aas 05-480 the quest for brazilian space research - DEM

AAS 05-480
THE QUEST FOR BRAZILIAN SPACE RESEARCH
Hélio Koiti Kuga*
Roberto Vieira da Fonseca Lopes*
Valcir Orlando*
Maria Cecília F. P. S. Zanárdi†
This paper describes how QUEST1 (QUaternion ESTimator algorithm) influenced Brazilian space research activities. Indeed, we present a short survey paper on researches in attitude determination and propagation in Brazil arising
from the influence of the author of QUEST. We show how Brazilian researchers
started implementing “QUEST,” “tasting” it, and later deriving other applications based on it. Some Brazilian researchers worked out further investigations
through direct interaction with the QUEST author, Dr. Malcolm Shuster, addressing attitude alignment and calibration problems. Further related researches
show the influence of Dr. Shuster’s work on Brazilian space research.
INTRODUCTION
This paper describes how the QUEST1 (QUaternion ESTimator) algorithm influenced Brazilian space research activities. Its really was a “quest” for Brazilian researchers to build up the background needed to carry out the tasks in attitude determination for
artificial satellites. We begin with the description of the early initiatives of INPE (Brazilian Institute for Space Research) in this area, then we report on the work of Dr. Malcolm
Shuster as well as on his friendship toward the Brazilians. In the early days, his famous
QUEST paper was almost required hazing for the rookies in the field at INPE. We began
implementing QUEST and performing related research such as other QUEST-based applications. In Brazil, such activities were restricted at that time to INPE. From the beginning we realized the potential of QUEST as a fast accurate attitude preprocessor which
could afterwards by smoothed by a Kalman filter. We even applied the idea to GPS positioning, creating the algorithm “ORBEST” named after QUEST. ORBEST uses essentially the main chain of concepts applied in QUEST. Some Brazilian researchers (from
INPE and Academia) have had a long and close interaction with Dr. Shuster in the USA
(in Florida and in Maryland) carrying out research related to attitude alignment and calibration problems. At the end of this work we summarize the current researches in progress. The heritage of Dr. Shuster’s work in attitude algorithms developed in Brazil is
truly remarkable and continues to this day.
*
INPE - Instituto Nacional de Pesquisas Espaciais, PO BOX 515 - Sao Jose dos Campos, SP, 12245-970
Brazil
†
UNESP - Sao Paulo State University, Department of Mathematics, PO BOX 205 - Guaratingueta, SP,
12500-000 Brazil
533
EARLY INITIATIVES
In 1977, at the very beginning of the creation of the Division of Space Mechanics
and Control (DMC) at INPE, human resources were guided by the Brazilian Complete
Space Mission, a Brazilian government program for space research with the aim of
launching and operating Earth-orbiting artificial satellites. Within the DMC the area of
orbit and attitude dynamics was only beginning to be developed and was very dependent
on Brazilian Ph.D.s coming from American universities.* Orbit and attitude estimation
were strategic areas of development. At the end of the 70’s, Prof. Atair Rios Neto, who
had carried out research on orbit determination using Kalman filtering,2 was the head of
the DMC and teaching estimation theory at INPE. Soon the DMC became a den of enthusiasts on Kalman filtering, dynamic model compensation, adaptive noise and so on.† Attitude determination activities at INPE began with the work of Roberto Lopes,3,4 who applied the extended Kalman filter to estimate the attitude quaternion and the angular velocity vector of a three-axis-stabilized satellite. The dynamic-model-compensation technique
together with an adaptive noise scheme developed by Rios Neto and Kuga,5 coped with
the very limited information for the satellite attitude dynamics. The algorithm was intended for application to the first Brazilian meteorological satellite SCD-1, that was being
designed as a gravity-gradient-stabilized satellite. Later on, SCD-1 became a spinstabilized satellite, and the application of Lopes’ results would be postponed to a future
mission.
Following these earlier researches, Cardenutto6 in his master’s thesis used gyros
and a kinematic model for attitude estimation of a future remote sensing mission. Then
Valtair Ferraresi’s work7,8 addressed the singularity of the quaternion error covariance
matrix in a Kalman filter algorithm. In this scenario, it seemed natural to add QUEST1 to
the attitude estimation environment. The next to pursue his M.Sc. was Sebastião Varotto,
a highly gifted student, who accepted his difficult research assignment with gallantry‡. He
made a sequential combination of a static estimation based on the QUEST algorithm with
a state estimation of a dynamical system based on the dynamic model compensation
technique9. His work10 was presented to the Brazilian Control Society (SBA), which is
indeed a scientific community highly specialized in state-estimation theory and applications. Nevertheless, we felt that apart from INPE a full appreciation of Varotto’s work by
people with a background in spaceflight had not yet been achieved.
Closing that early cycle of research on attitude determination, Ulisses Guedes11 in
1989 applied the extended Kalman filter to the spin-stabilized satellite case in time to be
used in the SCD-1 mission, while Lopes12 studied the effect of the sampling rate on adaptive filtering techniques with applications to three-axis attitude determination. All those
works2-12 were in Portuguese.
*
Prof. G. E. O. Giacaglia and Prof. Atair Rios Neto, both from University of Texas at Austin, and Prof. O.
Maizza Neto from MIT.
†
Kalman filter was nicknamed “Bombril: 1001 utilities” at the DMC, named for a well-known Brazilian
kitchen cleanser and 1000 other applications. Getting a M.Sc. degree at DMC had became nearly synonymous of finding an application for the Kalman filter, despite some quite understandable jealousy from those
not sympathetic to the probabilistic approach.
‡
And survived the QUEST hazing.
534
INTRODUCING DR. SHUSTER
The work of Varotto9 using QUEST as a preprocessing algorithm to the extended
Kalman filter was a difficult task for the young INPE flight dynamics team at INPE. It
took countless hours of mathematical derivations in order to understand the intriguing
and fascinating algorithm QUEST. The members of the team had been working on developing software for non-real-time attitude determination for the ground-tracking and control segments. What was most important to this work was the QUEST measurement
model. Once the proper way to evaluate the attitude-error covariance matrix from direction measurements was understood, the team became keen to apply it to many problems,
starting with Varotto’s work. This work was not constrained to attitude determination, as
demonstrated by the newly created ORBEST algorithm13. The static orbit-estimation algorithm ORBEST using GPS measurements, took many ingredients from QUEST, starting with Wahba’s problem, developing the inner algorithm, and developing a similar error model. QUEST, clearly, was the main inspiration for this research.
Not much later, Dr. Luc Fraiture, a visiting attitude expert from ESA (European
Space Agency) advised us that the attitude determination software for the SCD-1 mission
should be modular (attitude sensor data preprocessor; static attitude estimator; and dynamic attitude estimator) in order to simplify software development and testing as well as
the identification of possible software flaws after launch. It was a first external indication,
although an indirect one, that a QUEST preprocessor was a good route.
An amazing letter* from Dr. Malcolm Shuster to Dr. Rios Neto on Varotto’s research surprised us all. Dr. Shuster was somehow aware of our work involving the
QUEST algorithm, and surprised us in the middle of 1989 with a letter in Portuguese! In
this letter he commented on his knowledge of the QUEST work at INPE, and that he
would appreciate contact with INPE engineers. This was again surprising, because our
publications were all written in Portuguese. Dr. Shuster did not hesitate to give us priority
for developing the procedure which uses QUEST as an observation preprocessor for the
Kalman filter in attitude determination9,10. There, the whole attitude estimation process is,
basically, performed in two phases. In the first phase a preliminary estimate of the attitude parameters is computed using QUEST for the current sample of simultaneous observations, while in the second phase, these single-time estimates are improved using the
Kalman filter. The state vector is composed of the four quaternion elements and by the
three components of the angular velocity, that is:
9
xT(t) = [qT(t) : ωT(t)].
(1)
The 4x4 error covariance matrix of the single-time quaternion estimates from
QUEST is singular, since the quaternion is constrained to have unit magnitude. Owing to
this, the direct use of the quaternion estimates generated by QUEST as attitude observations in the Kalman filter imposed an additional difficulty in the update step. This phase
requires the inversion of a 4x4 matrix, which is composed of the sum of two other matri*
A delightful account of the event and the follow-on can be found in the paper of Dr. Shuster14 in 1990 (in
Portuguese) and in a longer version in English15 in 2001.
535
ces presenting the same kind of singularity. The solution to this problem was to estimate
the update correction of the state vector defined by Equation 1 using an incremental quaternion, as in the multiplicative filter of Lefferts et al.16 Thus,:
δq = qˆ * ⊗ qV ,
(2)
where δq is the incremental quaternion, qV is the true quaternion, q̂* is the conjugate of
the quaternion estimate, and ⊗ denotes quaternion multiplication. The details of the further algebraic development can be found in Refs. 9 and 10.
Another INPE work7 that has been mentioned by Dr. Shuster14,15 was an analysis
of four procedures for autonomous attitude determination. The motivation was to analyze
and compare the performance of an attitude determination procedure developed in-house6
that combines the measurements generated by inertial sensors (gyros in a strap-down
configuration), and by non-inertial sensors (sun and horizon sensors), with three related
procedures presented by Lefferts et al.16 The analyses encompassed aspects of order reduction of the covariance matrix, re-normalization of quaternion estimate, numerical
problems due to the singularity of the 4x4 quaternion covariance matrix, and adaptive
noise estimation to deal with filtering divergence.
Thus began a quite fruitful cooperation between INPE' and the author of QUEST.
The first official visit of Dr. Shuster to INPE was in 1990 as an invited lecturer15 at the
BSAT (Brazilian Symposium on Aerospace Technology). The first meeting of Dr. Shuster with INPE people occurred late in 1989 at the Space Dynamics Symposium held by
CNES (French Space Agency) in Toulouse, France. Dr. Shuster, at that epoch was at the
Applied Physics Laboratory (APL) of The Johns Hopkins University, where he presented
a paper.17 There, Dr. Wagner Sessin, a professor* at ITA (Brazilian Technological Institute of Aeronautics), and INPE engineer Valcir Orlando had the opportunity to meet Dr.
Shuster personally and prepare for his visit to Brazil the following summer.
INPE and CTA (Technical Center of Aeronautics) in 1989 and 1990 were jointly
organizing the (first) Brazilian Symposium on Aerospace Technology (BSAT) at São
José dos Campos, headquarters for both INPE' and CTA. This event was the occasion for
Dr. Shuster’s visit to Brazil. In this way, the possibilities of technical contact with Brazilian researchers would be restricted not only to INPE staff, but could be extended to other
Brazilian research institutions and universities attending the symposium. INPE’s attitude
determination people could finally face the man who they considered a kind of intangible
international personality. Besides the very profitable technical meetings with Dr. Shuster
a remarkable and surprising fact also needs to be in the records: he presented his lecture
speaking in Portuguese.†
*
The beloved and deceased Prof. Wagner Sessin was an expert in Celestial Mechanics and became a very
good friend of Dr. Shuster.
†
At this memorable occasion Dr. Shuster presented the DMC with a plaque bearing a bottle of aspirin to
atone for the headaches endured by the DMC staff when trying to understand QUEST.
536
In Brazil Dr. Shuster is known to many people as Dr. Malcolm. Brazilians tend to
use either the first name or the last name in all occasions, and Dr. Shuster preferred to be
called Dr. Malcolm by strangers rather than to be called Shuster by his friends. We will
follow this practice where appropriate in the remainder of this paper.
SPACECRAFT SENSOR CALIBRATION AND ALIGNMENT
In 1993, a postdoctoral fellowship was arranged for Roberto Lopes allowing him
to collaborate with Dr. Malcolm for two years in the United States.* The research focused on in-flight distortion and misalignment calibration of star-trackers. Of special interest was the interference of distortion and alignment parameters in the calibration. The
work was presented at an AAS conference18 and was published later in the Journal of the
Astronautical Sciences19.
Meanwhile, the INPE flight dynamics team of the DMC survived its trial by fire
with the successful orbit and attitude determination for SCD-1 satellite launched in February 1993, as reported at the International Symposium on Space Flight Dynamics20 held
in Brazil at the one-year anniversary of the launch. Dr. Malcolm was invited to be a
member of the program committee of the Symposium, and was also a presenter. An account on the SCD-1 experience has been described.21 A second mission (SCD-2) followed in 1998 and was equally successful.22
The development of Brazilian work on spacecraft sensor alignment estimation
started during Dr. Cecília Zanardi’s post-doctoral fellowship at the Department of Aerospace Engineering, Mechanics and Engineering Sciences, at the University of Florida, in
a joint research project with Dr. Malcolm, who had become a professor of Aerospace
Engineering at the University of Florida. Dr. Zanardi’s interest arose during the First
BSAT in Brazil in 1990, where Dr. Malcolm’s lecture15 about the early history of
QUEST was presented. Dr. Zanardi† was primarily interested in attitude dynamics but at
the symposium she became interested in new developments in attitude estimation as well.
In 1995, she began her collaboration with Dr. Malcolm at the University of Florida. She
attended Dr. Malcolm’s lectures and had many discussions involving general problems of
spacecraft attitude determination and estimation theory. Afterwards Drs. Malcolm and
Zanardi directed their research toward developing better approaches to sensor alignment
estimation.
Alignment estimation plays an important role in space. A complete treatment of
batch estimation of spacecraft sensor alignments from flight data had been published previously23,24. The use of these batch techniques, however, required the attitude data to be
arranged in repeated frames of simultaneous measurements. Two different filter approaches for in-flight estimation of the attitude sensor misalignments were studied and
*
The research work took place at the University of Maryland, under the official supervision of Prof.
William S. Levine, an arrangement made necessary by the restrictions on foreign visitors at APL.
†
Prof. Maria Cecilia F. P. S. Zanardi currently holds a post at Sao Paulo State University and is very grateful for having the opportunity to work with Dr. Shuster.
537
presented by Zanardi and Shuster.25,26 The first approach is the application of the Kalman
filter, in which the sensor misalignments are part of the filter state vector. The dimension
of state vector can be very large as the spacecraft may have many sensors. This high dimensionality, coupled with the nonlinear dependence of the measurements on the attitude
can lead to poor convergence of the filter in addition to a large computational burden.
This approach was called “naïve” Kalman filter alignment estimation. In the second approach the alignment vector is not included in the state vector and the Kalman filter is
applied to estimate only the attitude quaternion and gyro biases. Since the alignment quaternions are static, these can be estimated by a simple batch least-squares method. Of
particular importance is the fact that such an approach greatly decreases the dimension of
the Kalman filter and, hence, should lead to enhanced numerical stability. In addition,
because the misalignments are computed in batch mode, there are no numerical problems
arising from the presence of a largely indeterminate state vector at the beginning of the
filter computation. This approach was named the “hybrid” method. Illustrations of the
efficacy of the hybrid method compared to the “naïve” and the batch ones were reported
for an increasing number of sensors (3, 5, 10, 15, 20) randomly oriented over the spacecraft as well as an account of computational burden savings. The hybrid method is also
expected to be less sensitive to outliers and is to be preferred in general. The details can
be found in Refs. 25-26.
RECENT DEVELOPMENTS
Since 1994, the research on attitude determination at INPE unfolded in two main
areas: star identification and attitude determination from the GPS carrier phase, which
includes integer ambiguity resolution and multi-path interference mitigation, as described
in the sequence. With time these activities included the participation of a wide academic
community including: the Universidade Estadual de São Paulo, the Universidade Federal
do Paraná, the Universidade Federal de Ouro Preto and the Universidade Estadual de
Londrina. It is also necessary to acknowledge that relevant researches were developed
nearly independently from INPE at the Instituto Tecnológico de Aeronáutica (ITA),
which is mainly concerned with aeronautical applications, but eventually these were used
in space applications as well. We cannot describe the full scope of Brazilian research in
this area in the present paper.. A short survey of Brazilian researches was published in
2000.27
Star Identification
Any practical work on attitude determination from star observations does not go
far before facing the star identification problem. This yielded a series of scientific works
at INPE culminating in the thesis of Carvalho,28 which implemented several star identification algorithms and compared their performance in different flight scenarios. The results were published in part in Ref. 29. The optimization of one of the algorithms was
addressed later by Lopes30 in 2002.
538
GPS applied to attitude determination
The advent of GPS (Global Positioning System) and the investigation of its application to spacecraft orbit determination had attracted the attention of INPE’s flight dynamics team long ago12. Interest was renewed during a short-course offered by Prof.
Leick at the University of São Paulo in 1995 based on his book31. After that, INPE and
the Federal University of Paraná carried out a joint experiment32 with two GPS antennas
on a rotating baseline. The experiment was part of a doctoral dissertation dealing with
spin-axis attitude determination from carrier-phase double differences. A simple scheme
valid for the spin-stabilized case at low angular rates was developed33 to cope with the
integer ambiguity. The algorithm was later improved during a program carried out at
DLR (German Aerospace Research Institute) in 1999 where the angular-rate constraint
was removed.34 This program also examined two GPS antennas on a rotating baseline,
but under better controlled conditions. Furthermore, there was an intentional multi-path
interference in order to study the effectiveness of mitigation techniques. This yielded
some interesting analogies with the star-sensor calibration problem studied by Shuster
and Lopes.18 The errors in the line of sight of the GPS satellites caused by multi-path
interference were considered as errors on the star observations due to distortion on the
star sensor. A first algorithm was developed using a series of surface spherical harmonics
to model the multi-path effect.35 The application of the Lopes-Shuster prescription that
the distortion and its curl vanish at the sensor null worked perfectly and assured the consistent convergence of the estimation process for the calibration parameters. As an alternative to the series approach, it was considered to use neural networks to represent the
effect of multi-path interference. The research was developed in two stages: first the attitude was considered to be perfectly known during the learning phase of the neural network algorithm,36 and then the attitude was estimated during the learning phase37. The
Lopes-Shuster prescription was slightly modified to adapt to the neural network case and
worked equally well.
As happened with the star-identification problem, in order to perform practical
work with attitude determination from the GPS carrier phase, it was necessary to study
the integer ambiguity resolution algorithms. One result in this field was published38 at the
ION-2002 (Institute Of Navigation) conference. It takes advantage of the dynamical motion of the GPS constellation as well as of the satellite attitude motion to find an attitudefree nonlinear matrix equation in the integer ambiguities.
Attitude Dynamics
In this field, most of the researches were addressed by Cecilia Zanardi who, after
her stay with Dr. Malcolm at the University of Florida, began research on optimal attitude
control, attitude estimation and the study of quaternion, and magnetic torque effects on
the attitude dynamics. Classical models of gravity-gradient, solar-radiation, aerodynamic,
and magnetic torques acting on a circular-cylindrical satellite were discussed in Ref. 39,
where the magnitudes of each torque are compared parametrically in terms of its size and
its orbital altitude.
539
A first-order analytical model for the general problem of artificial satellite attitude-adjustment maneuvers was discussed in Refs. 40-42. Basically the problem is approached using the Mayer formulation and Andoyer’s attitude variables. The Pontryagin
Maximum Principle is applied, with optimal attitude corrections obtained via Hamiltonian linearization. The numerical solution is generated by the application of the multipleshooting method to the two-point boundary-value problem.
Analytical approaches for spin-stabilized satellite attitude dynamics were presented in Refs. 43-46, where numerical simulations performed with attitude data from
Brazilian satellites showed good agreement between analytical solutions and actual satellite behavior.
The dynamical equations for the rotational motion of artificial satellite in terms of
different representations (Euler angles, Andoyer variables and the quaternion) have also
been analyzed47. Numerical solutions for dynamical equations in terms of the quaternion
and the angular velocity is discussed,48 taking into account gravity-gradient and residual
magnetic torques. Spacecraft attitude determination algorithms, using the maximum likelihood method49 and Kalman filtering16 are currently under investigation.
FURTHER ADVENTURES
Besides GPS and star sensors, there are some other related researches to be mentioned. Louro50 is currently studying the fusion of data from GPS and a MEMS (Micro
Electro-Mechanical System) gyro unit to deal with fault detection to obtain an algorithm
suitable for real-time implementation. Another area is the simultaneous estimation of
orbit and attitude. This problem was first studied51 using a three-axis magnetometer and a
one-axis digital Sun sensor to estimate the orbit and the spin axis attitude of the SCD-1
satellite with orbit accuracy on the order of 100 km. Recently, this subject is being addressed in a master’s thesis outlined in Ref. 52. The case of orbit and attitude determination from GPS measurements of a three-axis stabilized satellite is being investigated53 as
well.
Another field of recent interest is attitude determination from sensors based on
MEMS technology, namely magnetometers and gyros. The Brazilian Space Agency
(AEB) has induced some Brazilian universities to study this problem, and as a result there
are two independent teams at the Universidade Estadual de Londrina and the Universidade Federal de Ouro Preto developing algorithms under the supervision of INPE.
Finally, Lopes54 has followed the ideas of one of Dr. Malcolm’s masterpieces55
and extended the Euler equations for attitude dynamics to N-dimensional space. The
work defines a vector product as a skew-symmetric dyadic and finds the equivalent expression to the angular momentum conservation law. Despite its unknown practical usefulness, this work demonstrates the extension of the Dr. Malcolm’s impact on the Brazilian flight dynamics community, starting particularly at INPE and spreading further.
540
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541
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