Attitude Module Characterization of the Satellite Formation Flight Testbed

Andrea Valmorbida1, Francesco Scarpa, Mattia Mazzucato, Sergio Tronco, Stefano Debei and Enrico C. Lorenzini

Center of Studies and Activities for Space "Giuseppe Colombo" (CISAS) Department of Industrial Engineering (DII), University of Padova

Padova, Italy 1 andrea.valmorbida@unipd.it

Abstract—Satellite Formation Flying (SFF) is a key technology for several future missions, since, with respect to a single spacecraft, it allows better performances, new capabilities, more flexibility and robustness to failure and cost reduction. Despite these benefits, however, the SFF concept poses several significant design challenges and requires new technologies, including new sensors, actuators and Guidance, Navigation and Control (GN&C) algorithms.

Ground-based spacecraft hardware simulators can be used for the development and verification of both hardware (sensors and actuators) and software (GN&C) for SFF. In this paper we describe the main features of the Satellite Formation Flying Hardware Simulator under development at the University of Padova, presenting experimental activities results of the Attitude Module onboard cold gas thrusters force characterization and inertia tensor estimation.

Keywords—formation flight testbed; cold gas thruster force characterization; inertia tensor estimation.

I. INTRODUCTION Space missions based on formations of multiple

cooperative small satellites represent an efficient alternative to expensive and risky single satellite missions. Satellite Formation Flying (SFF) means two or more satellites whose positions and attitudes are permanently assessed and mutually controlled, so that the distributed payload over these satellites is equivalent to a very large dimension, single instrument in space [1-3]. Formation flight relies on sensors and actuators able to continually assess and maintain relative distances and attitudes with very high accuracy, and a system architecture ensuring that instrument performance is achieved by each individual satellite in the loop.

Some advantages that a satellite formation offers with respect to (w.r.t) a single spacecraft are: better performances, new capabilities, flexibility, robustness to failures and cost reduction. Despite these benefits, however, the formation flying concept poses several significant design challenges and requires new technologies, including Guidance Navigation and Control (GN&C) system complexity, new sensors and actuators, propellant consumption and inter-satellite communication.

In these years our research team at the University of Padova has been involved in the development of a SFF hardware simulator that allows to carry out on ground experimental

research on both Satellite Formation Flying (SFF) and Rendez-vous and Docking (R&D).

In order to test some attitude control maneuvers, a characterization of the hardware simulator was required, with the final aim of estimating both the on board thrusters force and the inertia tensor. The paper is organized as follows: following a brief review of some ground-based testbeds developed by other universities or research centers, we illustrate our hardware simulator main features providing a synthetic description of the Attitude Module (AM) main subsystems. After that, we describe some experimental activities aimed at determining the AM on board thrusters force and estimating the AM inertia tensor.

II. GROUND-BASED SPACECRAFT SIMULATORS Ground-based testbeds have been used since the beginning

of space exploration for both hardware and software development and verification. According to Schwartz et al. [4], spacecraft simulators are grouped into three main categories, depending on the allowed Degrees Of Freedom (DOF): rotational systems with partial or complete 3 DOF attitude motion; planar systems with two translational DOF on a planar surface and one rotational DOF about an axis perpendicular to the plane; and combined systems with up to 6 completely unconstrained DOF.

Attitude or translational motion can be realized using different systems, as for instance multiple gimbals systems or air bearing systems. In a multiple gimbals system, a set of pivoted mechanical supports guarantees the free rotation of an attitude platform w.r.t an external support. The low friction motion between gimbals is obtained using ball or magnetic bearings. In either planar or rotational air bearings, pressurized air passes through small holes creating a thin film or cushion between coupled moving sections. That air film supports the weight of moving sections and, acting as a lubricant, reduces the friction between the two sections of the bearing, allowing virtually torque-free rotational and force-free translational motions.

Examples of rotational air bearing spacecraft simulators are: the Naval Postgraduate School's Three Axis Attitude Dynamics and Control Simulator, the Virginia Tech's Distributed Spacecraft Attitude Control System Simulator (DSACSS), the Georgia Tech's Integrated Attitude Control Simulator (IACS) and the University of Michigan's Triaxial Air

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Bearing Testbed. The JPL-CalTech Formation Control Testbed (FCT) and the DLR Test Environment for Applications of Multiple Spacecraft (TEAMS) [5] are examples of combined spacecraft simulators on the ground with 6 DOF. Also, the MIT Space Systems Laboratory (SSL) developed the Synchronized Position Hold, Engage, and Reorient Experimental Satellites (SPHERES) system [6] with two main configurations. The Flat Floor and the Glass Table test facilities at the SSL are planar systems with 3 DOF, while a 6 DOF system flies on board the International Space Station in a fully representative microgravity environment.

III. THE FORMATION FLIGHT HARDWARE SIMULATOR The final aim of our project is to design, realize and

validate a representative facility, called Spacecraft Formation Flying Hardware Simulator, to carry out research activities in the fields of SFF and R&D [7]. This separated vehicles testbed will be as much as possible a representative dynamic environment for the development and verification on the ground of coupled position and attitude relative GN&C algorithms. This kind of facility can also be used for either educational or research purposes in the fields of satellite relative navigation sensors, proximity control algorithms and space robotics.

In its final configuration, the SFF testbed consists of two or more Spacecraft Simulators representing the units of a satellite formation and a Control Station (laptop) (see Fig. 1). Each Simulator is made of an Attitude Module (AM) with three rotational degrees of freedom provided by mechanical gimbals and a Translational Module (TM) with two position degrees of freedom that translates on a glass-covered plane using a low friction air cushion system. A laptop is used to boot-load the Simulators, to transmit commands to the Simulators and to receive and store telemetry data.

Fig. 1. Formation Flight Hardware Simulator testbed overview.

The main requirements that drive the facility design are: fateful representation of a satellite formation dynamics, easy configuration changes, reliability, safety and low cost. Also, the formation flight team has defined the following rough requirements on maximum position and attitude estimation accuracy for each unit flying in formation: 1 cm and 1 cm/s on translational position and velocity, 0.5° and 0.5°/s on attitude position and velocity.

IV. ATTITUDE MODULE MAIN FEATURES At the current state of the project, the AM is complete,

while the TM is being designed and planned for completion in the next few years. The Attitude Module (AM) is equipped with 5 main subsystems that allow it to execute an autonomous attitude maneuver (Fig. 2): (1) the Structural Subsystem; (2) the Propulsion Subsystem; (3) the Attitude Determination and Control Subsystem; (4) the Electric and Power Subsystem; (5) the Communication and Data Handling Subsystem.

Fig. 2. The Attitude Module (AM) at the current sate of the system.

In particular, the AM 3 DOF attitude motion is made possible by means of a Three-Joints System (see Fig. 3) with three consecutive rotational cylindrical joints�whose axes are orthogonal and meeting in a center of rotation. This system of joints is designed so that the first joint allows a rotation about the yaw axis coinciding with the vertical axis, the second one allows a rotation w.r.t. the pitch axis and the third one allows a rotation about the roll axis. Thank to this mechanical joints system, the AM can freely rotate around the yaw direction, while both roll and pitch angles are mechanically limited in the range [-40°, +40°].

In nominal conditions, i.e. with no friction and in a perfect balancing condition, the AM center of mass coincides with the Three-Joints System rotational center, resulting in a platform whose attitude dynamics does not depend on perturbing torques due to gravity and friction but only on control torques.

The AM mass balance was reached through a first placement of component pairs, as for instance two CFRP tanks or two manifolds (see below), or groups of components with similar mass at, as far as possible, symmetric locations w.r.t. the joints center of rotation. A more accurate mass balance was then achieved by placing trimming masses in a proper location following a trial and error procedure. Also, low fiction ball bearings were used to realize the joint system.

The Attitude Determination & Control Subsystem (ADCS) consists of attitude sensors that provide measurements on the AM orientation w.r.t. a Local Vertical - Local Horizontal (LVLH) External Reference Frame and electronic boards that perform the control action computation and properly command the Propulsion Subsystem for their actuation.

Satellite-to-Satellite link

Satellite-to-Control Station link

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Fig. 3. The Three-Joints System with roll axis in blue, pitch axis in green and yaw axis in violet.

In the current configuration, each simulator is equipped with two kinds of attitude sensors: (1) 3 Avago Technologies rotational optical incremental Quadrature Encoders (QE), which are used to measure the rotation of the joints with a resolution of 0 09°, thus directly providing Roll, Pitch and Yaw angular measurements; and (2) a Microstrain Inertial Measurement Unit (IMU), which provides an estimation of the AM attitude and attitude rate w.r.t. the External Reference Frame. Since the attitude estimation accuracy achievable with QE is by far better than the one achievable with the IMU, the QE angular measurements are used as a reference to evaluate drift and bias on the IMU measurements.

The AM is equipped with an electronic board assembly with a Digi International Rabbit RIO chip for the encoders reading and a Rabbit 29 MHz microcontroller that performs GN&C computation, thrusters actuations and communication processes with the Control Station and other Simulators using a dedicated communication protocol.

The on board Propulsion Subsystem consists of a high- pressure section with: (a) two CFRP tanks with a total capacity of 2 Lit. for the air storage at 200 bar maximum; (b) a fill & vent system for the pneumatic circuit loading; and (c) a pressure regulator that reduces the air pressure from the storage level to the nozzle operative level of 10 bar. The low-pressure section of the subsystem includes: (a) two 6-way manifolds that divide the air flow coming from the pressure regulator outlet to supply the thrusters; (b) 6 pairs of thrusters to actuate control torques; and (c) variable size plastic pipes to connect the elements of the low-pressure pneumatic circuit. Each thruster has a solenoid valve and a nozzle. Since this is an on-off system, a Pulse Width Modulation (PWM) scheme is adopted to actuate a control torque profile.

V. ATTITUDE MODULE ON BOARD THUSTERS FORCE AND INERTIA TENSOR CHARACTERIZATION

In order to test specific attitude control strategies, we needed to carry out some preparatory experimental activities aimed at characterizing the AM thrusters in terms of force levels and estimating the AM inertia tensor. Different methods for the inertia tensor identification of complex bodies are available [8]. Torsional or torque pendulum methods can be used to estimate the moment of inertia about a specified rotation axis passing through the system center of mass. The system under test oscillates about the rotation axis by means of a restoring torque generated by springs (or equivalent systems). The moment of inertia w.r.t. the rotation axis can be calculated from the measured oscillation period if the rotational spring stiffness is known.

We used a steel wire as the elastic torsional spring of a rotational measurement setup with two possible configurations: a Torque Pendulum system and a Torque Balance system. We first needed to characterize the rotational stiffness of the steel wire, since it is the sensitive element of the measurement setup for both the aforementioned configurations. The experimental activities plan is described in the following and summarized in Table I.

TABLE I. EXPERIMENTAL ACTIVITIES CONDUCTED

# Used System Measured quantity Estimated Quantity

1 Torque Pendulum

free oscillation period, T wire rotational stiffness, k

2 Torque Balance

equilibrium angle, θeq

thrust force, S

3 Torque Pendulum

free oscillation period, T AM inertia tensor, J

A. Torsional wire characterization To estimate the rotational stiffness of the torsional wire, we built a Torque Pendulum system with well known moment of inertia about the wire axis, I, and with the center of mass along the wire axis, as shown in Fig. 4, using components with well known mass and geometry. Making the Pendulum oscillate about the equilibrium position and taking several measurements of its free oscillation period T, the wire rotational stiffness k can be computed according to the following formula:

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TIk π= (1)

To measure the oscillation period of the pendulum, we used a photo-resistance system, in which a laser is mounted on the Torque Pendulum and a photo-resistance is placed along the trajectory that the laser follows during the pendulum oscillation. The photo-resistance is connected in series with a 1-kΩ measurement resistance Rm and integrated into the electronic circuit shown in Fig. 4. An Arduino UNO board connected to a laptop is used to measure the voltage Vm between the measure resistance ends over time with a acquisition frequency of 40 Hz. When the laser ray hits the photo-resistance, its electric resistance decreases, resulting in a peak on the measured voltage Vm. A Matlab program was then used to automatically evaluate the oscillation period T as the time period between two corresponding peaks in the acquired voltage time profile.

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Fig. 4. Experimental setup used for the Torque wire characterization with the photo-resistance based acquisition system.

There are two main uncertainty sources in this kind of system. The first one is related to lateral oscillations of the pendulum. These lateral oscillations can be manually damped using a thin stem placed at the pendulum base and along the rotation axis. The second uncertainty source is related to Vm sampling frequency f. This directly affects the accuracy of the oscillation period estimate, since the last one is the time interval between corresponding peaks in the Vm time profile. For a given maximum sampling frequency, which is related to the acquisition system clock-speed, lower relative uncertainty on T due to f can be achieved with a higher T or, equivalently, a higher pendulum moment of inertia I.

To validate the photo-resistance method, we used a second method, called webcam method, in which a web cam is used to record the laser ray passage over a reference point Pr marked on an external white screen. We then manually evaluated the time instants tk when the laser passed over Pr on the screen, calculating the pendulum oscillation period T as the difference of corresponding couples of tk's.

Several tests were conducted using both the photo-resistance and the webcam methods with a maximum angular amplitude of oscillation between 30° and 140° and a wire length of lw,1 = 956 mm. Fig. 5 shows a comparison between photo-resistance and webcam experimental results. Analyzing the experimental results we can state that measurements of T acquired with different θmax and with the two different methods previously described are consistent, since there exist a band between 4.69 s and 4.70 s that is common to all the measurements error bands. We can therefore exclude systematic error intrinsic to both methods. The photo-resistant method was therefore validated and it was used in the next two tests since it is simpler and more easy to automate than the webcam method. We can also conclude that the wire torsional stiffness does not significantly depend on the maximum angular amplitude of oscillation if θmax < 140°, since the mean value of T stays within the root mean square of each measurement.

Fig. 5. Test results of the photo-resistance method vs. webcam method.

The expected value of k for a steel wire with radius r = (1.00 ± 0.02) mm, length lw,1 = (956 ± 1) mm and modulus of rigidity G = (75 ± 6) GPa can be computed as:

%]14[)014.0123.0(2 1,

4

1 radmN

lGrk

w

±== π (2)

We estimated a Torque Pendulum moment of inertia about the wire axis of I = (6.07·10–2 ± 4·10–4) kg-m2 and a free oscillation period T = (4.70 ± 0.02) s. Using equation (1), the rotational stiffness of the wire k results k1 = (0.109 ± 0.002) N m/rad (2σ), where the uncertainty of k1 is computed with the following Kline-McClintock formula:

22

22 44 ⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=

Ti

Ii

TIi TI

k π (3)

where iI and iT are the uncertainties of I and T respectively. The relative uncertainty of k is ik,rel = 1.8% (2σ). The experimental result for k1 is also consistent with the expected theoretical value given by equation (2).

We conducted further tests setting the length of the wire to lw,2 = 935 mm by changing the wire length tightened between the two clamps. Experimental results gave us k2 = 0.111 Nm/rad, which is consistent with the previous experimental result k1 since k1·lw,1 = k2·lw,2 = πr4G/2 = const = 0.104 N m2/rad.

B. Thrust force estimation To estimate the thrust force produced by the AM thrusters,

we built a Torque Balance system (Fig. 6) with a vertical torque wire (the same wire characterized in the previous test), a pair of AM thrusters placed on an horizontal profile beam at a distance b/2 from the wire, two lasers at the ends of the profile beam, the AM attached under the beam (not shown in Fig. 6 for simplicity) and an external goniometer with an angular resolution of 0 5° to detect the angular position θ of the Torque Balance. The goniometer also has a set of concentric circles used with the pair of lasers to keep the wire axis on the goniometer center.

The Torque Balance system is in an equilibrium condition with θ = θeq when the torque of a pair of thrusters, τthr = S b, is balanced by the elastic torque due to the wire, τw = k θeq. Taking therefore measurements of the equilibrium angle θeq

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with known k and b, it is possible to estimate the thrust force as S = k θeq / b.

Fig. 6. Test results of the photo-resistance method vs. webcam method.

To characterize the AM thrusters in terms of thrust force as a function of the total pressure entering the nozzle, we conducted several tests measuring the Torque Balance equilibrium angle θeq for given values of the total pressure in the range 1.5 bar - 10 bar. The total pressure was measured using a pressure transducer placed at the thruster inlet. Experimental results are shown in Fig. 7.

Fig. 7. Thrust force S vs. total pressure p0 with: (a) experimental results with error band in red, and (b) least square linear regression results with 2σ error band in blue.

The experimental profile of S as a function of p0 is linear with good accuracy for 1.5 bar < p0 < 10 bar, as confirmed by the following results of a least squares linear regression: %]99[0457.0/0435.0)( 00 >−= rNpbarNpS (4) where r is the linear correlation coefficient of the two variables and p0 is in bar. When supplied with air at the operative total pressure p0,thr = 10 bar, the AM thrusters can produce a thrust force of S = (0.389 ± 0.007) N [2σ]. The thruster force is estimated with a relative uncertainty iS,rel = 1.80% [2σ].

C. Inertia tensor determination The aim of this last experimental activity was to estimate

the AM inertia tensor in the Body Reference Frame using a

Torque Pendulum setup, shown in Fig. 8, consisting of: (a) the torque wire in vertical position; (b) a horizontal profile beam with two lasers at the ends; (c) lateral profile beams and plates to support the AM in the required orientation and with the pendulum axis passing through the AM center of mass; and (d) an external photo-resistance based acquisition system. Taking measurements of the pendulum free oscillation period T with the photo-resistance setup, it is possible to estimate the moment of inertia of the whole rotating system Im,i,tot, which is equal to the AM moment of inertia about a selected direction, Im,i, plus the moment of inertia of the support system moving part Im,i,frame: )4/( 22

,,,,, πTkIII frameimimtotim =+= (5) Im,i,frame can be either computed, if the support system is simple with well known geometrical and mass properties, or experimentally evaluated using the same setup with only the AM supporting frame. The AM moment of inertia about a selected direction can be evaluated as Im,i = Im,i,tot � Im,i,frame.

Moment of inertia measurements about at least 6 independent directions, called measurement directions in the following, are in general needed to identify the complete inertia tensor, since in general (i.e., for a non principal reference frame) the inertia tensor is symmetric with 6 independent components.

Fig. 8. Torque Pendulum setup used to estimate Ixy and Ixz.

The AM inertia tensor accuracy is strongly dependent on both the measurement directions w.r.t. the AM Body Reference Frame and the number of measurement directions taken into account. A preliminary analysis was carried out to identify the measurement directions that could lead to a better estimation of the AM inertia tensor. Using past moment of inertia measurements and test results and considering the AM geometry, we estimated the three AM principal moment of inertia and the orientation of the principal reference frame w.r.t. the Body frame. This allowed us to compute the inertia tensor w.r.t. the Body frame, J, and simulate the moment of inertia measurements Im. Indeed, if ui is the i-th measurement direction, the corresponding AM moment of inertia is: ii

Tiim rI += Juu,

(6) where ri is a random noise with zero mean value used to generate more representative measurements, following previous tests. Let x = [Jxx, Jxy, Jxz, Jyy, Jyz, Jzz]T be the vector

Ixy Ixz

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with the n = 6 unknown independent components of the inertia tensor, then the following linear system holds: mIxA = (7) where A is a matrix whose components depend on the measurement directions and Im is the moment of inertia measurements vector. We selected a number of measurement directions, m, greater than 6 in order to improve the AM inertia tensor accuracy. The 6 components of the inertia tensor can be estimated as: m

TT IAAAx 1)( −= (8) The uncertainty associated to the inertia tensor components can be evaluated using the covariance analysis. The covariance matrix associated with x is: 12 )( −= AAC Tσ (9) where σ is the standard deviation of the moment of inertia measurements. We assumed a relative standard deviation of 4·10�3 at 1σ. For given uncertainties on the m moment of inertia estimates, lower uncertainties on the inertia tensor components can be achieved with a smaller value of the condition number of A and smaller values of the eigenvalues of C.

This preliminary analysis allowed us to identify the measurement directions shown in the first 3 columns of Table II. The corresponding condition number of A is 1.41 and the 6 eigenvalues of A are between 8·10�6 and 10�5. The selected measurement directions are a trade-off solution between: (a) simplicity of the corresponding hardware system; (b) good estimation accuracy; (c) number of measurement directions, thus acquisition time; (d) homogeneity of the error hyper ellipsoid.

TABLE II. SELECTED MOMENT OF INERTIA MEASURE DIRECTIONS AND MOMENT OF INERTIA EXPERIMENTAL RESULTS.

Estimated quantity

azimuth [deg]

elevation [deg]

estimate [kg m2]

uncertainty [%] (1σ)

Ixx 0 0 0.8851 3.05

Iyy 90 0 0.7760 2.82

Izz 0 90 1.4213 1.66

Ixy 45 0 0.7210 2.11

Iyx �45 0 0.9329 2.10

Ixz 0 45 1.1520 2.50

Izx 0 �45 1.1454 2.57

Iyz 90 45 1.0943 2.63

Izy 90 �45 1.0961 2.68

Following the procedure described above, we obtained an AM inertia tensor w.r.t. the Body reference frame of:

2

1.41860.0009-0.00330.0009-0.77390.1060-0.00330.1060-0.8823

mkg⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=J (10)

The principal inertia axes can be computed from the eigenvalues analysis of the AM inertia matrix. The resulting orientation of the principal reference frame w.r.t. the AM Body Reference Frame is given in terms of the following “1-2-3” rotations sequence: [φ, θ, ψ] = [�0.143, �0.381, �58.545] deg. These results were expected considering the AM mass distribution.

VI. CONCLUSIONS AND FUTURE PERSPECTIVES In this paper we presented the design and characterization

of the Attitude Module for the Satellite Formation Flight Testbed under development at the University of Padova. We used a simple and low cost rotational system in two configurations, torque balance and torque pendulum, in which a metallic wire acting as a torsional spring is the sensitive element. After the estimation of the wire torsional stiffness with a relative uncertainty of 1.8% (2σ), we estimated the force actuated by the thrusters on board the Attitude Module with a relative uncertainty of 1.8% (2σ) and the Attitude Module inertial tensor components with a maximum relative uncertainty of 4% (2σ).

Future activities for this project are: (a) testing of attitude control strategies using the AM; (b) design and realization of the Translational Module (TM), which will allow the hardware simulator to translate on a low friction plane by means of an air cushion system; (c) design and calibration of a 2D positioning system to estimate the TM position; and (d) testing of combined position and attitude control maneuvers.

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[3] D. P. Scharf, F. Y. Hadaegh, and S. Ploen, "A Survey of Spacecraft Formation Flying Guidance and Control (Part II): Control", Proceedings of 2004 the American Control Conlerence, 30 June - 2 July 2004, Boston, Massachusetts.

[4] J. L. Schwartz, M. A. Peck, and C. D. Hall, "Historical Review of Air-Bearing Spacecraft Simulators", Journal of Guidance, Control and Dynamics, vol. 26, no. 4, pp. 513-522, July- August 2003.

[5] M. Schlotterer and S. Theil, "Testbed for on-orbit servicing and formation flying dynamics emulation", AIAA Guidance, Navigation, and Control Conference, 2 - 5 August 2010, Toronto, Ontario, Canada.

[6] A. Saenz-Otero and D. W. Miller, "SPHERES: a platform for formation-flight research", MIT Space Systems Laboratory, Cambridge, Massachusetts.

[7] A. Caon, M. Cesaro and E.C. Lorenzini, "An attitude testbed for satellite formation flying research", Proceedings of 3rd CEAS Air & Space Conference, 24-28 October 2011, Venezia, Italy.

[8] C. Schedlinski and M. Link, "A Survey of Current Inertia Parameter Identification Methods", Mechanical Systems and Signal Processing, vol. 15, no. 1, pp. 189 - 211, 2001.

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