MiRaTA 3-U CubeSat used for modeling the host spacecraft [9] Geometry of pitch angle and angle of elevation with ground station in orbit plane Bode plot of FSM response data and transfer function model Environmental disturbance torques for ground tracking maneuvers at 400 km Coarse and fine stage pointing error with beacon feedback and compensation for environmental disturbances Receiver power as a function of slant range, normalized to peak power Probability density function of effect of atmospheric scintillation on downlink power Mitigation of atmospheric scintillation with time-averaged power measurements (t avg =100t d ) Example of calibration performance for uncertain search and compass search Normalized histogram of Monte Carlo (N=1000) calibration results for compass search and uncertain search Testbed used for FSM characterization Geometry of FSM testbed Thermal chamber setup for FSM characterization Commanded FSM voltages for X axis sweep Commanded voltages for 5-sided die repeatability pattern Ramp and soak profile #1 used for testing FSM response Ramp and soak profile #2 used for testing FSM thermal deformation

15 4-8 X-axis response hysteresis in FSM device S No hysteresis in response of FSM devices S4044 and S Thermally-induced angular shift of testbed setup with fixed mirror Thermally-induced angular shift of FSM devices calibrated against fixed mirror Angular shift of FSM devices on HV enable Error in 5th order polynomial fit to voltage sweep data at 20 Cfor S4044, showing an increase in device sensitivity at low temperature Tip/tilt repeatability of S4044 in random dice pattern

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17 List of Tables 1.1 Summary of major free-space lasercom missions Key design parameters for LCT and LLCD systems Summary of key three-axis-stabilized nanosatellite missions Control modes for the OCSD mission Summary of key parameters of NODE Comparison of key parameters for OCSD and NODE Host spacecraft performance requirements for compatibility with NODE NODE fine steering requirements NODE beacon detector requirements NODE on-orbit calibration requirements Commercial focal plane array options for beacon detector Commercial fast-steering mirror performance and operational characteristics Simulation parameters for beacon detector Simulation parameters for gyroscope Simulation parameters for reaction wheel Simulation parameters for FSM Simulation results of tracking performance of fine and coarse stages Effect of sources of error (added incrementally) on ground tracking performance Summary of FSM thermal testing and sources of pointing error

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19 Nomenclature ADCS ALEX APD BCT BRITE CanX CMOS COTS DIP DOF EDRS ESA FOV FPA FWHM Gbps Attitude determination and control subsystem Airborne Lasercom Experiment Avalanche photodiode Blue Canyon Technologies Bright Target Explorer Canadian Advanced Nanospace Experiment Complementary metal-oxide-semiconductor Commercial-off-the-shelf Dual in-line package Degree of freedom European Data Relay Satellite System European Space Agency Field of view Focal plane array Full width at half maximum Gigabits per second 17

20 GEO GeoLITE GPS HV IMU IR ISL ISS JAXA JPL LCT LEO LLCD LOS LUCE MAI Mbps MEMS MIT MPE MTI Geosynchronous Earth orbit Geosynchronous Lightweight Technology Experiment Global Positioning System High voltage Inertial measurement unit Infrared Intersatellite link International Space Station Japanese Aerospace Exploration Agency Jet Propulsion Laboratory Laser Communication Terminal Low Earth orbit Lunar Laser Communication Demonstration Line of sight Laser Utilizing Communications Experiment Maryland Aerospace, Inc. Megabits per second Microelectromechanical systems Massachusetts Institute of Technology Maximum permitted exposure Mirrorcle Technologies Inc. 18

21 NASA NODE NRL National Aeronautics and Space Administration Nanosatellite Optical Downlink Experiment Naval Research Laboratory 19

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23 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 cm 3 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 cm 3 21

24 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

25 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/cm 2 )ofthesignalandisdependentonwavelength[19].forlasercom 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

26 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: P Rx / P TxA Tx A Rx 2 R 2 (1.1) where P Rx is received power (W), P Tx is transmitted power (W), A Tx is transmitter area (m 2 ), A Rx is receiver area (m 2 ), 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

27 K a -band. In contrast, lasercom wavelengths are typically between 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 The primary aim of this thesis is developing a lasercom PAT subsystem that addresses this challenge and is compatible with current nanosatellite technology 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

28 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

29 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

30 2V rel c (1.2) where V rel 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

31 Figure 1-5: Generic block diagram for PAT subsystem [3] 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

32 Table 1.1: Summary of major free-space lasercom missions. Year Mission Organization Link Type Data Rate (Gbps) 2001 GeoLITE/ MIT Lincoln GEO-ground/ >1 ALEX Laboratory GEO-air 2001 SILEX ESA LEO-GEO LUCE JAXA LEO-GEO 0.05 LEO-ground 2008 NFIRE/ Tesat Spacecom LEO-LEO 5.65 TerraSAR-X LEO-ground 2013 LLCD MIT Lincoln Moon-ground Laboratory/NASA 2014 OPALS JPL ISS-ground EDRS Tesat Spacecom/ LEO-GEO 1.8 ESA GEO-ground 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

33 Table 1.2: Key design parameters for LCT and LLCD systems. LCT (2nd Gen.) LLCD Link type LEO-GEO-ground Moon-ground Tx wavelength (nm) Data rate (Gbps) Range (km) >45000 > Tx power (W) Aperture (cm) Mass (kg) Power consumption (W) #ofpatstages 4 4 RMS pointing accuracy (µrad) 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

34 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 kg and consuming >100 W of power. A 3-U CubeSat measuring cm 3 weighs no more than 4 kg and typically consumes only 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

35 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 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 SNAP-1 ADCS consisted of a magnetometer, three-axis magnetorquers, and a single momentum wheel. With only amagnetometer,orientationaroundtheb-fieldvectorcannotberesolved,soalarge 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- ) in these axis, resulting in an overall pointing accuracy within about 15 (3- ) [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

36 Table 1.3: Summary of key three-axis-stabilized nanosatellite missions. Year Mission Organization Size Bus Pointing Accuracy 2001 SNAP-1 Surrey Space 6.5 kg * 15 (3- ) Centre 2008 CanX-2 UTIAS-SFL cm 3 2 (1- ) 2010 QbX NRL cm 3 5 (3- ) 2011 PSSCT-2 The Aerospace cm 3 15 (3- ) Corporation 2012 AeroCube-4 The Aerospace cm 3 3 (3- ) Corporation 2013 BRITE UTIAS-SFL cm (1- ) *Dimensions not available. 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- ), allowing control to approximately 2 (1- ). 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 cm 3 nanosatellites dedicated to astronomy. BRITE attitude sensors include sun sensors, a three-axis magnetometer, a three- 34

37 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 (1- )[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- ). 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- )ofpointingaccuracyand 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 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 This constellation conducts Earth imaging, and therefore three-axis stabilization is necessary, but published results do not include information on pointing accuracy [14] 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: magnetome- 35

38 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 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 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 MAI- 400, 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 in cross-boresight axes and in boresight. Given the growing market of COTS hardware, nanosatellite ADCS capabilities should continue to improve in the upcoming years. 36

39 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 In considering alasercomsystemfornanosatellites,constraintsonswapruleoutmanyapproaches used for larger systems. A different design approach is required for implementation of lasercom on a nanosatellite 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 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

40 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

41 Table 1.4: Control modes for the OCSD mission. Control Mode Sensors RMS Pointing Accuracy Sunlit open loop Sun and Earth horizon 0.6 Eclipsed open loop Earth horizon, magnetometers 0.7 and gyros 0.7 Star tracker open loop Magnetometers and star trackers 0.1 Beacon closed loop Uplink receiver 0.2 and magnetometers 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 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 NODE will utilize an uplink beacon to locate and track the ground station. NODE provides a high rate optical downlink of 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

42 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 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

43 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 5summarizesthekeycontributionsofthisthesisanddiscussesthepathforwardto flight. 41

44 42

45 Chapter 2 Pointing, Acquisition & Tracking Approach While existing lasercom systems have weighed between 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 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

46 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 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 ( cm 3 ) 44

47 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 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

48 Figure 2-2: Functional block diagram of NODE 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

49 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 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 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

50 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 (uncoded) apple 1000 km 2.1 mrad (FWHM) Space Segment Parameters Size cm 3 Mass 0.5 kg Power consumption 10 W (max. during Tx) Fine pointing range ± 1.0 Fine pointing accuracy ±1.05 mrad (3- ) Beacon detector type CMOS focal plane array Beacon detector FOV 6.6 Receive aperture 2.54 cm Ground Segment Parameters Beacon wavelength Beacon power Acquisition detector type Comm. receiver type Receive aperture 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 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

51 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 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 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

52 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- ) 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- ), 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

53 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- 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

54 Table 2.2: Comparison of key parameters for OCSD and NODE. OCSD NODE Link range 900 km 1000 km Size cm cm 3 (NODE module) cm 3 (target host satellite) Data rate 5-50 Mbps Mbps Pointing requirement ±0.1 (1- ) ±0.06 (3- ) ±1.7 mrad (1- ) ±1.05 mrad (3- ) FWHM Beamwidth mrad 2.1 mrad Peak power consumption 50 W 10 W Ground station aperture 30 cm 30 cm 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 = 4 A (2.1) where A 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 is: With a small angle approximation, this becomes: A =2 (1 cos ) (2.2) A 2 (2.3) 52

55 This gives directivity as a function of beamwidth : D 4 2 (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 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 feed- 53

56 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. Alinkbudgetwasconductedontheuplinkbeaconanda25mmdiameterontheRx 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: Output Input = D Input D Output (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

57 Figure 2-7: Angular magnification with beam reduction. (green) as compared to on-axis light (red) for reference. Off-axis incoming light 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 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

58 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

59 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 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- ). 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- ). 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 Performance Req. Reason Pre-acq. pointing ±3 (3- ) Beacon must be within camera FOV. (no beacon) 52 mrad (3- ) Post-acq. pointing ±1 (3- ) Must overlap with fine stage range. (beacon feedback) 17 mrad (3- ) Slew rate 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

60 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- ), 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 Performance Req. Reason Range >1 Must overlap with coarse stage postacquisition pointing. Pointing accuracy ±0.06 (3- ) Max. pointing loss of 3 db mrad (3- ) 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

61 Table 2.5: NODE beacon detector requirements. Parameter Performance Req. Reason Field of view >6 Must overlap with coarse stage preacquisition pointing. Centroid accuracy ±0.006 (3- ) 1/10th of fine pointing requirement. 0.1 mrad (3- ) 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 Performance Req. Reason Time to converge 120 s Can occur during LEO pass. Post-calibration bias <0.03 1/2 of fine pointing requirement. 2.4 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

62 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 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

63 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. CMOSIS Fairchild Aptina CMV4000-3E12 CIS1910F MT9P031 Read noise (RMS e ) Dark current (e /pixel/sec) Quantum efficiency Full well capacity (e ) Pixel pitch (µm) Focal length for FOV (mm) 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 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

64 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 Closed loop feedback in which 62

65 Table 2.8: Commercial fast-steering mirror performance and operational characteristics. Thorlabs OIM PI MTI GVS001 OIM101 S L2.2 Type Galvo Voice coil Piezo MEMS Mirror size (mm) 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 (mm 3 ) Driver dimensions (mm 3 ) Peak power (W) <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 Figure 2-11: NODE fine stage MEMS fast-steering mirror. 63

66 64

67 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 ). 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- ) which meets the ±1.05 mrad fine pointing requirement with a large margin. 3.1 Ground Tracking Simulation Asingle-axissimulationisdevelopedtomodelthecoarseandfinestagebeacontracking. NODE is designed to operate within the constraints of a standard CubeSat with 65

68 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 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, ˆR, extends from the center of mass of Earth to the center of mass of the satellite. The cross-track component, Ŵ, is perpendicular to the orbit plane. The along-track component, Ŝ, completesaright-handedset. Ifthesatelliteisinacircularorbit,Ŝ will be aligned with the velocity vector of the satellite. Figure 3-1: RSW satellite reference frame [8]. 66

69 If the RSW set is rotated 180 about the Ŝ axis, a roll-pitch-yaw configuration results. The pitch corresponds with a rotation about the Ŵ axis, which is the axis modeled in this simulation. It is assumed that one of the satellite body axes is aligned with the Ŵ vector, resulting in the pitch maneuver occurring about one body 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

70 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 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 down- 68

71 Figure 3-4: Block diagram of tracking simulation. link. Physical parameters modeling the host CubeSat are generated from MiRaTA specifications 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

72 Figure 3-5: MiRaTA 3-U CubeSat used for modeling the host spacecraft [9]. J! ~ = (3.1)! ~ (J~! ) + ~ where J3 3 is the inertia matrix,! ~ 3 1 is the angular velocity vector, and ~ 3 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: 2 ~x = ~x cmd dist 1 J 1 J (3.2) h it where ~x = is the state composed of angle and angular rate, J is the moment of inertia, cmd is the commanded torque, and dist is the disturbance torque acting on the system. 70

73 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: ~r + µ r3~r =0 (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 " 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,. Using the law of sines, an implicit equation for the angle of elevation can be determined: 71

74 cos (" + ) R E = cos " R E + h (3.4) where R E is the radius of the Earth and h is the altitude of the orbit. The rate of change of 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: " = (R E + h)sin(" + ) R E sin " (R E + h)sin(" + ) (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, is propagated forward and " is calculated using Equation 3.4, followed by " using Equation 3.5. For generating disturbances, angle of elevation can be converted to a pitch angle by once again using the law of sines: =sin 1 RE R E + h cos " (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 kg/m 3 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]: ~ drag = 1 nx 2 C D V 2 ~R cp,i [A i (ˆn i ˆv)ˆv] (3.7) i=1 72

75 where C D is the drag coefficient (2.5 is used), is the atmospheric density, V is the velocity of the spacecraft, R ~ cp,i is the vector from the center of mass to the center of pressure of the i th surface, A i is the surface area of the i th face, ˆn i is the unit normal of the i th surface, and ˆv 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]: ~ mag = ~m B ~ (3.8) where ~m is the residual magnetic dipole in the body frame (0.001 A/m 2 in roll axis is used) and B ~ is the geocentric local magnetic field (T) in the body frame. The local magnetic field is calculated with the IGRF-11 model [59] following the approach outlined in [60] using terms up to 6 th 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]: ~ GG = 3µ ~Rs (J R ~R s 3 s ) (3.9) where µ is the gravitational constant of the earth, ~ R S is the position of the satellite in the body reference frame, and J 3 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

76 ~ SRP = F S c nx A i (ŝ ˆn i ) R ~ cp,i i=1 apple (1 C s )ŝ +2 C s (ŝ ˆn i )+ 1 3 C d ˆn (3.10) where F S is the solar constant taken to be 1367 W/m 2 at 1 AU, c is the speed of light, A i is the area of the i th surface, ŝ is the unit vector from the spacecraft to the sun in the body frame, ˆn i is the i th surface normal in the body frame, ~ Rcp,i is the vector from the spacecraft center of mass to the center of pressure of the i th surface in the body frame, C s is the specular reflection coefficient (0.4 is used), and C d is the diffuse reflection coefficient (0.2 is used) 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 35 mm Centroid noise 0.5 pixel (1- ) Pixel size 2.2 micron Probability of fade 0.05 Centroiding error is modeled as zero-mean Gaussian white noise. Occasional fades 74

77 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. Parameter Value Resolution /s Range ±75 /s Angular random walk 2 / p hr In-run bias stability /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

78 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 kg m 2 Maximum torque N m Maximum speed rpm Quantization 8bit 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: FSM (s) cmd (s) =! 2 n s 2 +2! n s +! 2 n (3.11) where FSM is the FSM response angle, cmd is the commanded FSM angle,! n is the first resonance of the FSM at 1764 Hz, and is the damping ratio fit to The FSM is also quantized into 8-bit commands and noise is added based on results from device testing, described in Section 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- ) Quantization 14 bit 76

79 Figure 3-7: Bode plot of FSM response data and transfer function model 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

80 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: ~x = h d i T (3.12) where is the angle, is the angular rate, and d is the disturbance torque. The continuous process is modeled as: ~x = A~x + B + ~w (3.13) or, ~x = J ~x J w(t) (3.14) where is the commanded torque, J is the moment of inertia, and!(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

81 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: ~x k+1 = A k ~x k + B k k + ~w k (3.15) where ~w k is a white noise sequence with covariance matrix R w. Process observations, consisting of the beacon detector and gyroscope measurements, are modeled as: ~z k = C k ~x k + ~v k (3.16) or, 2 3 ~z k = ~x k + ~v k (3.17) where ~v k is the sensor noise modeled as a white noise sequence with covariance matrix R v. 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: The Kalman gain is calculated as: ˆx k = A k 1ˆx k 1 + B k 1 k 1 (3.18) P k = A k 1 P k 1 A T k 1 + R w (3.19) L k = P k C T k C k P k C T k + R v 1 (3.20) 79

82 The state is then updated by the new measurement: ˆx k =ˆx k + L k ~z k C kˆx k (3.21) And finally the covariance is updated: P k =(I L k C k ) P k (3.22) The covariance is initialized to its steady-state value, which can be determined by solving the discrete algebraic Ricatti equation: P SS = A k h P SS P SS C T k C k P SS C T k + R v 1 Ck P SS i A T k + R w (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: cmd = K p r ˆ + K d (! r ˆ!)+J! r ˆd (3.24) where cmd is the commanded torque, r is the reference angle,! r is the reference angular rate, K p and K d are the proportional and derivative controller gains, and ˆd is the estimated environmental disturbance torque. The first two terms are the 80

83 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: K p = J! n 2 (3.25) K d =2J! n 2 (3.26) The controller gains are defined by the closed loop damping ratio and natural frequency! n. These terms are selected to be 0.7 for for good system response and! n 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

84 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 kg m 2 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 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

85 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 amoreanalyticunderstandingofcontributionstoerrorafrequencydomainanalysis 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

86 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 3 Error Coarse stage 0.82 mrad 2.32 mrad (0.044 ) (0.13 ) Fine stage mrad 0.18 mrad help highlight major error contributions. The environmental disturbances and slew maneuver are challenging to the Cube- Sat 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

87 Table 3.6: Effect of sources of error (added incrementally) on ground tracking performance. Knowledge Sensors Actuators Baseline simulation Coarse Stage Fine Stage RMSE (mrad) RMSE (mrad) +discretization environmentaldisturbances inertial knowledge error orbital knowledge error point-aheaderror sensorfeedbackdelay gyroscopequantization gyroscopenoise detectornoise reaction wheel quantization reaction wheel noise FSMquantization FSMnoise Overall performance 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 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

88 few minutes at most Motivation & Overview Calibration of the Tx/Rx alignment is necessary because the transmit and receive paths are decoupled, as described in Section 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. 86

89 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. 87

90 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 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. 88

91 Algorithm 1 Uncertain search 1: x cur x init 2: F cur f(x cur ). Evaluate objective function f(x) 3: 0 4: while true do 5: x step step x in direction from x cur 6: F step f(x step ) 7: if (F step F cur )/F cur > threshold then. Step is better 8: do nothing 9: else if (F step F cur )/F cur < threshold then. Step is worse 10:. Turn around 11: else. Step is uncertain 12: +. Change direction by 13: end if 14: x cur x step 15: F cur F step 16: end while 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/R 2. The slant range between the ground station and satellite (refer to Figure 3-6) is given by: rslant 2 = RE 2 +(R E + h) 2 2R E (R E + h)cos (3.27) where R E is the radius of the Earth, h is the orbital altitude, and 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 89

92 this case, the rate of change of 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 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: L atm =1 ln N µ, 2 (3.28) where the parameters µ and are functions of the scintillation index i sc, as follows: µ = i sc 2 (3.29) 90

93 2 = i sc (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 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 t d of the atmospheric measurements. The decorrelation time is related to the isoplanatic angle 0, 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 91

94 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 t d. 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 2, the variance of the sample mean will approach 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 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 92

95 Figure 3-12: Mitigation of atmospheric scintillation with time-averaged power measurements (t avg =100t d ). 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 Calibration Results An example calibration for both algorithms is shown in Figure The step size is non-dimensionalized as a function of the Gaussian beamwidth, which is set to /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- of the Gaussian beamwidth, the algorithm fails to converge. For NODE, the FWHM beamwidth is 0.12 and 1- is related to FWHM by: = FWHM 2 p 2ln2 This results in a region of convergence of ±0.13 (3.31) initial error for NODE. If the pointing bias is worse than 0.13, the averaging time on the ground will need to 93

96 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 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 94

97 Figure 3-14: Normalized histogram of Monte Carlo (N=1000) calibration results for compass search and uncertain search. (or ), 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

98 96

99 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- )pointingrequirement, 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. 97

100 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 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: F 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 mm, which results in a total FOV of mrad ( ). 98

101 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 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 mm 3. The chamber utilizes an air-cooled condenser and supports heating and cooling rates of several degrees per minute. Temperatures over the range of 20 Cto60 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

102 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

103 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 mm 2 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 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 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

104 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 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. 102

105 Figure 4-5: Commanded voltages for 5-sided die repeatability pattern 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 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 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

106 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 adiscussionofthefoursourcesoferroridentifiedatthebeginningofsection

107 Figure 4-7: Ramp and soak profile #2 used for testing FSM thermal deformation 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

108 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 S 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