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Acta Astronautica
Acta Astronautica 105 (2014) 444–462
http://d0094-57
n CorrE-m
davidpeastrorosdaniele.bevilr@
journal homepage: www.elsevier.com/locate/actaastro
A six-degree-of-freedom hardware-in-the-loop simulatorfor small spacecraft
K. Saulnier a, D. Pérez b, R.C. Huang a, D. Gallardo a, G. Tilton a, R. Bevilacqua b,n
a Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute (RPI), Troy, NY 12180, USAb Department of Mechanical and Aerospace Engineering, University of Florida (UF), 308 MAE-A Building, P.O. Box 116250, Gainesville, FL32611-6250, USA
a r t i c l e i n f o
Article history:Received 26 December 2013Received in revised form25 August 2014Accepted 17 October 2014
Keywords:Small spacecraftHardware-in-the-loop verificationGuidance, navigation and control
x.doi.org/10.1016/j.actaastro.2014.10.02765/& 2014 IAA. Published by Elsevier Ltd. A
esponding author. Tel.: þ1 352 392 6230.ail addresses: [email protected] (K. [email protected] (D. Pérez),[email protected] (R.C. Huang),[email protected] (D. Gallardo), [email protected] (R. Bevilacqua).
a b s t r a c t
This paper presents a novel six degree of freedom, ground-based experimental testbed,designed for testing new guidance, navigation, and control algorithms for the relativemotion of nano-satellites. The development of innovative guidance, navigation andcontrol methodologies is a necessary step in the advance of autonomous spacecraft. Thetestbed allows for testing these algorithms in a one-g laboratory environment. The systemstands out among the existing experimental platforms because all degrees of freedom ofmotion are controlled via real thrusters, as it would occur on orbit, with no use ofsimulated dynamics and servo actuators. The hardware and software components of thetestbed are detailed in the paper, as is the motion tracking system used to perform itsnavigation. A Lyapunov-based strategy for closed loop control is used in hardware-in-theloop experiments to successfully demonstrate the full six-degree-of-freedom system'scapabilities. In particular, the test case shows a two-phase regulation experiment,commanding both position and attitude to reach specified final state vectors.
& 2014 IAA. Published by Elsevier Ltd. All rights reserved.
1. Introduction
The development of innovative guidance, navigationand control (GNC) strategies for relative spacecraft man-euvering will increase the efficiency and autonomy offuture space missions [1]. Air bearing-based spacecraftsimulators enable validation of GNC strategies prior tolaunch with hardware in the loop. Air bearings can providenear frictionless rotational and translational motion whichcan be utilized to create one-g laboratory conditions thatare much closer to those encountered in a micro-gravity
ll rights reserved.
),
il.com (G. Tilton),
environment. Reference [2] provides a thorough review ofair bearing based testbeds until the year 2003. The samepaper also elaborates on how such testbeds have beendeveloped over the last 50 years with the intention ofvalidating GNC strategies for spacecraft, on the ground.A hardware-in-the-loop facility, enabling rapid prototyp-ing of GNC algorithms for experimental testing, dramati-cally reduces the need for lengthy simulations every time(re-)tuning of the algorithms is performed. Ground test-beds can also support the advancement of the TechnologyReadiness Level (TRL) of spacecraft subsystems (see [3]).
Systems classified as only planar or only rotational arestill widely used in on-the-ground testing. Examples ofthese include a rotational testbed at Georgia Tech, which isused for attitude matching experiments, and a planartestbed at Cornell University called FloatCube, which wascreated specifically for testing maneuvers of small scalecooperative satellites [4,5]. More complex systems combine
Nomenclature
A error system matrixBðθÞ error input matrixðbx; by; bzÞ body principal axis reference frame
componentsCðθÞ mapping from relative angular velocity to
Euler anglese combined rotation and translation errorF force vectorGðθÞ rotational input matrixH thruster mapping matrixJ moment of inertia matrixK reference model gain matrixM moment vectorO orbiting reference pointP Lyapunov matrixQ positive definite matrix in Lyapunov equationRðθÞ direction cosine matrixu vector of thruster forces (N)V Lyapunov functionðx ; y ; zÞ LVLH frame components (mm)
ϵ error vector between ξ and linear referencemodel
η collection of nonlinear termsθ 2-1-3 Euler angle vector (rad)ν reference model inputξ combined roto-translational displacement vectorρ position vector relative to O (mm)ω angular velocity (rad/s)
Superscripts and subscripts
c control inputF associated with forceL local vertical local horizontal frameM associated with momentm associated with reference modelS spacecraft body fixed framex; y; z x,y,z-component respectivelyρ associated with translationω associated with rotation
1 http://dssl.technion.ac.il/2 http://ssco.gsfc.nasa.gov/index.html
K. Saulnier et al. / Acta Astronautica 105 (2014) 444–462 445
a planar translation stage and a rotational attitude stage toachieve five or six degrees of freedom. A five degree offreedom (5DOF) testbed has been developed by the Lawr-ence Livermore National Laboratory [6]. It combines arotational platform with full freedom yaw, 7151 pitchand 7301 roll on a dynamic air bearing platform but doesnot have a vertical degree of freedom. More recent researchrelated to 5DOF simulators has been done by GeorgiaInstitute of Technology and Harbin Institute of Technology.Both projects combine a lower platform guaranteeing twotranslational degrees of freedom with an upper platformwhich uses a spherical air bearing, to provide an additionalthree rotational DOF [7,8]. An interesting example of a 6DOFtestbed is the MIT “SPHERES” project [9,10]. This testbedcan reach full 6DOF when used in the International SpaceStation (ISS)'s micro-gravity environment. However it canonly achieve 3DOF on the ground with the assistance of aplanar air bearing platform. 6DOF platforms have beendeveloped by NASA Jet Propulsion Laboratory and NewMexico State University. In both cases the vertical motiongiving the 6th degree of freedom is provided by a poweredvertical system, which is actively controlled to provide asimulated zero-g environment for the attitude stage (AS)[11,12]. Reference [13] describes one of the most recentfacilities reproducing 3DOF spacecraft relative motion inItaly, still under development. Reference [14] providesinteresting observations on the benefits and need todevelop and test algorithms on the ground with experi-mental platforms before actual flight. Other examples of3DOF simulation facility testbeds can be found at the NavalPostgraduate School, looking at the different generations ofrobots utilized in the Spacecraft Robotics Laboratory [15,16].The Distributed Space Systems Laboratory at Technion pres-ents an interesting 3DOF system powered by ducted fansinstead of compressed air thrusters, and floating thanks to a
very specialized “hockey table”.1 A recent use of air bearingbased testbeds focuses on validation of contact dynamics, tocalibrate the algorithms and tools used in spacecraft servi-cing, refueling and assembly.2 A different ground testingapproach consists in employing robotic arms in conjunctionwith numerically simulated dynamics. Software integratesthe equations of motion and those command the motion ofservo actuators. This is a limited testing capability, wherealgorithms are validated with no use of real, space-likeactuators. On the other hand, this approach enables the full6DOF simulation with hardware-in-the-loop, at least forpartial validation of subsystems like vision based navigationsystems (see, for example, reference [17]).
This paper presents the 6DOF spacecraft simulatordeveloped at the ADvanced Autonomous MUltiple Space-craft laboratory. To the authors’ knowledge, the presentedsystem is the first reproducing all degrees of motion usingreal thrusters, without simulated dynamics and servoactuators used, for example, in the testbeds in References[11,12]. The goal of this work is to present the keycharacteristics of the ADAMUS testbed, and show its cap-abilities through an experimental test. Shown in Fig. 1, theADAMUS testbed is similar to other 5 and 6DOF testbeds,which integrate the capabilities of planar systems androtational systems. It differs from the existing 6DOF systemsbecause it guarantees a realistically actuated motion along/about the full 6DOF. The motion in the vertical direction isaccomplished using a unique method that employs amatched variable-mass counterbalance to the attitude stage(AS) and near-frictionless air bearing pulleys to allow closeto gravity-free motion. The counterbalance system replaces
Fig. 1. ADAMUS testbed.
K. Saulnier et al. / Acta Astronautica 105 (2014) 444–462446
the powered vertical stages of other 6DOF testbeds andallows for control of all 6DOF using only the onboardthrusters. The resulting behavior of the system is muchcloser to the actual dynamics of satellites in space, ascompared to systems that use linear motors or othersolutions based on numerically modeling the verticalmotion.
The design of the ADAMUS platform potentially allowsfor testing different spacecraft below 10 kg by switchingout the AS. Fig. 1 shows the interchangeable AS, connectedto the testbed base through the spherical air bearing. Anadditional restriction is given by the presence of thevertical pedestal, limiting the motion on two rotation axes,depending on the outer shape of the spacecraft.
The foremost contributions reported in this paper are:
1.
Presentation of the ADAMUS 6DOF testbed hardware,reproducing a spacecraft motion controlled via thrus-ters only.2.
Implementation of a Lyapunov-based thruster activa-tion control system on the 6DOF testbed for transla-tional and rotational motions.3.
Demonstration of the capabilities of the 6DOF testbedfor validating GNC algorithms for spacecraft performingautonomous maneuvers via hardware in the loopexperiments.This work is organized as follows: Section 2 gives anoverview of the 6DOF testbed hardware, Section 3 illus-trates the navigation method and supporting hardwareused for the experiments, Section 4 describes the imple-mented Lyapunov-based thrusters’ controls system,Section 5 explains the automatic generation of code fromSimulink models used to program the onboard computer,and the results of GNC experiments that were performedon the 6DOF testbed. Section 6 presents the conclusions.
2. Testbed hardware
2.1. General overview
The testbed, shown in Fig. 1, is composed of a transla-tional stage (TS), which was designed by the ADAMUS laband built by Guidance Dynamics Corporations (GDC) andan attitude stage, designed and built at the ADAMUS lab.The overall system operates on a flat epoxy surface.The position and attitude of the testbed is provided inreal time by the PhaseSpace Impulse Systems (PhaseSpaceSystem), illustrated in the lower right picture in Fig. 1.The PhaseSpace System is a third party motion capturesystem, which streams tracking navigation data to thetestbed's onboard computer.
K. Saulnier et al. / Acta Astronautica 105 (2014) 444–462 447
The AS represents the satellite and contains the sub-systems required for the GNC to be tested. These sub-systems include an onboard PC104 computer, thrusters,navigation components, and fuel. The AS is connected tothe TS via a spherical air bearing, which allows for lowfriction rotational motion of the AS. The TS facilitatestranslation of the AS. For vertical motion, a system of airpulleys on the TS connects the central column and AS to acounterbalancing deck (CD) with a matching mass. Themass of the CD compensates for the mass of the AS toallow for gravity-free motion. For translation in the othertwo degrees of freedom, three linear air bearings create anair cushion between the TS and a 13 ft�15 ft epoxy floor,allowing the TS to translate with very little friction. Theepoxy floor was built by Precision Epoxy Products, adivision of Rock Art, Ltd. The TS also carries the com-pressed air required to run all of the air bearings in thetestbed. Further details on the TS and AS are provided inthe following sections.
2.2. Translational stage
The function of the TS is to provide the 3 translationaldegrees of freedom. The two horizontal degrees of freedomare provided by linear air bearings, which create an aircushion to separate the structure from the epoxy floor,
Fig. 2. Translational stage. (a)
Table 1Components of translational stage.
Component Model numb
Platform Custom4500 psi, 70cu Paintball Air Tanks, 3x Pure EnergyRegulators, 3x 969Hand Valve, 3x 104104-N01Stabilizer PPSP01190*Flat Round Air Bearings, 3x S105001
allowing for nearly friction free motion. Hanging on thestructure of the TS is the counterbalancing system thatprovides the third translational degree of freedom. Thissystem will be further detailed in Section 2.3.
The main structure of the TS was custom built byGuidance Dynamics Corporations, according to the ADA-MUS laboratory design. Fig. 2 shows a rendering alongsidethe actual TS. Table 1 provides a list of the main compo-nents of the TS and their sources.
The TS also carries the compressed air tanks and pneu-matics that store and distribute the air used by all the airbearings and air bushings of the platform. The pneumaticsystem of the translational stage is shown in Fig. 3.
In this diagram, each “Tank” is a 4500 psi paintball tankas listed in Table 1. The tanks are connected in parallel tothree separate regulators that step down the tank pres-sures to 100 psi, 90 psi, and 30 psi. At the output of eachregulator there is a valve that is controlled manually toturn the air flow on or off to each of the air bearingsubsystems. One valve controls the connection of a 100 psiline that connects to the linear air bearing feet. A separatevalve is used to connect a 90 psi line to a set of bushingsthat are involved in guiding the counterbalance system.Lastly, a third valve connects a 100 psi line to the sphericalcup air bearing that supports the spherical segment ballattached to the AS.
Rendered and (b) actual.
er Company
Guidance Dynamics CorporationP11G-001 Luxfer
Aqua EnvironmentIngersoll RandPalmersNewway
Fig. 3. Translational stage pneumatics.
Fig. 4. Counterbalancing concept.
K. Saulnier et al. / Acta Astronautica 105 (2014) 444–462448
2.3. Counterbalancing system
The vertical degree of freedom is provided by a coun-terbalancing system consisting of a counterbalancing deckof the same mass as the AS and supporting column. Fig. 4contains a diagram of the counterbalancing concept withthe minimum and maximum heights reached by the AS.
The deck and central column are connected via an airbearing pulley system. The counterbalance motion isguided by two sets of vertical bars attached to the TS.One set of bars guides and stabilizes the CD, which isconnected to the bars using air bushings. The other set ofbars guides and supports the central column, andby extension the AS, via another set of air bushings.
K. Saulnier et al. / Acta Astronautica 105 (2014) 444–462 449
The guides also serve to prevent collisions between theclosely moving parts. The air bushings used in the pulleysystem and for the guides are supplied with air from theTS tanks as illustrated in Fig. 3. Flexible tubing is used tobring the air to the counterbalancing system withoutinterfering with its motion. Table 2 contains all the majorcomponents used in the counterbalancing system and theCD is shown in Fig. 5a.
During an experiment, the mass of the CD is changed tocompensate for the AS mass lost as air is released throughthe thrusters. In order to maintain the zero gravity effecton the AS motion it is important to maintain the balance inthe counterbalance system. Although the CD and AS can bebalanced using static weights before each experiment, theAS can change mass by up to 300 g as the experiment isrun and the air in its tanks is depleted. To reduce this
Table 2Components of counterbalance system.
Component Model nu
Platform Custom mPulley Bushing, 3x S301901Pulley Bushing Mounting Block, 3x S8019P02CD Guide Bushing, 3x S301201CD Guide Bushing Mounting Block, 3x CustomColumn Air Bushings, 6x S301201Column Bushing Mounting Block, 6x CustomPulleys D 17964500 psi, 50cu Paintball Air Tanks, 2x Carbon FiRegulator 969Pressure Sensor A-10Solenoid Valve 23KK7DEComputer UnoWireless Connector WiFlySolenoid Battery, 2x UBBL20-FArduino Battery RLI-9600
Fig. 5. Counterbalancing system. (a) Deck, pulleys
disturbance to manageable levels, the CD also releases airfrom its two tanks during each experiment. The associatedpneumatic system is shown in Fig. 5b. The release of air iscontrolled by an Arduino Uno, which receives pressurereadings from the AS tanks from the PC104 over WiFi viathe WiFly expansion board. A reading is then taken fromthe CD tanks using a pressure transmitter and the twovalues are compared. If the value received from the AS islower, the Arduino opens a magnetic latching valve, whichvents air from the tanks that have been reduced inpressure to 80 psi using a regulator. The valve remainsopen to release air from the CD until the pressures areequalized. If the value received from the AS is higher orequal, no air is released. Through this method, the pres-sure in the AS and CD tanks remains equal within a marginof 750 psi, as dictated by the precision of the pressure
mber Company
ade Guidance Dynamics CorporationNewwayNewwayNewwayD & KNewwayD & KPrime-Line
ber N2 NinjaAqua environmentWIKA
LM Peter Paul ElectronicsArduinoRoving Networks
L ULTRALiFEHiTECH
, and bushings and (b) pneumatics scheme.
K. Saulnier et al. / Acta Astronautica 105 (2014) 444–462450
transmitters used. Air from the CD is released from a Tjoint to prevent the released air from affecting the move-ment of the counterbalancing system or TS in general.The limitations of this method are covered further inSection 5.4
The electrical system on the CD consists of a pressuretransducer, Arduino Uno, WiFly expansion board, magneticlatching valve, and a diode and relay circuit that shields theArduino and allows it to control the current supplied tothe valve. The system is powered by a 9 V battery with theexception of the valve, which has a separate 6 V source. TheArduino reads the pressure of the CD tanks from the pressuretransducer through an A/D port and compares it to thepressure of the AS tanks, which is received wirelessly fromthe PC104 using the WiFly board. The Arduino controls therelease of air using digital I/O ports and a relay circuit. The twostates of the relay circuit which are used, control the directionof current received by the magnetic latching valve. This circuitcan be seen in Fig. 6. In one state, the current received is suchthat the valve opens, releasing air. In the other the current isreversed, so the valve closes and the release of air is stopped.
2.4. Attitude stage
The AS represents the satellite and provides the threerotational degrees of freedom of the testbed. The rota-tional degrees of freedom are provided by a spherical airbearing, shown in Fig. 7, which serves to connect the AS tothe TS central column.
Fig. 8 shows the AS detached from the TS in a front andtop view respectively.
Fig. 6. Counterbalancin
In addition, the major pneumatic and electrical com-ponents of the AS are listed in Table 3.
The AS is composed of a disc made of compositematerial (fiber glass and high density foam) connected tothe spherical air bearing. Attached to the AS are four armsmade of ABS and PVC. Two arms extend upwards and theother two arms extend downwards. The arms are attachedsymmetrically to the disc to facilitate mass balancing and toprovide a symmetric thruster layout. There are threethrusters mounted orthogonally on the end of each arm.Using a unique combination of active thrusters it is possibleto obtain independent translational and/or rotationalmotions. The AS provides full 3601 freedom in yaw butthe structure limits it to 7301 about the pitch and roll axes.
The pneumatic system of the AS, illustrated in Fig. 9, isused to supply air to the thrusters, which control themotion of the testbed. Thruster fuel in the form ofcompressed air is stored in two carbon fiber paintballtanks attached to the AS. The tanks are connected inparallel to a regulator, which steps the pressure down to165 psi before it is distributed to the thrusters. Thethrusters, shown in Fig. 8b, consist of solenoid valvesattached to custom made nozzles. Over the course of anexperiment, mass is lost from the tanks as air is releasedfrom the thrusters. By connecting the tanks in parallel andby aligning the center of mass of the tanks with the centerof mass of the AS, the change in mass does not affectthe overall balance of the AS. A pressure transmitter isconnected before the regulator to allow the PC104 toreceive measurements of the pressure left in the tanks.The pressure readings are used in the counterbalancingsystem as described in Section 2.3.
g deck electrical.
Fig. 7. Spherical bearing. (a) Bearing and (b) cup.
Fig. 8. Attitude stage. (a) Front and (b) top.
Table 3Components of attitude stage.
Component Model Number Company
Platform Custom ADAMUS lab.Spherical Bearing Custom D & K4500 psi, 50cu Paintball Air Tanks, 2x Pure Energy P07B-001 LuxferRegulator 1247-2 Aqua EnvironmentSolenoid Valve, 12x EH2012 Gems SensorsThrusters 12-056 Gordon EngineeringPressure Sensor A-10 WIKAPC/104 Computer ADLS15PC ADL Embedded SolutionsPC/104 Relay Board IR-104 Diamond SystemsPC/104 I/O Module DMM-32DX-AT Diamond SystemsMotion Control Card DMC-2133 Galil Motion ControlMotor Driver Board SDM-20242 Galil Motion ControlDC-ATX Converter DC123SR OceanServerDC-DC Step-Up Converter DC1U-1VR OceanServerBattery Management Module BB-04SR OceanServerBattery Pack, 2x BA95HC-FL OceanServerWireless Receiver WNCE2001 NetgearAS Balancing Motors 35F4N-2.33-024 Haydon KerkAS Balancing Platform Motor 35H4N-2.33-049 Haydon Kerk
K. Saulnier et al. / Acta Astronautica 105 (2014) 444–462 451
The flat disk of the AS also supports some components ofthe PhaseSpace System, the on-board computer, wirelessreceiver, and a balancing system. A diagram detailing the ASelectrical system and its connections to the other systems inthe testbed is provided in Fig. 10. The on-board portion of thePhaseSpace system consists of a string of six LEDs and a device
called the “puck.” The puck controls the power to the LEDs,which are necessary for the PhaseSpace System to determinethe state of the AS. The PhaseSpace LEDs are positioned on theedges of the arms and on the middle of the upper platform.
Central to the electrical system on the AS is an AdvancedDigital Logic ADLS15PC Rev. 1.3 computer (PC104), which
K. Saulnier et al. / Acta Astronautica 105 (2014) 444–462452
runs Real-Time Application Interface (RTAI) Linux. ThePC104 in turn is connected to an I/O board and a relayboard, which allow it to obtain pressure readings from thetanks and to control the thruster valves according to thecurrent GNC algorithm. The PC104 is also able to control amotor driver and motor controller card, which are used inthe balancing system of the AS. The PC104 is controlledwirelessly from an off-board desktop computer by meansof a Netgear wireless receiver. The same receiver is then
Fig. 9. Attitude stage pneumatics.
Fig. 10. Attitude stage electronic
used during experiments to communicate with both theoff-board components of the PhaseSpace System and theArduino Uno on the CD.
All of the AS electrical subsystems, except the Phase-Space puck and LEDs, rely on 2 lithium-ion batteries forpower. The batteries are situated on the lower arms to helpcompensate for the mass of the systems above the disk.These batteries are connected to a Power ManagementSystem from Ocean Server Technology (IBPS: IntelligentBattery and Power System). The IBPS recharges the batterieswhen connected to the 120 V grid using a safety chargingcircuit, and provides power to the AS subsystems at severalvoltages. The IBPS provides 5 V power to the PC104 and12 V power to a separate 12 V to 24 V DC–DC converter. TheIBPS also provides power to the motor driver and motorcontroller card. The 12 V to 24 V DC–DC converter outputs24 V to the thrusters through the relay board controlled bythe PC104.
An important consideration when dealing with rota-tional testbeds is that the center of mass and center ofrotation must be co-located to eliminate gravity torques.The center of rotation of the AS is located in the center ofthe spherical air bearing that connects it to the TS. Roughbalancing is performed with static weights placed in fourlocations around the AS platform, as shown in Fig. 8a.Although the AS can be completely balanced using thestatic weights, the movement of small masses, such aswires and the small changes of position of parts, which are
s connections and signals.
Fig. 11. Positions of LEDs on AS indicated with white circles.
K. Saulnier et al. / Acta Astronautica 105 (2014) 444–462 453
removed for charging and repairs can shift the center ofmass between experiments. To deal with small misalign-ment in the center of mass and center of rotation, a fineactive mass balancing system called the balancing plat-form (BP) is also present on the AS. The BP consists ofthree linear motors, which translate along the three bodyaxes, shown in Fig. 8b. The motor's translation causes ashift in the center of mass of the AS. Current balancingtechniques are human-in-the-loop with the motors con-trolled via a motor driver board with a serial connection tothe onboard computer. Before each experiment, themasses are moved incrementally until the AS does notmove when placed in several angled configurations. Sincethe balancing is done human-in-the-loop, this does notremove all disturbances from gravity torques; it serves toreduce the effects to a disturbance easily overcome by thethrusters. Controlling the alignment electronically alsoopens the door to alignment using adaptive methods[18,19]. When implemented, automatic methods will pro-vide a more finely and consistently balanced AS.
3. Testbed navigation and attitude determination
The navigation of the testbed is accomplished using aPhaseSpace Impulse Systems. The PhaseSpace System(which is further explained below) outputs a state vectorthat contains the position of the AS in millimeters, relativeto a coordinate frame positioned at one of the corners ofthe epoxy floor, and quaternions representing the attitudeof the AS. The error has been calculated in [20] to be1–5 mm with a mean latency of 8 ms. This data is sentwirelessly to the PC104 where an executable real timeprogram uses it to generate the linear and angular velo-cities of the AS using a Kalman filter and extended Kalmanfilter, respectively.
The PhaseSpace System is a third party system thatconsists of a set of cameras mounted on the walls aroundthe test area, a set of red LEDs mounted on the object to betracked, and a server which runs the proprietary softwarefrom PhaseSpace Inc. The system is easily configurable andcan be set up to track new objects without excessivecalibration or data post-processing. The PhaseSpace servercomes equipped with a software suit which includes Cþþlibraries to which can be used to make the data availableto other applications. The ADAMUS lab used those librariesto create S-functions which allow the position and attitudedata collected by the PhaseSpace software to be accessedby MATLAB in Simulink and by real time executablescreated using the Simulink Coder [21].
3.1. Hardware
The PhaseSpace hardware consists of an on-board LEDsystem and an off-board data collection system. The on-board system consists of a small rechargeable battery packand a string of LED circuits. On the testbed the LED stringconsists of 6 LED circuits positioned around the AS, but thePhaseSpace System can be configured to track as many as72 LEDs which could be used to define a nonrigid ASstructure. Fig. 11 shows the distribution of LEDs on the AS.
Each LED circuit contains a red LED which blinks rapidlyin a unique pattern. To conserve power, the battery pack iswirelessly controlled to go to a low power state when thesystem is not in use. The off-board system consists of adedicated server computer provided by PhaseSpace, Inc.,which communicates over Ethernet with each of a set of 8PhaseSpace cameras posted around the epoxy floor, asillustrated in Fig. 1. The cameras pick up the blinking LEDsand that data is used by the server to determine positionand attitude of the AS, which can be transmitted to thePC104 with a latency of 8 ms and precision of 1–5 mm.
3.2. Software
The testbed uses a Cþþ communications library pro-vided by PhaseSpace, Inc. to allow the PC104 to requestdata from the PhaseSpace. The PhaseSpace Server comespreloaded with software which is used to configure thetracking program. In order to determine the attitude andposition of an object equipped with PhaseSpace LEDs, thesystem must be configured using the PhaseSpace software.This configuration process assigns the location of theorigin in the cameras’ field of view as well as the orienta-tion of the AS which corresponds to zero attitude. After theone time configuration is performed, an S-function devel-oped in the lab can be used to acquire real time positionand attitude measurements. The S-function outputs asingle 7-element vector of the position and quaternionfor the tracked object, as calculated by the PhaseSpaceserver. Fig. 12 shows the steps taken to acquire positionand attitude data.
The position data is processed through a Kalman filter inorder to estimate the position and velocity. An extendedKalman filter processes the measured attitude data toestimate the attitude of the AS. The angular velocity datais computed using a discrete derivative of the filteredattitude data, which is passed through a low pass filter todecrease noise. The filter is chosen to balance the speedof the filter and the noise rejection. It is important tomention that a different AS, with a different actuationsystem, and different GNC software could be used, providedthat this software can interact with the PhaseSpace system.
4. Lyapunov controller for thrusters
The control strategy, chosen to demonstrate the test-bed's capabilities, is adapted from the Lyapunov thruster
Fig. 12. Flowchart showing the basic steps to acquire position and attitude data.
K. Saulnier et al. / Acta Astronautica 105 (2014) 444–462454
selection approach described in [22]. The active thrustersare chosen at each time step to maintain a negativederivative to a Lyapunov function created with a linearreference model, thus ensuring stability of the trackingerror. The Lyapunov method of selecting thrusters elim-inates the need for thruster mapping and providesa computationally simple, and non-iterative, method for6DOF control of a spacecraft.
4.1. Dynamics
The equations of relative motion for a spacecraft aredeveloped from the local-vertical-local-horizontal (LVLH)frame (x ; y; z) attached to an orbiting reference point O,where the x axis points in the radial direction from thecenter of the attracting body to the spacecraft, the y pointsalong the local horizon in the direction of motion of O, andz points in the direction x � y . Another reference framethat will be used is the spacecraft body principal axisreference frame (body frame) (bx; by; bz), which can beseen in Figs. 1 and 8.
If the reference point O is assumed to be in a circularorbit, and the relative distance of the spacecraft from O issignificantly smaller than the orbital radius, then the Hill–Clohessy–Wiltshire linear equations describe the transla-tional motion [23]. They are
€x ¼ 3n2xþ2n _yþ 1m
LFcx
€y ¼ �2nxþ 1m
LFcy
€z ¼ �n2zþ 1m
LFcz ð1Þ
where n is the mean motion, x, y, and z are the compo-nents of the relative position in the LVLH frame, and LFcx,LFcy, and
LFcz are the components of the control forces inthe LVLH frame. For the case where a spacecraft ismaneuvering very close to O and the maneuvers durationis much shorter than the orbital period, the coupling termscan be ignored, then the relative translational motion canbe approximated by
€ρ ¼ 1m
LFc ð2Þ
where ρ¼ ½x y z�> and LFc ¼ ½LFcx LFcyLFcz�> . For the max-
imum relative positions (4 m and 4.5 m in the plane,0.56 m in the vertical direction) and velocities (startingapproximately from rest) achievable with the platform, thecoupling terms are at least one order of magnitude smallerthan the remaining terms in the right-hand side of Eq. (1)for orbits with a radius of at least 6041.4 km. This value is
below the mean radius of the Earth (6378.1 km); hence,this assumption is reasonable for any physically realizableorbit about the Earth.
In this case, the translational dynamics closely matchesthat of the ADAMUS 6DOF testbed. Eq. (2) is what is usedto develop and test controllers on the testbed.
The controller presented in this paper uses rotationalequations of motion developed from 2-1-3 Euler anglerepresentation of the attitude of a spacecraft body framerelative to the LVLH frame. In the case of the testbed, theLVLH frame is the frame fixed to the epoxy floor andcorresponds with the PhaseSpace object coordinate frame.The rotational kinematics of the body frame relative to theLVLH in terms of 2-1-3 Euler angles
_θ ¼ CðθÞ½ωS�SRLðθÞωL� ð3Þ
where θ¼ ½θx θy θz�> has the Euler angles reordered intoa vector, ωS is the inertial angular velocity expressed interms of the body fixed principal axes of inertia of thespacecraft, which define the S frame, ωL is the inertialangular velocity of the LVLH frame. SRLðθÞ is the directioncosine matrix from the LVLH frame to the S frame which is
SRLðθÞ ¼czcyþszsxsy szcx �czsyþszsxcy�szcyþczsxsy czcx szsyþczsxcy
cxsy �sx cxcy
264
375 ð4Þ
where cx≔ cos ðθxÞ, sx≔ sin ðθxÞ, cy≔ cos ðθyÞ, sy≔ sin ðθyÞ,cz≔ cos ðθzÞ, and sz≔ sin ðθzÞ. CðθÞ is the mapping from therelative angular velocity to the rates of change of the Eulerangles, and in this case it is
CðθÞ ¼cz �sz 0
sz=cx cz=cx 0sztx cztx 1
264
375 ð5Þ
where tx≔ tan ðθxÞ.For a rigid body, the rotational dynamics is
_ωS ¼ J�1ð�½ ~ωS�JωSþSMcÞ ð6Þ
where J is principal moments of inertia matrix, SMc isthe vector of control torques in the S frame, and ½ ~ωS� isa skew symmetric matrix representing the cross productoperation in matrix form. That is,
½ ~ωS� ¼0 �ωz ωy
ωz 0 �ωx
�ωy ωx 0
264
375 ð7Þ
where ωx, ωy, and ωz are the components of ωS. Rearran-ging Eq. (3) an expression for the angular velocity of the
Fig. 13. Testbed thruster configuration.
K. Saulnier et al. / Acta Astronautica 105 (2014) 444–462 455
spacecraft can be obtained as
ωS ¼ C�1ðθÞ _θþSRLðθÞωL ð8ÞA second-order set of differential equations governing
the evolution of the 2-1-3 Euler angles can be obtained bytaking the derivative of (3) and using (6) and (8):
€θ ¼ fðθ; _θ;ωL; _ωLÞþGðθÞSMc ð9Þwhere GðθÞ≔CðθÞJ�1 and fðθ; _θ;ω; _ωÞ is a nonlinear vectorfunction. WithωL ¼ 0 and _ωL ¼ 0 as in the laboratory fixedreference frame, these become the equations of motionused for the attitude control of the testbed.
€θ ¼ fðθ; _θÞþGðθÞSMc ð10ÞDue to the fact that thrusters are being used to control
the testbed, the attitude and translational control arecoupled, and thus SMc and
LFc must be designed together[22]. It is also necessary to determine the contributionof each thruster to SMc and LFc. With this in mind, firstdefine a vector of thruster forces for each thruster asu¼ u½u1 u2⋯un�> where
ui ¼0 ith thruster off1 ith thruster on
i¼ 1;2;…;n�
ð11Þ
and u is the magnitude of the thrust a single thrusterproduces.
The forces and moments in the body frame can becalculated by
SFcSMc
" #¼
HF
HM
" #u¼Hu ð12Þ
where H is a matrix that maps the vector of thrusts u tothe forces and moments in the body frame, which arewritten as SMc and SFc. The submatrices HF and HM
individually map u to SFc and SMc, respectively.SFc are
the input forces in the S frame and can be found usingSFc ¼ SRLðθÞLFc. H is determined based on how the thrus-ters are physically laid out on the AS. In this case thethrusters are configured as shown in Fig. 13, which resultsin the following matrices:
HF ¼c �c 0 c c 0 �c �c 0 �c c 00 0 1 0 0 �1 0 0 �1 0 0 1c c 0 c �c 0 �c c 0 �c �c 0
264
375
ð13Þ
HM ¼�c �c 0 c �c 0 �c c 0 c c 0�0:5 0:5 0 0:5 �0:5 0 0:5 �0:5 0 �0:5 0:5 0c �c 0 �c �c 0 c c 0 �c c 0
264
375d
ð14Þwhere d is the moment arm and c¼0.7071.
Let ξ ≔½ρ θ�> be the combined roto-translational dis-placement vector, then Eqs. (2), (10), and (12) can allbe combined to produce the following coupled thrustercommanded dynamics:
€ξ ¼ pðξ; _ξÞþNðθÞHu ð15Þwhere
pðξ; _ξÞ ¼0
fðθ; _θÞ
" #ð16Þ
and
N θ� �¼ 1
mLRS θ
� �0
0 GðθÞ
" #ð17Þ
where LRSðθÞ ¼ SRL>L ðθÞ.
4.2. Reference model tracking
The goal of the controller will be to follow ρm and σm,which are defined as the solutions to the following linearreference models [22]:
€ρmþK1 _ρmþK2ρm ¼ νρc €θmþK3_θmþK4θm ¼ νθc ð18Þ
where K1, K2, K3, and K4 are 3�3 symmetric positivedefinite matrices, and νρc and νθc can be thought of asinput variables to the linear reference models. The valuesof νρc and νθc will determine the type of control problem.If νρc ¼ 0 and νθc ¼ 0 then tracking the linear referencemodel becomes a regulation problem; otherwise, ρm andσm are the responses of the second order system describedin Eq. (18) to inputs νρc and νθc.
In order to track the linear reference model Eq. (18),error variables between the linear reference model andthe nonlinear dynamics are defined as ϵρ ¼ ρ�ρm andϵθ ¼ θ�θm. The controller is designed to drive the errorsystem asymptotically to zero. Combining these errorvariables with Eqs. (2), (10), (12), and (18) result in thefollowing equations governing the evolution of the error
€ϵρþK1 _ϵρþK2ϵρ ¼1m
LRS θ� �
HFu� νρc�ηρl� �
€ϵθþK3 _ϵθþK3ϵθ ¼GðθÞHMu�ðνθc�ηθlÞ ð19Þ
K. Saulnier et al. / Acta Astronautica 105 (2014) 444–462456
where
ηρl ¼K1 _ρþK2ρ
ηθl ¼ fðθ; _θÞþK3_θþK4θ
Defining state variables as eρ ¼ ½ϵ>ρ _ϵ>
ρ �> , eθ ¼ ½ϵ>θ
_ϵ>θ �> ,
and e¼ ½eρ eθ�> , Eq. (19) can be written in first order statespace form as
_e ¼AmeþBðθÞðHu�wÞ ð20Þ
with
Am ¼A1m 03�3
03�3 A2m
" #; A1m ¼
03�3 I3�3
�K1 �K2
" #;
A2m ¼03�3 I3�3
�K3 �K4
" #ð21Þ
and
B θ� �¼
03�3 03�31mLRS θ
� �03�3
03�3 03�3
03�3 GðθÞ
266664
377775
w¼wF
wM
" #¼
mSRLðθÞðνρc�ηρlÞG�1ðθÞðνθc�ηθlÞ
24
35 ð22Þ
K1, K2, K3, and K4 are designed to be positive definite, A1m
and A2m are Hurwitz and therefore, A is also Hurwitz. Theterm w can be thought of as the ideal controls for trackingthe reference model Eq. (18) since if Hu¼w the system ofEq. (15), the tracking error goes exponentially to zero.
The controller was designed for the error system usingthe Lyapunov approach to control design. A Lyapunovfunction is used to design the controls such that the errorequation (20) is asymptotically stable. To begin, the fol-lowing candidate function is selected:
VðeÞ ¼ e>Pe ð23Þ
where P¼ P> 40. Differentiating Eq. (23) with respect totime and using Eq. (20) results in the following Lyapunovderivative
dVdt
¼ e> A>m PþPAm
� �eþ2e>PB θ
� �Hu�wð Þ ð24Þ
Since Am is Hurwitz, for every specified positive definitesymmetric matrix Q there exists a unique positive definitesymmetric matrix P that is a solution to the Lyapunovequation:
A>m PþPAm ¼ �Q ð25Þ
and if 2e>PBððθÞÞðHu�wÞr0, then Eq. (20) is asymptoti-cally stable [24]. The only term that can be modified inEq. (24) by the thruster values is the term
2e>PBHu ð26Þ
Thus at each time step u is chosen such that expression(26) is negative. To accomplish this, let a¼ e>PBH, then
the components of u are computed as follows:
ui ¼u
ai�jaij2ai
� �for aia0
0 for ai ¼ 0for i¼ 1;…;12
8><>: ð27Þ
This results in ui¼0 or ui ¼ u, which designates thethruster being OFF or ON, respectively. An estimation ofthe Lyapunov derivative, Eq. (24), is calculated at each timestep using previous values of the Lyapunov equation. Fuelcan be saved by having the testbed not thrust when theLyapunov derivative is already negative below a chosenthreshold. This has the added effect of slowing down themovement towards the final position but does not causeinstability since it still requires a negative Lyapunovderivative.
5. Testbed GNC experiments
5.1. Experiments
The 6DOF testbed hardware and GNC systems weretested by performing hardware-in-the-loop experiments.These experiments validate the ability of the testbed toaccurately simulate complex spacecraft autonomousproximity maneuvers, which allows for the validation ofnovel GNC algorithms.
The experiments presented here consist of having theAS move to a target state from an initial state using thecontrol generated from the Lyapunov-based thruster selec-tion described in the previous section. In the experimentsrun so far on the testbed, the control has been used forregulation alone. In other words, starting from a giveninitial position and attitude, the AS is forced to reach adesired position and/or attitude without the path beingspecified (no guidance). These experiments corroboratethe control strategy stability and assess the performance ofthe testbed.
5.2. Simulink model
MATLAB's Simulink is used to implement the controlstrategy as well as handle the navigation systems and controlthe thruster relays. The Simulink model, shown in Fig. 14, isused to generate C code, which can be compiled and run onthe onboard Linux computer. The PC104 and a desktopcomputer, which runs MATLAB and Simulink, both use RealTime Application Interface (RTAI) Linux. The RTAI operatingsystemwas chosen because it allows the applications to run inreal time without being interrupted by operating systemtasks. Having the same operating system on the two compu-ters allows executables generated on the desktop through theSimulink Coder to be transferred to, and run on, the PC104.The main blocks in the model are the Sensor Package, theState Estimator, Lyapunov Controller, and the Diamond RelayBoard. The Sensor Package block contains the PhaseSpaceSystem block created in the ADAMUS lab to communicatewith the PhaseSpace server and to output the current positionand attitude of the AS. This block also can be used insimulation via a global variable switch, which changes theblock to use the Simulink Aerospace Blockset 6DOF dynamics
Fig. 14. Simulink model.
K. Saulnier et al. / Acta Astronautica 105 (2014) 444–462 457
block to propagate the position and attitude. The StateEstimator block contains a Kalman filter and extended Kalmanfilter which are used to estimate the position, velocity,attitude, and angular velocity information from the positionand attitude information from the Phasespace data. TheLyapunov Controller block contains the implementation ofthe Lyapunov-based thruster selection, which is described inSection 4.2. The output of the Lyapunov Controller block is the12�1 vector, which contains 1's for the thrusters whichshould be turned ON and 0's for the thrusters which shouldbe kept or turned OFF. The Diamond Relay Board blockoperates the onboard relays using the output of the controlblock. The block Save Data collects the data held to be held inRAM until then end of an experiment when it is saved to anonboard flash hard drive. The data is taken from the harddrive back to a desktop computer running Linux and MATLABso the data can be plotted and analyzed. The blocks associatedwith CD balancing can also be seen. The first block, calledRead Pin Voltage, reads the pressure value from the A/D pinconnected to the pressure transmitter. The next block, UDPSend to Arduino, continuously sends the pressure data to theArduino over UDP.
5.3. Results
Experiments were run starting at an arbitrary initialcondition with the testbed floating freely but not moving onthe epoxy floor. The testbed software, represented in Fig. 14,was executed causing the testbed to regulate to a set ofpredetermined points. The results presented here show thetestbed as it is regulated to a point near the center of the
epoxy floor. Once all DOF were below the thresholds at once,the testbed then returned to its initial state, except for thevertical one, going only in one direction. A flowchart of theexperiment can be seen in Fig. 15, while Table 4 summarizesthe requirements for a successful test.
The change in target state can be seen in the experimentaldata shown in Fig. 16 at around 80 s. An exception was madefor the vertical translation, which first regulated like the otherDOF but then simply maintained its position for the returntrip. The results for regulation in 6DOF are shown in Fig. 16and can be seen in video online at url:http://www.riccardobevilacqua.com/multimedia.html, opening the video entitled “6DOF (8 degrees attitude tolerance – “there and back”)”. The 8degrees error tolerance on attitude was chosen via numericalsimulations, as a satisfactory balance between thrusting effortand a final trajectory showing a successful maneuver. Thisprocedure is an example of one of the most importantbenefits of ground based testbeds: being able to tune GNCvia computer simulations, and then perform experimentalvalidation to confirm their validity. The experiment demon-strates that along the three axes in position, the control wasable to move from the initial state to the desired state thenreturn to the initial state. The same can be seen in the Eulerangles. The overshooting shown in some of the states could bereduced/increased in numerical simulations first, then newexperiments could be run, once again showing the main goalof rapid prototyping of GNC algorithms and ground tests.The multimedia web page provided above shows additionaltests performed with the ADAMUS simulator. Particularly, anadditional experiment with 5 degrees attitude tolerance canbe seen.
Table 4Requirements for the experiment.
State Desired intermediate state Desired final state Desired accuracy
x 1500 mm Random state at initial time 50 mmy (vertical state) 1600 mm 1600 mm 50 mmz 1500 mm Random state at initial time 50 mmθx 0 deg Random state at initial time 8 degθy �100 deg Random state at initial time 8 degθz 0 deg Random state at initial time 8 deg
Fig. 15. Flowchart showing the steps performed when running an experiment.
K. Saulnier et al. / Acta Astronautica 105 (2014) 444–462458
The experiment also included a threshold for positionand attitude, which allowed small errors to be ignored toreduce chatter at steady state. For position, this thresholdwas 5 cm and the effects cannot be seen in the plots inFig. 16. For attitude, the threshold used was 81. Euler anglesθx and θz are close to or under this threshold for nearly theentire experiment, which can be seen in the movement toand from the goal line when under 81. The movementunder the threshold was not caused by the thrusters butinstead caused by small imbalances in the AS.
The commanded signals to the thrusters are shown inFig. 17.
The thrusters on the testbed are ON-OFF thrusters witha constant thrust force of .3 N per thruster. The density ofthe thrust profiles is largely affected by a threshold on theLyapunov derivative, which determines whether thrust is
currently necessary to decrease the error. Choosing adifferent threshold or the controller itself would greatlychange the density and magnitudes of the thrust profiles.This experiment clearly shows the 6DOF capabilities of thetestbed as it is able to move from an initial to a finalcondition in a controlled way in 6DOF.
5.4. Limitations and future work
There are a few aspects of the testbed vertical motionwhich either require improvement or represent limitationsin design. Motion in the vertical direction appears tocurrently encounter more friction than the motion inthe other two translational directions. This friction ismostly due to imperfections in the air bushing alignment,tube connections, and pulley cables; however, not all
Fig. 16. 6 DOF Regulation Results. See also Table 4. (a) Position and (b) orientation.
K. Saulnier et al. / Acta Astronautica 105 (2014) 444–462 459
vertical disturbances can be eliminated with the currentdesign.
The largest disturbance is caused by the difference inmass between the vertical DOF and the two other transla-tional DOF. The entire testbed must be moved whentranslating in either of the DOF along the epoxy floor. Incontrast, AS motion in the vertical DOF involves themovement of only around 70% of the mass of the testbed- the counterbalance deck, AS, and supporting column.This difference in mass is an aspect of design, which
cannot be eliminated with the counterbalance approach.The current control method was designed ignoring thedifference in mass in the two DOF with no ill effects,thanks to its feedback nature. Future software may con-sider this difference in mass, and filter the thrust com-mands sent to the thrusters appropriately.
The second largest source of disturbance is found in thebalancing of the AS and the balancing of the counter-balancing system. The AS balancing is currently donehuman-in-the-loop. However, the disturbances caused by
Fig. 18. Weight test: the difference in mass between the counterbalanceplatforms remains below 6 g as the thrusters are fired. Each firingsequence lasts 4 s, and the onboard software runs the code used for theexperiment presented earlier in the paper.
Fig. 17. Thrusters commands history. 1 indicates firing, 0 indicates thruster off.
K. Saulnier et al. / Acta Astronautica 105 (2014) 444–462460
the lack of alignment of the center of mass and the center ofrotation are definitely within the ability of the controller toaccommodate, as can be seen in the results of the testbedexperiments. In the future, the balancing of the AS can beimproved through adaptive balancing, which can removehuman error and provide far more accurate results.
The counterbalancing system dynamic mass adjust-ment is currently done by measuring the pressures inthe two AS tanks and maintaining the same pressure in thetwo CD tanks. It was desired that the balancing ofpressures would correspond to a rough balancing of mass.With air being released in equal quantities, the two ends ofthe counterbalance would remain equal as air is releasedthrough the thrusters. The use of pressure difference toapproximate mass difference is justified by the assumptionthat the two sets of tanks should be at roughly the sametemperature as long as they are filled over the same timeand release air at the same rate. This assumption wastested through an experiment where the AS was pro-grammed to run through a GNC experiment using simu-lated dynamics. This caused the thrusters to release air in afashion resembling that of an actual experiment, thoughover a much shorter time period. During this timethe counterbalance deck released air to compensate forpressure differences in the same way it does for theexperiments. After each thruster firing sequence, the TSand AS were weighed to measure the change in mass ofboth portions of the testbed. Since the only cause ofchange was the air released from both sets of tanks, thisallowed for a direct measurement of the mass of air lost.As can be seen in Fig. 18, the mass released from the
counterbalancing deck follows closely the mass lost fromthe AS with a maximum difference of 6 g. With eachthruster capable of providing .3N of force, the disturbancecaused by 6 g difference in the counterbalance should beeasily overcome by control forces. If a case is encounteredwhere more precise balancing is required, the massdifference calculation would be improved by includingtemperature measurements of the tanks, along with thealready measured pressure.
Lastly, the tubing running from the bottom deck of theTS platform to the counterbalancing deck to provide air for
K. Saulnier et al. / Acta Astronautica 105 (2014) 444–462 461
the air bushings will cause some disturbance as the decksmove relative to each other. Experiments to quantify theeffect can be run, but the effect is expected to be minimalsince the tubing can move freely.
The long term goal of the ADAMUS laboratory is tobuild multiple units and employ them for full 6DOFrelative motion experiments, as the facility can accommo-date several simulators.
6. Conclusion
The six degrees of freedom small spacecraft simulatortestbed developed at the Advanced Autonomous MultipleSpacecraft laboratory is a unique platform, which reproducesall degrees of motion using air bearings. The experimentalfacility described herein is currently able to operate spacecraftweighing less than 10 kg and their algorithms in real time. Inthis work, the hardware and software details of the testbedhave been presented, along with a Lyapunov-based thrusteractivation strategy, which was chosen to demonstrate thecapability of the testbed to evaluate Guidance, Navigation, andControl algorithms. The experiment for validating the func-tions of the testbed and for assessing Guidance, Navigation,and Control algorithms with hardware-in-the-loop isdescribed. The results of this experiment confirm the testbed'sability to move and be controlled in six degrees of freedom.Use of the testbed in validating the Lyapunov-based thrusterselection control method demonstrates the utility of thetestbed for the design and testing of Guidance, Navigation,and Control methodologies. Future work on the testbed willinvolve efforts to reduce the friction in the vertical translationas well as further experiments to quantify the disturbancescaused by friction and balancing in the system. Future workwill also include the implementation of balancing software forthe Attitude Stage center of mass alignment with the center ofrotation. This will allow the testbed to exhibit the desireddynamics more accurately.
Acknowledgements
This research was partially supported by the UnitedStates National Aeronautics and Space Administration(NASA), under a subcontract from the Satellite ServicingCapabilities Office (SSCO) at NASA Goddard Space FlightCenter (subcontract of Grant no. NNX10AD17A).
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Kelsey Saulnier graduated with a Bachelor ofScience in Computer Engineering fromRensselaer Polytechnic Institute in 2007. Shebegan research in the ADAMUS lab as anundergraduate and continued her work thereas a graduate student. Kelsey completed herMaster of Science, also in Computer Engi-neering, in 2013. Her work at the ADAMUSlab focuses on the 6DOF testbed and controlsoftware.
David Pérez is a Postdoctoral ResearchAssociate in the ADvanced Autonomous MUl-tiple Spacecraft (ADAMUS) Laboratory. Davidsmain research interests are Guidance, Navi-gation and Control of autonomous Spacecraftand Robotics. He received his B.Sc. (2008) inMechanical Engineering from St. Cloud StateUniversity, St. Cloud, Minnesota and his M.Eng (2009) and Ph.D. (2013) in MechanicalEngineering and Aeronautical Engineeringrespectively from the Rensselaer PolytechnicInstitute, Troy, New York.
Rosemary Huang is a native of SouthernCalifornia. After graduating from Laguna HillsHigh School, she went on to attend theUniversity of California, Berkeley, where sheearned a Bachelor of Science degree inMechanical Engineering in May of 2000.Following the completion of her undergrad-uate education, she continued her studies atBerkeley, earning a Master of Science degree,also in Mechanical Engineering, in August of2003. She then moved to Indiana, to pursue aPh.D. at Purdue University in West Lafayette.
She completed her Doctorate in Aeronauticaland Astronautical Engineering in 2012. Rosemary was the ADAMUS labmanager in 2013 and 2014.
Daniele Gallardo received his Ph.D. inMechanical Engineering from RensselaerPolytechnic Institute in 2014. Daniele holdsa Bachelor and a Master Degree in Mechan-ical Engineering from the Politecnico di Tor-ino, Italy. Daniele spent one year of hisMaster at the Massachusetts Institute ofTechnology as a research assistant where hedeveloped his thesis related to PEM fuel cellsdegradation. The foci of Danieles Ph.D.research are the study of fluid–structureinteractions and the development of novel
mathematical models tailored for controlpurposes and based on reduced order modeling techniques. His currentprojects are related to vibration mitigation of airfoils and cross windresponse of tall buildings.
Grace Tilton graduated from RPI in 2014 witha dual degree in aerospace and mechanicalengineering. She has been a member of theADAMUS lab since 2011, assisting with avariety of projects related to spacecraft simu-lation and design as well as participating inmultiple varsity sports and Tau Beta PiNational Engineering Honor Society. Shemaintains a high level of academic successand these efforts have been recognized withthe 2011 RPI Founders award and 2013 BarryGoldwater Scholarship.
Riccardo Bevilacqua is an associate professorof the Mechanical and Aerospace EngineeringDepartment at the University of Florida. Heholds a M.Sc. in Aerospace Engineering(2002), and a Ph.D. in Applied Mathematics(2007), both earned at the University ofRome, “Sapienza”, Italy. He was a US NationalResearch Council post doctoral fellow from2007 to 2010, and an assistant professor atRPI before joining University of Florida. Healso worked as a project engineer in MissionAnalysis at Grupo Mecanica del Vuelo in
Madrid, Spain, during 2003. Dr. Bevilacqua'sresearch interests focus on Guidance, Navigation, and Control of multiplespacecraft systems and multiple robot systems.
