Design and development of a small satellites three axis attitude simulation platform

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POLITECNICO DI MILANO

SCHOOL OF INDUSTRIAL AND INFORMATION ENGINEERING

Master degree in space engineering

Design and development of a small satellites three axis attitude simulation

platform

Supervisor: Prof. Francesco TOPPUTO Co-supervisor: Prof. Mauro MASSARI

Candidate: Luca MARIANI Matr. 875806

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Luca Mariani: Design and development of a small satellites three axis attitude

simulation platform | Master thesis in Space engineering, Politecnico di Milano.

c

Copyright October 2019.

Politecnico di Milano:

www.polimi.it

School of Industrial and Information Engineering:

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Ringraziamenti

Inutile dire che tutto questo lavoro non è solo frutto della mia fatica e del mio sudore. Senza il sostegno e laiuto di tante persone non sarebbe stato così completo e, spero, valido. Pertanto mi sento in dovere di ringraziare pubblicamente varie persone che mi hanno dato il loro aiuto in questi mesi: se nella tesi cè qualcosa di buono lo si deve principalmente a loro. Grazie, quindi, al mio relatore, il professor Topputo, sempre prodigo di consigli e di indicazioni, per l’opportunità di scegliere e sviluppare questo lavoro. E poi, come ringraziare la mia famiglia, primo sostegno per la mia carriera accademica come per la vita; senza di voi tutto questo non sarebbe stato possibile. Grazie anche a tutti gli amici e i colleghi che mi sono stati vicini in questi anni, magari anche solo con una parola gentile. Se riuscirò a laurearmi, sarà in parte anche grazie a loro. Infine, permettetemi di ringraziare anche me stesso, o meglio la mia forza di volontà: ho faticato e sudato sui libri per molto tempo e se sono arrivato fin qui lo devo soprattutto a lei.

Milano, October 2019 L. M.

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a te, ovunque tu sia, e qualunque percorso di vita tu abbia intrapreso.

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viii CONTENTS 5.5 System identification . . . 70 5.6 Results . . . 71 Conclusions 75 5.7 Future works . . . 75 A Technical drawings 77 B Determination algorithm 89 C Codes 93 C.1 Matlab codes . . . 93 C.2 Simulink models . . . 103 Acronyms 113 Bibliography 117 Cited references . . . 117

Manuals and publications . . . 117

Online . . . 120

Additional consulted material . . . 120

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List of Figures

1.1 Air bearings configurations . . . 4

1.2 Spherical air bearings configurations . . . 5

1.3 Load-lift curves . . . 6

1.4 Air bearing geometry . . . 7

1.5 Air bearing range increase . . . 8

1.6 Air bearing center of rotation position . . . 9

1.7 Simulator disturbances due to gravity . . . 10

1.8 SFS simulator . . . 16

2.1 Air bearing historical classification . . . 19

2.2 NASA attitude simulators . . . 19

2.3 MCS/LOS attitude simulator . . . 20

2.4 NPS attitude simulators . . . 22

2.5 DSSACS attitude simulator . . . 22

2.6 UNAM attitude simulator . . . 23

2.7 IACS attitude simulator . . . 23

2.8 AMME attitude simulator . . . 24

2.9 TACT attitude simulator . . . 25

2.10 FACE attitude simulator . . . 25

2.11 JPL spherical tesbed facility . . . 26

2.12 UNAM spherical attitude simulator . . . 27

2.13 JPL spherical tesbed facility . . . 27

2.14 CSEM Reaction Sphere . . . 28

2.15 Robotic arm air bearing facility . . . 28

3.1 SRA250-R30 . . . 31

3.2 ISO air quality standards . . . 32

3.3 Air purification assembly . . . 33

3.4 F18-04-SL00 . . . 34 3.5 M18-04-SL00 . . . 34 3.6 D4 . . . 35 3.7 M18-04-SL00 . . . 35 3.8 Junior King . . . 36 4.1 Plates CAD . . . 40 4.2 Balancing mechanisms . . . 42

4.3 External linear actuator . . . 43

4.4 Linear guide . . . 44

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x LIST OF FIGURES

4.5 Non-captive linear actuator . . . 45

4.6 Rotation-preventing devices . . . 45

4.7 Adafruit R _{DC & Stepper Motor HAT . . . .} ₅₁

4.8 IMU . . . 51

4.9 StromPi 3 power shield . . . 52

4.10 Li-ion battery . . . 53

4.11 RS components R_{power bank . . . .} ₅₄

4.12 Structural skeleton . . . 54

4.13 Motor interface . . . 55

4.14 Balancers interface . . . 55

4.15 Batteries and electronics interface . . . 56

4.16 Fully integrated platform . . . 58

4.17 Upper plate static analysis . . . 59

4.18 Lower plate static analysis . . . 59

5.1 Simulation reference frames . . . 61

5.2 Euler equations Simulink R _{model . . . .} ₆₂

5.3 Kinematics equations Simulink R _{model . . . .} ₆₃

5.4 Gyro Simulink R _{model . . . .} ₆₅

5.5 Gyro DLPF Bode plots . . . 66

5.6 Gyro digital filter model magnitude response . . . 67

5.7 Accelerometer Simulink R _{model . . . .} ₆₈

5.8 Accelerometer digital filter model magnitude response . . . 69

5.9 Gyro measurements . . . 72

5.10 Accelerometer measurements . . . 73

5.11 Euler angles estimation . . . 73

A.1 SRA250-R30 technical drawing . . . 78

A.2 D4 air dryer technical drawing . . . 79

A.3 Upper table technical drawing . . . 80

A.4 Lower table technical drawing . . . 81

A.5 Stepper motor technical drawing . . . 82

A.6 Stepper motor bracket technical drawing . . . 83

A.7 Linear guide assembly technical drawing . . . 84

A.8 Strut technical drawing . . . 85

A.9 Roll-in T-Slot Nut technical drawing . . . 86

A.10 Raspberry Pi battery . . . 87

A.11 Stepper motors battery . . . 88

B.1 Simulation reference frames . . . 90

B.2 Acceleration vector in the IMU frame . . . 91

C.1 Full SIMULINK model . . . 104

C.2 Euler’s equations block . . . 105

C.3 Euler angles kinematics . . . 106

C.4 Gravity torque computation . . . 107

C.5 Three-axis gyro model . . . 108

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LIST OF FIGURES xi

C.7 Three-axis accelerometer model . . . 110

C.8 Single-axis accelerometer model . . . 111

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List of Tables

1.1 Air-bearing based simulator disturbances . . . 11

3.1 SRA250-R30 air bearing performances . . . 32

4.1 Plates design procedure . . . 39

4.2 Linear guides comparison . . . 46

4.3 Balancer selection . . . 47

4.4 CG controllability . . . 48

4.5 Raspberry vs Arduino . . . 50

5.1 DLPFs performances . . . 68

5.2 System identification results . . . 74

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Listings

5.1 Gyro data digital filtering . . . 66

5.2 Gyro data digital filtering . . . 67

5.3 Accelerometer data digital filtering . . . 68

5.4 Accelerometer data digital filtering . . . 69

5.5 Yaw angle manual update . . . 72

C.1 Main code for the platform dynamics simulation . . . 93

C.2 Computation of the gyro estimation . . . 101

C.3 Cost function for the determination algorithm . . . 102

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Sommario

I sistemi di determinazione e controllo d’assetto (ADCS) sono di fondamentale importanza per le operazioni dei satelliti che comportano la determinazione e il controllo dell’orientamento del satellite in orbita. Questo sistema opera in condizioni di attrito ridotto e micro-gravità che rendono la simulazione e i test di veicoli spaziali a terra un compito impegnativo. Tuttavia, la simulazione dell’ADCS è fondamentale per la riduzione dei rischi di missione e per aumentare l’affidabilità del sistema: eseguire simulazioni hardware in the loop (HIL) che coinvolgono l’intero sistema ADCS aiuta gli ingegneri ad avere una migliore comprensione del comportamento del sistema e riduce la probabilità di eventi imprevisti quando i satelliti eseguono le operazioni durante la missione.

Lo scopo di questa tesi è di progettare e sviluppare la parte hardware di un simulatore ADCS in grado di riprodurre condizioni in orbita all’interno del laboratorio DAER del Politecnico di Milano (PoliMi). Il sistema si basa su un cuscinetto d’aria sferico di tipo tableto che impiega un set di 8 motori passo-passo non-captive a scopo di bilanciamento e due unità di misurazione inerziale (IMU) per la determinazione d’assetto e l’identificazione del sistema. Il banco di prova comprende l’elettronica necessaria per gestire tutti i componenti e il sistema di alimentazione, costituito da 5 batterie diverse, per fornire energia a tutti i dispositivi. È stato sviluppato un modello preliminare in Simulink per analizzare le prestazioni del sistema che dovrà essere validato in lavori futuri. L’obiettivo finale di questa tesi è quello di sviluppare la parte hardware del simulatore, fornendo una base per lo sviluppo di un banco di prova di simulazione d’assetto pienamente funzionante.

Parole chiave: Simulatore d’assetto, hardware in the loop

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Abstract

Attitude Determination and Control Systems (ADCS) are of fundamental importance for thesatellotes operations involving determination and control of the satellite attitude. This system operates in reduced friction and micro-gravity conditions that makes the on-groung simulation and testing of spacecraft ADCS a challengimg task. However, ADCS simulation is fundamental for the reduction of mission risks and for the increase of the affidability of the system: performing hardware in the loop (HIL) simulations involving the whole ADCS system helps engineer to have a better insight in the system behavior and lowers the probability of unexpected events when the satellites perform its operations.

The purpose of this thesis is to design and develop the hardware part of an ADCS simulator able to reproduce on-orbit conditions within the Politecnico di Milano (PoliMi) DAER Laboratory. The system is based on a tabletop style spherical air bearing employing a set of 8 non-captive stepper motors for balancing purposes and two inertial measurement units (IMU) for attitude determination and system identification. The testbed includes electronics required to handle all the components and the power system, consisting in 5 different batteries, to give power to all the deviced. A preliminary Simulink model has been developed to analyze the system performances which should be validated in future works. The fi

nal objective of this thesis is to develop the hardware part of the simulator, giving a baseline for the development of a fully capable attitude simulation testbed.

Keywords: ADCS simulator, hardware in the loop

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Introducion

HIL1 simulation of spacecraft systems operations is a challenging task to perform on ground: micro-gravity, reduced friction, radiation are only few of the characteris-tics of the space environment that must be reproduced to obtain meaningful results. However,HILsimulation is of primary importance for successful operations for three reasons:

• to provide realistic responses of the system complete satellite to the applied control

• to increase the experience of engineers in design, development ad testing of ADCS2 system

• to validate the satellite’s mission operations.

ADCS system simulation relies on micro-gravity, friction free environment, but the equipment needed to simulate these of the space environment is not available for purchase. However, withoutHIL testing in a simulated micro-gravity, reduced friction environment,ADCS engineers must rely only on isolated component testing and simulation to validate the operation of the integrated system. In this case, the subsystem will not be fully operational until it is on orbit where design and development errors likely cannot be corrected and can easily cause mission failure.

Motivations

Developing an attitude simulator at PoliMi3 will have major impact in two different frames. Firstly, it will allowHIL simulations for space missions developed within the university. The first spacecraft that will experience the simulator will likely be LUMIO4 spacecraft, and the simulator will enable the experimental verification of it’s innovative camera-based attitude algorithm. Using a bearing able to lift up several tenth of kg of payload, as it will be explained in 4, allows to extend the application of the simulator also to bigger spacecrafts, enlarging it’s field of application. Moreover, the development of an attitude simulator will have also educational advantages: it will provide students the means to testADCS hardware components, software algorithms, and integrated subsystems in a simulated micro-gravity, reduced friction environment. Many students at the undergraduate and

1_{Hardware In The Loop}

2_{Attitude Determination and Control System} 3_{POLItecnico di MIlano}

4_{LUnar Meteroid Impacts Observer}

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2 Introduction

even graduate level have no experience in satellite design, much lessADCSsubsystem design. Therefore, providing these students with a means to validate HIL systems after conceptual designs and simulations have been performed is fundamental to satellite mission assurance. Students and engineers will be able to gain confidence in a givenADCS subsystem once "test as you fly" results are available to verify the system’s simulation results.

Thesis objective

The primary objective of the thesis is the design and development of the hardware for a small satellites three axis attitude simulator satisfy the following requirements: • to provide a platform that allows simulation in a micro-gravity, friction-free

environment

• to provideADCS components testing capability

• to provide a platform for integrated subsystem testing.

Thesis outline

Chapter 1 describes the working principle of a generic air bearing based attitude

simulator, focusing on the integration of different components. The main design issue are outlined and the most common solutions are presented and discussed with a focus on small satellites operations.

Chapter 2 provides an overview of the state of the art of tattitude simulators

with particular attention to the common and different features.

Chapter 3 provides an overview of the components already available in the

labo-ratory, and checks their compatibility with the design.

Chapter 4 outlines the design strategy and the trade-offs faced during the platform

development.

Chapter 5 presents the preliminar numerical model developed for the analysis of

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Chapter 1 Spacecraft simulators technology

1.1 Requirements

Spacecraft attitude simulators must be able to provide reduced friction, micro-gravity environment to test the spacecraftADCS subsystem consistently with the conditions that it will experience during real operations. Boynton, 1996lists some of the methods to simulate weightlessness consditions: neutral buoyancy, magnetic levitation, parabolic flight and drop towers successfully provide nearly gravity-free environment, but spacecraft attitude simulators requires additional features. The simulator should be able to accomplish

• unconstrained rotational motion

• unconstrained translational motion (if orbital motion has to be taken into account)

• long simulation times, consistently with the duration of the tested attitude mode operation

• electronics compatible environment

• wireless communication with the model spacecraft

Each of the methods reported does not satisfies all the requirements. Neutral buoyancy requires the spacecraft to be enclosed in a waterproof envelope, thus jeopardizing the possibility to fire thrusters. Optical communication and instruments does not work and the water viscosity introduce disturbances that would affect the tests. Magnetic levitation has stability issues, requiring at least a spinning satellite and limitating the rotation about other axis to a few degrees. Moreover, the electronics could be affected by the presence of a magnetic field. Parabolic flight simulate weightlessness pretty well but for a very short time, and no guidance test can be performed as the platform and the model spacecraft move independently. Drop tower free falling introduces high aerodynamic disturbances as well as short simulation times. The motion of the model spacecraft should be analyzed through high speed cameras and fragile models can be damaged during the drop. With this in mind, the best way to test spacecraft motion on ground is represented by suspending the model spacecraft on an air bearing, which simulates spacecraft environment pretty well, as outlined in the reminder of this chapter.

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4 Chapter 1. Spacecraft simulators technology

1.2 Air bearings

Air bearings working principle is the same of air-hockey tables: pressurized air flows through holes in the grounded section of the bearing and generates a film that supports the weight on the moving section1_{. They are able to provide}

unconstrained motion, both translational and rotational, exploiting the air film as lubricant to reduce friction between the fixed (stator) and the moving part (rotor). Different configurations, depending on the application, are shown in Figure1.1. Figure1.1ashows a planar bearing, where the payload is able to move with 2DOFs2 in the plane of the supporting table; Figure1.1bdisplays a spherical air bearing, where the payload is free to rotate along 3 DOFs, two of which are constrained by the bearing geometry. Of course combinations of these two configurations can be exploited to build an hybrid simulator with 5 overallDOFs for translation and rotation, as shown in Figure1.1c. The 6th degree of freedom can be obtained by counterbalancing masses.

(a) Planar air bearing (b) Spherical air bearing (c) Hybrid air bearing3

Figure 1.1: Two different types of bearings for translational (planar bearing) and

rota-tional (spherical bearing) motion, and the hybrid version combining them

Attitude simulators employs spherical air bearings as only rotational motion is required: depending on the modes of the mission and their requirements, along with physical constraints in the simulator mounting process, three configurations are available, shown in Figure1.2. Tabletop configuration is the simplest and cheapest: it provide unconstrained rotational motion along the yaw axis and constrained rotational motion along the roll and pitch axes. The range of constrained motion depends on the bearing geometry. If the range of motion around roll and pitch is not sufficient, the umbrella configuration becomes the first choice. Like for the tabletop one, unconstrained motion is available only for the yaw axis, but the range of motion for roll and pitch axes increases. The price to pay is the insertion of the support beam, which increase mass and inertia of the table, as well as plate vibration. Moreover, the center of mass of the system raise in height making the system closer to gravitational instability. Dummbbell configuration combines two

1_{Schwartz, Peck, et al.}_,₂₀₀₃ 2_{Degrees Of Freedom}

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1.2. Air bearings 5

umbrellas to give unconstrained motion along two axes, yaw and roll, but again the price is an increase of mass and inertia. Center of mass issues are not relevant for this configuration, however the range of motion for the pitch axis is reduced with respect to the umbrella configuration.

Spherical air bearing performances can be described in terms of five parameters: • capacity

• range of free motion

• height of the rotor’s center of rotation (CR4) • disturbance torques

• feed line requirements.

(a) Tabletop configuration (b) Umbrella configuration (c) Dumbbell configuration

Figure 1.2: Different configurations of spherical air bearings

1.2.1 Capacity

Capacity refers to the ability of the bearing to sustain a certain load without getting the moving parts in touch. The maximum allowable load affects different parameters: the rotor surface area, the pressure that can be tolerated before instability and the thickness of the air film. Once the maximum allowable load has been determined depending on the maximum payload weigth that must be carried, the bearing selection is performed through the load-lift curves, which relates the lifting force with the air film thickness. An example of these curves is reported in Figure1.3. The curves defines the stiffness of the bearing corresponding to a given air film thickness, that can be computed from the derivative of the load with respect to the thickness. This means that it is possible to derive information about the frequency range of the air film induced vibrations deriving from perturbation in the load that must be carried. By properly selecting the bearing size and operating pressure, once the "mean value" of the load is fixed the bandwidth of the bearing

4_{Center of Rotation}

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Figure 1.3: Load-lift curves for different bearing sizes5

vibration is determined by the load-lift curves knowing the amplitude of the load perturbations. It can be noticed that Figure1.3 does not include mentions for what concerns other bearing parameters such as the air flow rate or the number of channel in which air flows. As reported in Ezenekwe and Lee,1999, it is possible to obtain an analytical approximation for the dynamics of the air film thickness as a function of the inlet pressure, which can be directly related to the load to be lifted from the bearing manual. Assuming linear pressure loss along the channels, and considering that the radius of curvature of the rotor is far larger than the film thickness, it is possible to drive the equation governing the thickness oscillations due to the inlet pressure perturbations around the equilibrium configuration:

mh = A¨˜ eqp˜p (1.1)

where

• m is the rotor mass

• ¨˜h is the oscillation in the film thickness

• ˜pp is the perturbation of the inlet pressure and Aeq can be derived from

Aeq= π " R2_b − 2R 3 b + R3p− 3Rb2Rp 3(Rb− Rp) # . (1.2)

It is worth to notice that the Aeq parameter depends only on the bearing geometry; the parameters in the equation are referred to Figure1.4.

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Figure 1.4: Air bearing geometry6

1.2.2 Range of free motion

As outlined at the beginning of the chapter,at least one between the bearing roll or pitch axes has constrained motion, meaning that it can rotate within a maximum and a minimum tilt angle defined by the bearing geometry. If the rotor exceeds the tilting limits, the air flow exiting towards the environment generates whirls and turbulent motion that create unstable loads on the bearing, thus preventing it to go back within the tilting limits. The choice of the range depends directly on the application considering the desired ADCSmodes to be simulated. A wide range of free motion can be achieved in two ways:

• by increasing the bearing depth - Deep bearing • by increasing the bearing radius - Shallow bearing

Figure1.5shows the two approaches. The selection of one of the two comes from a trade-off that involves bearing stability against side loads and height of the CR. A shallow bearing entails a very high CR location, which is a positive feature as explained in subsection1.2.3, but decreases the ability to counteract side loads that can drive the rotor out of its range limits. An infinite radius bearing (which is a planar bearing) has zero resistance against side loads: if a load acts in an horizontal way it will push the rotor out of its position without the possibility to go back autonomously. Deep bearings have the opposite problem: they have good stability against side loads but the CRheight is reduced.

1.2.3 Height of the rotor’s center of rotation

The height of the CR of an air bearing quantifies its stability with respect to gravity. The rotor acts like a pendulum: its mass can be considered a point mass suspended by a wire with a length equal to the distance between theCR and the

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(a) Depth increase (b) Radius increase

Figure 1.5: Two approaches that can be exploited to increase the spherical air bearing

range of free motion

rotor’s center of gravity (CG7). If the CRis above the CG, the rotor acts like a stable pendulum: any perturbation makes it oscillating around the equilibrium position corresponding to the CRand CGvertically aligned. As long as the CRcomes closer to the CGthe length of the wire decreases and the oscillation frequency rises, until theCRand theCGbecome coincident. In this configuration the rotor is in a neutral stability condition. If theCRgoes below theCGit behaves like a reversed pendulum. The rotor is in an unstable configuration. Adding mass above the rotor decreases the distance between theCRandCG: that’s way is recommended to have a bearing with a good degree of gravitational stability. Shallow bearings in this sense are optimal: however, the contribution to the system inertia added by a shallow bearing rotor is higher since more mass is accumulated far from theCR, which is far of the rotor, as shown in Figure1.6. On the contrary, a deep bearing will have stability problem but the inertia contribution of the rotor to the full system will be less.

1.2.4 Disturbance torques

Allan Smith, 1964 gives a classification and a preliminary estimation of the

disturbance torques that can affect an air bearing based attitude simulator. Four main sources are identified:

• the bearing itself

• the equipment mounted on the rotor • the environment

• the test system

Bearing disturbances The bearing is a source of aerodynamic disturbances. The main cause is the manifacturing of the air flow channels. If they are not exactly symmetrical or not exactly contoured an aerodynamic torque arises and the rotor,

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(a) Deep bearingCRlocation (b) Shallow bearingCRlocation

Figure 1.6: Location of theCR of a deep and a shallow bearing

due to the negligible friction of the air film, starts to rotate: equilibrium is reached when the aerodynamic force is counteracted by the payload aerodynamic drag. Another source of disturbance is the imperfect scavenging of the bearing that causes exhaust air impinging on the simulator. Both effects can be minimized by a precise bearing manufacturing and maintenance.

Simulator disturbances The equipment mounted on the bearing, together with the rotor, constitutes the attitude simulator, and characterize its distribution of mass. As outlined in subsection1.2.3, the relative position of the system CRand CGdetermines the stability of the simulator, thus defining the torques that may arise during rotational motion.

Static disturbances arise when the CG and the CR are not vertically aligned: referring to Figure1.7a, the simulator feels a torque of magnitude

T = −mgXcos(ϑ) − mgY sin(ϑ) ∝ ϑ (1.3)

where the direct proportionality comes from the assumption of small X, Y , and ϑ. Gravity gradients (GG8) disturbances are due to the variation of the gravity acceleration with respect to the distance from the Earth center. For big simulators it can become a disturbance to be aware of: the torque arising can be estimated, referring to Figure1.7b, as

T = M g0L

2_{∗ sin2ϑ}

R ∝ 2ϑ (1.4)

where R is the distance between the Earth center and the simulator. Direct proportionality comes from the assumption of small ϑ.

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Ansioelastic disturbances are linked to the flexibility of the table material: deformations can change the mass distribution and the relative position of the CR and CG, inducing a torque that can be estimated, referring to Figure1.7c, as

T = M gd0(sinϑ −

1

2sin2ϑ) (1.5)

where d0 is the platform maximum deflection, corresponding to ϑ = 0, and the

actual deflection is

d = d0cosϑ (1.6)

It can be noticed that the ansioelastic disturbances has components proportional to ϑ and 2ϑ if ϑ becomes sufficiently small.

(a) Static simulator disturbance (b)GGsimulator disturbance

(c) Ansioelastic simulator disturbance

Figure 1.7: Disturbances arising on the simulator due to the relative position ofCRand

CG9

Environment disturbances The environmental torques are particularly trou-blesome. An aerodynamic damping torque aries as the simulator rotates through the air. One of the most serious torques is due to the effect of stray air currents acting on the platform. It may not be convenient to place it in a vacuum chamber,

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but work to any reasonable degree of precision requires the simulator to be located within some sort of shielding enclosure. An effort should be made to construct the table from nonmagnetic materials. Some current research platforms are placed between three pairs of large Helmholtz coils which can neutralize the Earth’s field. Vibration effects are minimized by mounting the air bearing support pedestal on an isolated seismic block.

Test system disturbances These disturbances depend upon the scheme used to execute the control system being tested. Unsymmetrical depletion of tanks as compressed gas is used for reaction thrust can be appreciable. Mass unbalance torques within batteries as they discharge are difficult to compensate as well as modification in mass distribution due to different equipment positioning. Table1.1

summarizes the disturbances acting on an air-bearing based attitude simulator.

EFFECT MITIGATION

Turbine effect Bearing manufacturing Exhaust air impingement Bearing maintenance Static unbalance Simulator balancing

GG Equipment positioning

Ansioelasticity Plate material and equipment positioning Drag torque Simulator geometry and enclosure Magnetization Simulator materials

Vibrations Support structure

Table 1.1: Air-bearing based simulator disturbances

1.2.5 Feed line requirements

Air bearings, as the name suggest, are fed by compressed air to generate the film on which the rotor is sustained. The precision required for attitude simulators reflects also on the quality of the air that is sent to the bearing. Atmospheric or ordinary shop air cannot be used directly to feed the bearing because they contains:

• moisture

• oil and water vapour • solid particles

Contaminated air exiting from the compressor must be specifically treated before entering the bearing to avoid bad functioning or rotor damage. A combination of filters and air dryers should be employed to guarantee the desired level of air quality indicated on the bearing manual for its correct operations.

Another key aspect is the pressure of the air at the inlet of the bearing. Pressure losses from the supply must be considered as components like filters and dryers are employed. A correct value of the inlet pressure makes the bearing able to lift the load without becoming unstable, and this value must be compliant feed line losses from the compressor to the bearing. The pressure at the exit compresssor should be adjusted accordingly, either manually or automatically.

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1.3 Balancing system

Spherical air bearings satisfy all the main requirements of an attitude simulator except one. Despite being able of providing friction-free rotational motion and electronics compatible environment, they are not able to provide micro gravity conditions alone. As outlined in subsection1.2 and in subsection1.2.4, gravitational effects are present when the mass distribution of the simulator gives aCGthat does not coincide with the CR of the system. During the simulation the system feels additional torques with respect to the desired ones that can be order of magnitudes higher depending on theCG-CRoffset. The attitude simulator dynamics is governed by the Euler equations for rotating, rigid bodies: considering a coordinate system that is attached to the rotor, the dynamics can be described as

I ˙ω = Iω × ω + mrB× gB+ TACT (1.7) where

• I is the simulator inertia matrix

• ω is the simulator spin rate in the rotor frame • m is the simulator mass

• rB is theCG-CRoffset in the rotor frame

• gB is the gravity acceleration in the rotor frame

• TACT is the torque produced by the on-board actuators.

In order to reproduce micro gravity conditions the gravity torque mrB× gB must be cancelled out by additional hardware that should be compliant with the requirements outlined at the beginning of the chapter. There are two ways to counteract gravity-induced torques:

• command TACT = −mrB× gB • let rB → 0

In the first method, the actuators should continuously output an assigned torque, equal and opposed to the gravitational one. The actuators should be sized on the maximum predictable CG-CR offset, which correspond to the highest torque to be applied. Moreover, accurate knowledge of the offset time function is required to generate the control law to feed them. A manual balancing phase can be performed before the tests, adjusting the position of the equipment to reduce the offset and the required output torque accordingly. Moreover, the actuators momentum storage should be designed to avoid saturation to happen during the scheduled tests.

In the second method, the mass distribution of the simulator is changed, manually or automatically, to align the CGwith the bearing CR. Adjusting the position of the equipment on the simulator is not sufficient to have a precise control on the CG position, therefore moving masses and counterbalances are added to the system: once the equipment has been positioned, by varying the position of the added masses

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1.3. Balancing system 13

the CG can be driven to the CR. Moving masses control can be performed both manually (open loop balancing) or automatically (closed loop balancing) but the preferred method is a hybrid one: in the manual phase the equipment is positioned to bring the CG into the controllable area using the moving masses. Then the system is balanced automatically. In this way, it is possible to have a sufficient control authority that is also precise even with small hardware for the moving masses: the position of the CG, assuming that no flexibility is present and that the mass distribution is discrete, can be computed as

rB= r0+

mSMrSM

m (1.8)

where the last term is the shift that can be imposed on a simulator of mass m with a moving mass of mass mSM that can travel a distance rSM. Assuming that the reference system is centered in the CR makes r to be the actual offset and r0 to

be the one before the balancing procedure. As it can be noticed, a single mass able to move in three directions or a set of three masses that move along three mutually orthogonal directions is enough to control the 3D space position of theCG. The resolution of the position control is determine by the smallest achievable rSM. Manual methods are good to reduce the initial offset by equipment positioning, but lacks in precision because of the manual positioning of the moving masses. Automatic methods, on the contrary, provide very high positioning precision but do not act on the initial offset, thus requiring higher control authority that means heavier sliding masses or longer travels. Hybrid methods combine the benefits of the former two, reducing the initial offset in the manual phase and applying precise control in the automatic phase, where the required control authority is lower . Knowledge of the offset is required in order to determine the target position of the sliding masses.

1.3.1 System identification

Both the balancing methods proposed in section1.3 require the CG-CR offset and the mass properties of the system to be known. While an estimation of that properties can be derived from accurate CAD10 models, precise balancing requires levels of accuracy thatCADmodels can’t reach. System identification is the solution to the problem.

System identification is a methodology for building mathematical models of dynamic systems using measurements of the systems input and output signals11.

The application of system identification to attitude simulators consists in: • excite the system

• collect measurements from the sensors • estimate the required parameters

10_{Computer-Aided Design} 11_Mathworks_,₂₀₁₉

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As outlined inSchwartz and Hall,2004, there are essentially two ways of application of system identification to attitude simulators, depending on the balancing procedure that one may select.

The first method is suitable for off-line balancing procedure only: the system is excited and a particular set of performance parameters P is measured. The properties to be estimated are extracted directly from P. Let’s consider a dynamical system described by its state x and external inputs g and τ :

˙x = f (x, Π, t) + g + τ (1.9) where Π is the set of parameter to be estimated. The performance parameters can be computed as

P = h(Π) (1.10)

and inverting the relation one can obtain the estimated parameter vector. This method can be performed only if the number of estimated parameters equals the number of performance ones, and cannot be used for on-line balancing procedures. An example of the method is the measure of the period oscillation as a performance parameter to estimate the vertical offset betweenCGandCR, providing that due to bearing symmetry the horizontal offset is null12_{. It is possible to reach precision}

of about 5% of the real value of the parameter to be estimated13_.

The second method is suitable for both off-line and on-line balancing procedure: the system is excited, then data are collected and at the end of data sampling an estimator is used to elaborate the collected data and generate an estimation of the desired parameters. Referring to Equation1.9 as the system dynamics, it is possible to rewrite it as a parameter equation, where a known term is expressed linearly in terms of the parameters: assuming as the known term the control input τ the parameter equation becomes

τ = Ω(x, ˙x)Π (1.11)

which is a set of linear equations in the unknown parameters provided that mea-surements of the state and its derivatives are available. There are many methods to obtain the transition matrix Ω(x, ˙x): one can simply derive it directly from measurements or it is possible to process data to smooth them and remove noise components that can degrade the estimation quality. Equation1.11can be solved a posteriori through LSE14 techniques after the collection of a sufficient amount of measurements, or it can be directly included in the filters as an output equation, to automatically derive the needed estimation. Many estimation algorithms have been successfully tested on existing simulators15,16,17.

In both methods system excitation is fundamental. All the parameter to be estimated must be sufficiently excited to obtain meaningful results. Excitation can be performed by control profiles executed by the actuators or by imposing non-null initial conditions and let the system evolve in its dynamics. It must be noted that

12_Fullmer_,₁₉₉₆

13_{Prado, Bisiacchi, et al.}_,₂₀₀₅ 14_{Least Squares Estimation} 15_{Schwartz and Hall}_,₂₀₀₄ 16_{Chiesi et al.}_,₂₀₁₄ 17_{Kim and Agrawal}_, ₂₀₀₆

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1.4. Environment simulators 15

if the satellite is left free to rotate, the estimation of the vertical offset becomes troublesome since the gravitational torque is confined in the horizontal plane.

1.4 Environment simulators

In order to succesfully reproduce the space environment to test the whole ADCS system, reduced friction and microgravity conditions are not always enough. Con-cerning control algorithms validation and complex physical phenomena modelling, it is not important how the simulator gets attitude data, and therefore IMU18 and inertial guidance are employed to avoid introducing additional hardware for different sources simulation. However, environmental references for attitude sensors should be included when a completeADCS test is required. Most of the operating spacecraft determine their attitude by referencing to the Sun position or to the fixed star position, employing sun sensors and star trackers. Another source of attitude information is the Eart magnetic field. These sources must be reproduced to generate a complete orbital environment.

Sun simulators are easy to implement, as a lamp or a monitor is used to reproduce the Sun: by calibrating the brightness one can obtain a very precise Sun simulator to feed the spacecraft Sun sensor. The distance of the monitor from the simulator, as well as the monitor surface must be carefully determined to set the correct field of view of the Sun with respect to the spacecraft.

Stellar field simulators are more troublesome, as they must reproduce a source that changes in term of spacecraft attitude. It is impractical to surround the simulator with a monitor displaying all the star field that the spacecraft could see in orbit; however, a reduced-size monitor able to update itself depending on the spacecraft attitude requires a huge computational capacity, considering that the update should be performed in real time. That is why stellar field simulators are relatively new technologies, that started developing when the on board computational capacity has become compatible with the simulator requirements.

Filipe et al.,2017 developed a stellar field simulator at JPL, shown in Figure1.8,

which is composed by a 5" monitor rigidly attached to the model spacecraft in such a way that the the monitor is always in the star tracker field of view. The processing unit contains a star catalogue and taking as input the attitude determined by the sensors displays on the monitor the part of the star field that would be in the star tracker field of view if the spacecraft is in orbit, allowing correct attitude determination. A collimating lens is applied between the monitor and the sensor to make the light rays from the monitor to be parallel, as they come from an infinite distance source. Both the spatial and time resolution of the simulator are key design parameter, as the stellar field simulator could be considered a time and space discretized version of the real star fields. The space resolution depends directly on the monitor number of pixels and determines the accuracy attainable by the star tracker with respect to itself operating within the spatial-continue sky. The time resolution is linked with the update time of the monitor an determines the smallest possible rotation angle that can be detected by the star tracker with the stellar field simulator.

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(a) The stellar field simulator during a test (b) The assembled stellar field simulator

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Chapter 2 State of the art

Air bearing based attitude simulators have been playing a critical role in ADCS hardware and software verification from 1960. The facilities that have been developed through the years can be divided into three categories, called generations. It should be noted that this subdivision does not involve any time scale, as well as simulators of all the generations are continuously developed in depending on the scope of the tests to be performed. In this chapter only rotational testbed are considered, while planar and hybrid simulators are beyond the scope of the thesis.

The first generation of spacecraft simulators involves industrial applications: big platforms to support heavy payloads in the order of thousands of kg were the first simulators to be developed, in perfect agreement with the size of the spacecraft operating during these years. The first survey of existing air bearing technology

isAllan Smith, 1964, where several industrial systems are analyzed. Universities

did not play an important role for this category because they were not ready for the low cost development of such facilities. The primary objective of this class of simulator is to achieve the maximum possible load capacity and angular range trying to avoid structural vibrations that could have an impact on attitude results, and this explains the rigidity of such platforms. Metals are used for the building of the sustain structure, increasing the weight of the overall system. In this framework, balancing procedures require big moving masses and long strokes, so that manual balancing procedures are employed for the majority of the facilities, starting from equipment distribution on the platform to correct positioning of counterweights.

The second generation is the one in which universities started to play a leading role concerning the development of smaller, cheaper attitude testbeds intended for the simulation of internal project, accordingly to the rise of CubeSats and small satellites. Academic projects starded to give an educational baseline for ADCS validation intended for students, in order to start getting in contact with real life spacecraft design and validation. Smaller sizes, cheaper hardware and reduced capacity bearings and platforms started to appear in universities in the first years of 2000s, and now several system can be counted, each one with its proper features. New materials started to be used such as low mass composite or glass fibers for the support platform, intended to carry a lower mass payload. Balancing procedures becomes automatic: smaller linear actuators are fed by estimation of the CGoffset to compensate it through automatic mass movement. Accordingly, new estimation algorithms started to be tested. System identification procedures

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18 Chapter 2. State of the art

coupled well with the increased use of reaction wheels as attitude actuators, as well as CMG1: performances of these actuators, such as friction, vibrations and accuracy are extensively tested and validated on second generation simulators. The trend in increase the range of motion of the bearing leave space for more compact system, where vibrations and other disturbances do not interfere with attitude data, thus avoiding the need of expansive vibration insulators. Particular attention is dedicated to these systems as the simulator developed in this thesis will likely belong to this generation.

The third generation of attitude testbeds tries to conjugate the benefits of smaller platforms with an augmented range of free motion, with the goal of unconstrained motion about three axis. Moreover, more elastic simulators are under development, able to adapt themselves depending on the mission requirements. While previous generation simulators require specific equipment and settings depending on the tested system, this new generation testbeds are able to accomplish the requirements of a range of different payloads, adjusting their mass properties and performances accordingly.

The subdivision of attitude platforms is justified if one considers the perfor-mances of the existing testbed through the years in parallel with the development of spacecraft and satellites. Figure2.1 shows a survey of the existing simulators up to the firs years of 2000s, and the tendency is evident. First generation simulators dominates the early years up to 1980, where a sudden stop in simulators production has been experienced mainly due to saturation of the market. As expected, the largest values of capacity ad range of free motion belongs to this first generation, where heavy payload were flown with large angular range. Universities do not appear in this years mainly due to the incompatibility with the dimensions and performances required by the payload. The development of new facilities started again after 1990, when small satellites emerge. In this framework, low cost and low size university facilities began to grow in number and also industrial applications reappear. It is interesting to see how the angular range of new academic platforms is bigger than the new industrial facilities: the main cause is the interest of university researchers in testing new control schemes while industrial programs focus more on technological demonstration. Early development of third generation simulators can be seen in the top-right region of Figure2.1b, where a few unconstrained angular motion facilities can be identified.

2.1

1

st

generation

The first simulator on which complete informations are available is the NASA Marshall Space Flight Center’s air bearing platform, shown in Figure2.2a. The tabletop bearing can lift up to 400 kg payload with an impressive range in roll and pitch of ±120◦3, currently unmatched by other tabletop simulators. The platform, which was provided with mass balancers and counterweights, has been extensively used for characterization of the bearing imperfection and disturbing torques on

1_{Control Moment Gyro} 2_{Schwartz, Peck, et al.}_,₂₀₀₃

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2.1. 1st _generation ₁₉

(a) Attitude simulators capacity (b) Attitude simulators range of free motion

Figure 2.1: Performance of existing air bearings facilities2

the simulation. It has also been part of the NIMBUS second generation satellite testing program.

The first trace of an umbrella bearing dates back to 1976 with the simulator built at NASA Goddard Space Flight center. The simulator was provided with a spherical bearing to allow ±12◦ rotational freedom in the constrained axis. The objective of the simulator was to derive and validate models for energy dissipation during operations4_{: several tests has been performed concerning fluid sloshing and}

mechanical damping. The facility is shown in Figure2.2b

(a) NASA Marshall Space Flight center

facility

(b) NASA Goddard Space center

facil-ity

Figure 2.2: The Marshall Space Flight center and Goddard Space center facility

The latest first generation simulators were intended also for the validation of phenomena of wich analytical models are not readily available, or are too complex

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for the derivation of good analytical results without heavy approximation. Several industrial testbed have been developed following this consideration: the level of understanding of phenomena like structural vibrations and jitter, as well as sloshing and dissipative dynamics has been increased since dedicated platforms have been developed for this objective. The MCS/LOS testbed at Honeywell, showed in Figure2.3 has been developed for precise data about structural and rotational couplings in spacecraft dynamics, in order to integrate the analytical models and to validate them. The platform leans on an umbrella-style air bearing with a capacity of 1360 kg and a ±45◦ of motion. The testbed structure is built of modular truss elements, any of which can be replaced with structural dampers. The structure can be reconfigured to represent a number of spacecraft architectures. TheCMG array is mounted on a hybrid active/passive Vibration Isolation and Steering System (VISS) that reduces induced disturbances and can be used to augment the attitude control by steering the entire CMG array and introducing passive damping in the structure. Mirrors mounted on the testbed are used to redirect laser light from a pneumatically isolated table onto three charge-coupleddevice cameras mounted on the same table. The resulting focal-plane data are resolved into jitter measurements and, optionally, can be blended and used for attitude feedback as a virtual star tracker. The platform incorporates adaptive, closed-loop mass-balance system: three prismatic actuators with 5 - 22 kg weights used to eliminate mass-center offset from the air-bearing rotational center. The facility offers not only MCS and LOS research capabilities but also a testbed for inter-satellite communication and relative-attitude steering for formation flying.

Figure 2.3: The MCS/LOS air bearing facility at Honeywell

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2.2. 2nd _generation ₂₁

2.2

2

nd

generation

Second generation simulators are common in many universities around the world. The mother of university tesbeds has been developed at Stanford, with the objective to characterize mass properties of physical systems5_{. Online and offline algorithm}

for CG offset identification have been tested and compared, and balancing was achieved through manual trimming of sliding masses. Starting from there, today a large number of facilities has been developed, each one with its own features.

One of the first second-generation attitude simulators was built by students of the Utah State University: the Small Satellite Attitude Control Simulator (SSACS) is composed by a tabletop bearing able to provide ±45◦ and it has been designed properly for the testing of the Skipper spacecraft, from Space Dynamics Laboratory. The simulator is provided with N2 gas thrusters and a theatrical light

to simulate the Sun, Balancing is performed manually through lead screws after an identification procedure that involvesLSE estimation of filtered data to avoid noise and computational errors in the derivative of the spin rate, while the vertical offset was estimated by inspection of the period of oscillation of the satellite after planar balancing was performed.

The Naval Postgraduate School has two different simulation platforms that have been used and are currently employed in ADCSalgorithm and hardware validation. The TAS2 is a tabletop air bearing platform with a capacity of 800 kg and ±20◦ range of free motion for roll and pitch axis, used mainly for optical demonstration and verification for the Bifocal Relay Mirror spacecraft. The platform, shown in Figure2.4a, employs CMG in a pyramidal configuration to control the simulator and perform on-line balancing by controlling the position of 10 kg balancers with a resolution of 18 µm and a maximum offset of ±7.5 cm. The simulator is provided also with flexibility simulators to test the effects of jitter on the behavior of optical devices. System identification has been tested employing batch estimators and a reference sinusoidal trajectory imposed to the platform and adaptively by tracking a specified trajectory of the angular momentum vector. A trade-off has been performed between the speed of convergence of the algorithm, guaranteed by high control gains, and noise level6_{. The second attitude platform at NPS is the CubeTas,}

which has been developed primary for educational purposes. It is intended for small satellites only, and it has been used also for validation of automatic balancing algorithms that employ only linear actuators for the relocation of the CG. The tabletop bearing has a capacity of 40 kg with ±50◦ range of free motion for roll and pitch axis. The rotor is hollow, providing space for the accommodation of the hardware inside it, minimizing theCGexcursion due to equipment mounting. Baancing is achieved automatically through three perpendicular linear actuators and a two step algorithm involving an adaptive controller for horizontal offset and aUKF7 for the estimation and compensation of the vertical offset8_.

Virgina Tech hosts another couple of attitude simulators: Whor1 and Whor2 platforms are used alone for attitude validation and togheter for formation flying

5_{de Cordova and DeBra}_, ₁₉₇₅ 6_{Kim and Agrawal}_,₂₀₀₆ 7_{Unscented Kalman Filter} 8_{Chiesi et al.}_,₂₀₁₄

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(a) TAS2 (b) CubeTas

Figure 2.4: The TAS2 and CubeTas simulators at the Naval Postgraduate school

and relative dynamics tests9_{. Whor1 employs a tabletop bearing, with a capacity}

of 136 kg and a range of free motion of ±5◦. Whor2 platform leans on a dumbbell air bearing with a capacity of 170 kg and a range of free motion of ±30◦. Both platforms are compatible with every type of attitude actuators, and are balanced through linear actuators. Several identification procedures have been tested and validated, going from simple batch estimators to dynamic filters and adaptive algorithms. Figure2.5 shows the simulators.

(a) Whor1 (b) Whor2

Figure 2.5: Whor1 and Whor2 simulators at the Virginia Tech

Students at the Universidad Nacional Autónoma de México (UNAM) can gain experience aboutADCS hardware and software implementation at its specifically developed attitude simulator. The platform is carried by a tabletop bearing, shown in Figure2.6, with 80 kg capacity and ±50◦ range of free motion. The simulator is provided with a set of three reaction wheels and a magnetic coils, as well as sliding masses and counterbalances forCG positioning. Several balancing procedures have

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2.2. 2nd _generation ₂₃

been tested, resulting in an hybrid approach where, after a manual phase concerning equipment positioning, the automatic balancing was fed by an LSE estimator or by the signals coming from inclinometers. In this last case, the vertical offset is compensated manually.

Figure 2.6: The UNAM air bearing facility10

The Georgia Institute of Technology has developed an Integrated Attitude Control System (IACS) intended for ADCS testing and validation and for the characterization of the performances of the actuators carried on the platform. The air bearing is a tabletop one with a capacity of 130 kg and a range of free motion of ±30◦. Several actuators are mounted on the simulator, comprising an innovative variable speed CMG system, shown in Figure2.7, that can run both in reaction wheels or CMG mode, being able to change the wheel orientation and also their speed, allowing to save mass and space on the simulator11. System identification involves recursive algorithms for the computation of the inertia matrix and the CG offset.

Figure 2.7: The IACS air bearing facility at Georgia Institute of Technology

A small satellite attitde simulation platform has been developed also at the

10_{Prado, Bisiacchi, et al.}_,₂₀₀₅ 11_{Jung and Tsiotras}_, ₂₀₀₃

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University of Sydney, School of Aerospace, Mechanical and Mechatronics Engi-neering (AMME). The simulator is shown in Figure2.8. The equipment is mounted on an hemispherical bearing, tabletop configuration, with a ±60◦ range of free motion. The platforms employs reaction wheels as actuators, and is currently used for testing and validation of estimation and balancing procedures during attitude maneuvers.

Figure 2.8: The AMME air bearing facility at University of Sidney12

The University of Michigan hosts the Triaxial Attitude Control Tesbed (TACT), which has been developed as a test bench for a number of different experiments. The facility is based on a dumbbell air bearing capable of a ±45◦ range of free motion in the constrained axis and with 160 kg capacity, shown in Figure2.9. The platform is provided with reaction wheels and thrusters, and attitude determination is performed following an inertial guidance approach by combining measurements from a magnetometer, a three-axis gyro and three single-axis accelerometers. The facility has been used to perform several tests regarding mass properties identification, stabilization and attitude control in different conditions reported inBernstein et al.,

2001. A set of two linear actuators has been mounted on the system to test and validate a new non-linear control law that provides system stabilization with two linear actuators only13.

A unique facility has been developed at DLR at the Department of Guidance, Navigation and Control Systems. The Facility for Attitude Control Experiments (FACE) is sustained by a tabletop bearing capable of 180kg capacity and ±45◦ range of free motion. It houses reaction wheels, magnetometers, and linear moving masses for balancing procedure, which is performed through a first manual phase and refined by an automatic phase reaching gravitational torques in the order of 10−5N. The peculiarity of the simulator is the environment simulator, which can reproduce orbital magnetic field together with solar illumination. To accomplish this, a circular Helmoholtz cage surrounds the bearing platform and provides the desired real-time magnetic field as an elaboration of the IGRF magnetic field model depending on the results of on-board attitude determination. A high pressure lamp spotlight fixed on a tripod is employed to simulate the Sun with a system of mirrors

12_{Kwan et al.}_,₂₀₁₅

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2.3. 3rd _generation ₂₅

Figure 2.9: The TACT air bearing facility at University of Michigan

used to overcome the limitations in terms of illumination given by having a fixed light source and a limited angular motion14_{. The cage and the mirrors can be}

clearly seen with the facility in Figure2.10.

Figure 2.10: The FACE air bearing facility at DLR

2.3

3

rd

generation

The last generation of spacecraft simulators includes both developed testbed as well as prototypes that add unique features with respect to the previous generations. The mother of such testbeds has been developed in the first years of 2000 at NASA JPL. The simulator has a unique spherical configuration, shown in Figure2.11, where the model spacecraft is contained in a floating spherical envelope that allows unrestricted motion about three axis. The main objective of the simulator was the validation of formation flight control algorithms, involving relative rotation between different satellites feed-backed to the controller through relative laser measurements. Assuming to have two models, the leader and the follower, each of them measures two events: its sensor being hit by the other’s laser beam and the other’s sensor being hit by its laser beam: the communication happens through IR transmission.

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In such a way each spacecraft gains information about its rotational period and the one of the other satellite, and the spin rate control can be performed. The dynamics of the suspended equipment is provided by a motor whose stator is attached to a flywheel and the rotor is solidal with the spherical envelope. The motor is controlled through the error signal between the different of the spin rate measured by a tachometer attached to the rotor and the flywheel angular velocity15.

(a) Three model spacecrafts at the JPL facility (b) The inner structure

Figure 2.11: The spherical facility at JPL

The development of CubeSats and microsatellites has resulted in a boost for spherical bearings simulators due to the size of the spacecraft that can be easily fitted into a sphere. While the previous simulator contains only a few electronics in the spherical envelope, new testbeds have been designed to iclude the whole satellite mock-up. A spherical bearing testbed has been designed and developed at UNAM as an upgrade of the platform depicted in Figure2.6 intended to reduce the payload mass and increase the free range. A 3D printed spherical envelope surrounds a 3U CubeSat and levitates on the bearing stator, providing ±180◦ free motion about all the spacecraft axis. Command to the actuators are sent wirelessely to the spacecraft actuators, which include reaction wheels and magnetic torquers. The testbed is shown in Figure2.12.

An upgrade of the previous testbeds has been independently developed at the United States Naval Academy. The Unrestricted Satellite Motion Simulator is composed by a spherical bearing that contains the spacecraft mock-up, providing unconstrained motion about each one of the spacecraft axis. The bearing has a capacity of more than 50 kg and provides a unique regular air film through a porous surface instead of a set of air channels, being more robust against rotor surfaces imperfections. Besides that, the system has another unique peculiarity. A set of sliding masses is employed in a redundant configuration to allow the balancing procedure to be completed without using the whole set ofDOFs of the system. The additionalDOFs are used to match the simulator inertia with the desired one for the selected experiment, making the testbed to be able to adapt to different missions

15_{Wang and Yee}_,₂₀₀₁

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2.3. 3rd _generation ₂₇

Figure 2.12: The UNAM spherical air bearing facility16

just by actuating its sliding masses. After the balancing procedure, the masses are actuated by a software that ensure inertia matching without unbalancing the system. Since the mass of the simulator is fixed, inertia matching is performed through scaling the simulator inertia by the largest principal inertia and the simulator spin rate is maintained equal to the spacecraft one by reaction wheels scaling. Sizing of the moving masses is directly related to the range obtainable in inertia ratios and has been performed after a survey of existing satellites inertia ratios and spin rate limits.

(a) The Unrestricted

Satel-lite Motion Simulator

(b) Moving masses inside the

spherical envelope (the veri-cal mass has been removed)

Figure 2.13: The spherical air bearing facility at JPL17

An innovative concept of friction free environment is under development at CSEM, as a part of an ESA project18. The concept of spherical air bearing is upgraded to a spherical magnetic bearing, called Reaction Sphere, where the spherical rotor levitates by the magnetic force produced by the poles of the stator and the rotor. The Reaction Sphere is based on a 3-D permanent magnet motor

17_{Culton et al.}_,₂₀₁₇ 18_{Onillon et al.}_,₂₀₀₉

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obtained with a multipole rotor and stator having 20 poles, each corresponding to one vertex of a dodecahedron19_{. Different applications are suitable for such a device.}

The primary objective of the Reaction Sphere is to develop a valid alternative for spacecraft reaction wheels, condensing three different wheels for three axis control to a single device commanded by one electric motor only. However it can be successfully employed as a bearing for attitude simulators, by enclosing the model spacecraft in the rotor, provided that the rotor envelope can safely shield the model from the produced magnetic field.

Figure 2.14: The CSEM Reaction Sphere Assembly

Another simulator that should achieve unconstrained motion about three axis is under development at the Laboratory of Informatics, Robotics and Microelectronics at the University of Montpellier. The prototype, shown in Figure2.15involves 4 air bearings with the rotors distributed on a spherical envelope that surrounds the model spacecraft, which is intended to be a CubeSat. The stators are distributed on

Figure 2.15: The robotic arm air bearing facility prototype

an external sphere attached to a robotic arm, which must ensure the facing between

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2.3. 3rd _generation ₂₉

the stator and its rotor during spacecraft rotational motion. The concept requires the robotic arm to adjust its orientation depending on the spacecraft attitude determined by attitude sensors. In this framework, the bearings act as springs due to the stiffness introduced in subsection1.2.1, and it strongly depends on the simulator orientation. Preliminary studies shown that the CubeSat obtains some motion within the testbed due to the alternate lift force of air bearings. In order to avoid these undesired fluctuations of the CubeSat inside the testbed, a spring has been proposed to be used to preload one of the air bearings. With a spring, system is not over constrained anymore, so use of a spring makes the relative motion of CubeSat smoother and helps to decrease requirements to the assembling of the testbed20_.

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Chapter 3 Available components

3.1 Air bearing

The air bearing which sustain the platform was already available at PoliMi as an heritage from an old project. The model is SRA-250 from Specialty Components and it is shown in Figure3.1a, together with a CAD model of the rotor designed in Solidworks R_{. The bearing technical drawing is shown in Figure}_A.1_{. Table}_3.1 shows the performances of the bearing reported in the manual. Mass properties, excluded the rotor mass, are derived from theCAD model knowing that the rotor is entirely made by aluminum. However they cannot be more than good estimation values to be refined through system identification procedures. The load capacity of

(a) SRA250-R30 air bearing at PoliMi

laboratory

(b) SRA250-R30 rotor CAD model

Figure 3.1: The SRA250-R30 air bearing technical drawing

the bearing is far higher than what is needed for this thesis, however no limitations are imposed to the bearing concerning minimum load capacity: therefore the option

Design and development of a small satellites three axis attitude simulation platform

POLITECNICO DI MILANO

SCHOOL OF INDUSTRIAL AND INFORMATION ENGINEERING

Master degree in space engineering

Design and development of a small satellites three axis attitude simulation

platform

Ringraziamenti

Contents

List of Figures

List of Tables

Listings

Sommario

Abstract

Introducion

Thesis outline

Chapter 1

Spacecraft simulators technology

1.1

Requirements

1.2

Air bearings

1.2.1

Capacity

1.2.2

Range of free motion

1.2.3

Height of the rotor’s center of rotation

1.2.4

Disturbance torques

1.2.5

Feed line requirements

1.3

Balancing system

1.3.1

System identification

1.4

Environment simulators

Chapter 2

State of the art

2.1

1

generation

2.2

2

generation

2.3

3

generation

Chapter 3

Available components

3.1

Air bearing