International Global Navigation Satellite Systems Society IGNSS Symposium 2009
Holiday Inn Surfers Paradise, Qld, Australia
1 – 3 December, 2009
GNSS for Closed Loop Control of Space Manipulators
Giovanni B. Palmerini
DIAA Dipartimento di Ingegneria Aerospaziale e Astronautica/ Università di Roma La Sapienza/Italy Ph.+39.06.49919760/766 Fax+39.06.49919757 [email protected]
Paolo Gasbarri
DIAA Dipartimento di Ingegneria Aerospaziale e Astronautica/ Università di Roma La Sapienza/Italy Ph.+39.06.44585324 Fax+39.06.44585670 [email protected]
Riccardo Monti
DIAA Dipartimento di Ingegneria Aerospaziale e Astronautica/ Università di Roma La Sapienza/Italy Ph.+39.06.44585324 Fax+39.06.44585670 [email protected]
ABSTRACT
Future in-situ servicing space mission will be increasingly autonomous and
exploited by robotic manipulators to save risks and costs of human presence
onboard spacecraft. The accuracy and the bandwidth requested in such a
kind of manoeuvres are very high and a completely automatic control is
likely to be mandatory. Feedback control loops need the knowledge of the
state of the plant, usually gained in terrestrial applications by means of
encoders located at the joints of the manipulator. Due to specific
characteristics of space structures, i.e. the flexibility resulting from the limits
on the mass to be launched, encoders could not be really effective.
The paper proposes the possible use of GNSS signal – and specifically of its
phase - to define the kinematic state of the robotic arms during in orbit
(rendez-vous, docking, grasping) operations. Limited dimensions of typical
GNSS antennas allow for their distribution along the span of each
manipulator’s arm, to take into account flexibility effects. A really accurate
determination of the state of the system can be obtained, a result which
should be a quite complicate achievement by other possible techniques like
RF ranging or image analysis. The bandwidth granted for by GNSS receivers
is suitable for orbital manoeuvres, typically slow. As a drawback, a
substantial amount of computation is requested in order to perform a RTK
process; also, possible limitations due to multipath have still to be
considered. Preliminary experimental tests, performed with two-link robotic
arms moving on a limited friction table in order to validate the substantial
amount of modelling and the numerical simulation work already carried out,
are presented and discussed.
KEYWORDS: GNSS for Robotics, GNC (Guidance, Navigation and Control)
loop, GNSS in Space, RTK.
1. INTRODUCTION
Advances in aerospace engineering made the satellites, and above all the ones operating in
Low Earth Orbit (LEO), an essential component for several activities, including remote
sensing, telecommunications, search and rescue, geophysical studies and several others. The
very same advances in technique allow now to consider possible servicing of these satellite,
which are important assets to be maintained as long as possible by means of refurbishing,
refilling of hydrazine propellant, substitution of components failed due to launch loads, to
ageing or to radiation environment. A well known success story in servicing is represented by
the Hubble missions; at the same time, the problems that plagued NASA Shuttle suggested to
look deeper into the possibility of unmanned, therefore less risky and at the end less costly
robotic missions. DARPA actually succeeded in 2007 (see Wilson, 2007 and 2008, for an
overview) in showing the feasibility of automated autonomous in situ servicing missions. The
general concept can be depicted as a mission carried out by a grasper spacecraft which (1)
approaches the satellite to be serviced, (2) exploits the rendez-vous and the docking, (3) fixes
the satellite, (4) releases it and (5) comes back to a parking orbit, waiting for the next call on
duty. Essential element of this concept is the capability to build, deploy and operate in
autonomous mode a robotic manipulator. Being mounted on board of classical size spacecraft,
these manipulators should be maybe smaller in dimensions with respect to the successful
Shuttle Remote Manipulator System (SRMS) already known as CanadArm (length 15.2m /
diameter 38 cm / mass 410 Kg).
This paper is aimed to shortly explain the activities in this field currently carried on at the
Aero/Astro Engineering Dept of the Università di Roma La Sapienza, with a special focus on
the navigation aspects of the manipulator. The interest for the subject derived from previous
research activities performed in the field of multibody dynamics, with the build-up of detailed
models able to represent their special behaviour in orbit. In fact, the free-flying condition
remarkably differentiates the in-space from the terrestrial robotics, as any displacement of one
of the link invariably causes the reorientation of all the remaining. In addition the dynamics is
not easy to be numerically represented, due to the wide difference between the order of
magnitude of the acting forces, which are mainly the gravitational attraction, related to the
scale of the orbital radius, and its gradient, defined by the dimensions of the multibody links.
Moreover, due to peculiar characteristics of these structures, which are designed with the
constraint to limit as much as possible the mass at launch, also the flexibility effects, which
are related to the dimensions of the section of the arms, are to be considered. The availability
of numerical tools certainly allows for a better investigation of the guidance navigation and
control (GNC) loop needed to exploit in orbit servicing, but should be confirmed and
validated, at least partially, through even simple experiments. A short description of the test
bed built and of the foreseen future program is included.
2. MANIPULATOR GNC LOOP 2.1 GNC structure and requirements
As every feedback-controlled system, the manipulator behaviour depends on classical scheme
reported in following figure 1. The plant is represented by the dynamics of the manipulator,
which in this special case is capable to take into account, in addition to the gravitational
attraction and its gradient, also the more relevant perturbations which in LEO environment are
the oblateness of the Earth and the air-drag; specifically, the air drag has been included to
simulate ISS orbit (about 350 km altitude). The guidance portion is intended to define the
trajectory to be followed, once the requirements are known, and to possibly modify such
trajectory on-the-fly based on the current status of the system. Manoeuvres optimal with
respect to the time, to the torque needed or to the pointing maintained by the grasper satellite
during manipulator deployment and grasping are among the techniques for path planning
already coded, included in the GNC software and tested. The computation of the trajectories
can even include additional constraints as the obstacle avoidance, which is especially
important during the grasping in order to do not damage the satellite to be fixed (Toglia et al.,
2009). The control section currently refers above all to the actuators actually available in the
test-bed, i.e. stepper motors, even if Simulink (MATLAB) models for general classes of
electric motors have been prepared. The navigation section, which also includes the
estimation section based on Kalman filters to manage noisy measurements, is intended to
provide the current kinematic state (position and velocity) of the arms’ end as provided by
different possible sensors (see next paragraphs). As for closed loop logic, these measurements
are the elements of the comparison with the intended state, to be carried out by the guidance
system in order to provide required correction.
Figure 1. Closed GNC loop basic scheme
In the specific case, performance of the system guidance-control- navigation loop of the
manipulator should provide the required accuracy to make possible, without damaging it, the
approaching to and the grasping of the satellite-to-be-serviced, as well as the fixing operations
(order of the decimetre during the initial and of the centimetre in the final rendez-vous phases)
with even one order better during the fixing. Furthermore, this performance should be
provided with the required bandwidth (approximately 1 Hz with respect to the relative
motion, and possibly one order of magnitude more). Of course the GNC should perform
accordingly to the requirements even in presence of small variations in the plants’
characteristics, which are possible as a consequence of the stress at launch, as well as changes
in the computed environment, which is certainly modelled with the greatest accuracy but still
has remaining minor fluctuations (like density or solar radiation pressure), so that a
requirement for robustness also applies.
2.2 Possible Navigation sensors
The classical technique to determine the state of the links in robots is given by encoders
located at the joints. These devices, usually optoelectronic, can have analogic or digital
output, and easily provide the required accuracy at least for typical arms’ length (the angular
measure intrinsically leads to an error which increases with the distance from the joint). The
position of the end effector for a N-links’ arms can be found in a bi-dimensional geometry as
where L are the lengths of each link and are the relative angles at the joints of each arm with
respect to the previous one.
A different solution is offered by visual techniques, based on the analysis of the images
captured by cameras purposely located onboard the spacecraft or even on the manipulator
itself. From previous significant experiences, as the RDV-MON code (Casonato and
Palmerini, 2004) prepared as a preliminary study for the ISS-ATV rendez-vous later
performed by ESA’s Verne spacecraft, it is well known that such a technique requires a
substantial amount of data processing, whatever is the approach followed to recognize
suitable patterns in the images (in the recalled case, the Hough transform was the selected
method). Moreover, the visual techniques should require the allocation on the multibody’s
elements (and of the platform to be serviced) of a number of markers, which will be
recognized by the processing algorithms, and such a need actually limits the number and the
typology of the manoeuvres the system will be capable to perform. But the most important
constraint is given by the light condition, which deeply affect the process and which are
however strongly variable in the orbital environment (eclipse to sunlight transition,
reflectance of satellite’s surfaces). As a result, it can be agreed the significance of visual
technique for the last part of the grasping, and during fixing operations, where they probably
are the best and even the only solution; at the same time these techniques cannot be seen as a
possibility all along the manoeuvre. Also to be considered, remarkable variations in the
camera-to-the-scene distance during the intended manoeuvre can generate design drawbacks
for the optical system. Therefore, visual techniques cannot be considered as the sole mean to
exploit the navigation function of the loop. Instead, they will be the suitable solution for the
very last phase of the approaching manoeuvre, i.e. the docking, and for the servicing part:
during these phases, there should be limited variations of the light conditions, and the need for
markers should be superseded.
3. THE USE OF GNSS
The main weakness of the encoders is due to its mounting at the shafts, i.e. at the shoulder and
the elbow, preventing from the evaluation of the flexibility (see figure 2) . This is the reason
which suggested the possible use of GNSS. In fact, GNSS antennas are small and can be
located in discrete numbers all along the manipulator span (figure 3). Antennas’ output can be
redirected to a receiver processing the phase observables. Accuracies in the order of
centimetre or below is well inside the bounds required for the majority of the navigation tasks
of the manipulator (final docking and fixing phases would be intrinsically exploited by means
of visual techniques). With respect to the bandwidth requirement, such a GNSS solution could
certainly identify the deformed shape of the links due to flexibilities which encoders are blind
to. Moreover, in several case of practical interest it can also spot at least the first elastic mode,
which corresponding frequency is really low in typical space applications.
( )∑∑ ===
j
k kj
N
jEE Lx11
cos ϑ
( )∑∑ ===
j
k kj
N
jEE Ly11
sin ϑ
ϑ
Figure 2. The effect of the flexibility in a clamped beam
cannot be measured by an encoder located at the joint
Figure 3. GNSS antennas can be located all
along the arms’ span, to identify flexibility effects
Signal code- and carrier-based data should be considered in order to provide the centimetre
accuracy. Data can be prepocessed via a smoother algorithm, as the one originally proposed
by VanGraas and Braasch (1992), which recursive equations read at the step k as
)(11 −
+
−
−∆−∆+∆=∆
kPkPkCkC
kPkCkC qpp +=+
−
−
1
1)( −−−+=
kCkCkCk rppK
)(−−+
∆−+∆=∆kCkCkkCkC zK
−+−=
kCkkC pKp )1(
where ∆C is referred to pseudorange measurements double differences, ∆p to the carrier phases
observables double differences, pC is the covariance associated with carrier phases, and q and
r the relevant assumed variances on the process noise and on the measurements (represented
by zk), while Kk is the gain of the complementary filter which the previous equations
implement. Following figure 4 reports the smoothed solution with respect to the bare one,
directly computed by receivers’ provided pseudoranges, for a specific test-case which has
been exploited with the hardware introduced in the next paragraph.
0 50 100 150 200 2501.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
Figure 4. Smoothed double differences (m) vs. time (s) [blue line] w.r.t. bare data from
measurements. Data are referred to a test case similar to the one represented in following Figure 10
The level of accuracy obtained is still far from the one requested. A complete solution of the
classical interferometry problem resulting from the solution in terms of the GNSS signal
phase is requested, with the identification of the difference in the number of integer cycles
(ambiguitiy) among the lines of sight from the GNSS satellites to the antennas along the
manipulator’s arm. Following figure 5 and table 1 refer to the findings of a static case, still
obtained with the manipulator test-bed and the navigation hardware described later. The
solution for aligned arms (ideally provided by equal values for the angles α, β and γ defined
by three antennas located at the joints) has been obtained by an application of the LAMBDA
method (Theunissen, 1993 and Strange and Borre, 1997). Results are in good agreement with
data available in literature for baselines in the order of 1m.
Figure 5. Test geometry for 2 links manipulator
Angle
Α
β
Γ
GNSS processed
measurement (°)
9.81
9.03
9.71
Table 1. Attitude angles obtained for a 2D static test
4. THE EXPERIMENTAL SET-UP
In order to gain experience on real engineering problems, and to provide a meaning to the
simulations, a test bed, which is in continuous evolution, has been prepared in the DIAA labs.
Currently this set-up includes two arms commanded and controlled separately. The two
manipulators are similarly built, with shoulder and elbow motors, an arm of about 1 m length
and a forearm half of that length; while the shoulder is fixed, the elbow is hosted in a cradle,
supported by a sphere as in rotary bearings (figure 6). Different kinds of end effectors can
complete the arm in order to simulate a soft docking (via an electro-magnet) or a grasping (via
two fingers). All motors are stepper, and the relevant shafts are provided with digital opto-
electronic encoders (figure 7): even if steppers do not usually mount measurement units, in
this specific case such a coupling has been motivated to augment the available information
sources, monitor the motors’ performance in an independent way which allows for taking into
account the friction, and prepare for a possible change to brushless motors which are able to
provide higher torques. The shoulder motor is also equipped with a gear box to increase the
torque while reducing the speed, which is not actually a characteristic of interest for
manipulator applications. The two arms are controlled in a different way: one of them adopts
a typical industrial controller and the relevant software, while the other is controlled via an in-
house, ad hoc prepared MATLAB code running on a standard PC. In the latter, the control,
which clearly resulted as more versatile and flexible of the industrial unit, is exploited via the
PC-parallel port and two driver boards, one each for the motor. To completely separate logic
and power links, a board with opto-couplers has been interposed between the PC and the
drivers. Navigation data arrives to the PC via the RS232 port (and via the Bluetooth
connection for wireless GNSS receivers), while in the commercial controller case encoder
data can be directly input to the controller and GNSS data should be compared with targeted
position for the manoeuvre and then purposely formatted and inserted as constraints to the
motion. The arms move on a limited friction table while a complete frictionless suspension
system by means of air cushions is currently being completed.
Figure 6. One of the manipulators operating on the limited friction table,
with a side view of the elbow cradle and its rolling support
Figure 7. The encoder mounted on the elbow motor shaft
In addition to the encoders the state of the arms can be monitored by cameras fixed with
respect to the operating table, as well as determined via the GNSS. In detail, two possible
GNSS (currently GPS alone) setups have been tested. The first one, depicted in figure 7,
consists of a Septentrio PolaRx receiver, able to manage up to three different inputs which are
provided by three aeronautical grade antennas. The second setup, represented in figure 8,
include three separate compact receivers GARMIN G10 which download data wireless via
Bluetooth connection. Note that at the present time there is an indoor signal re-irradiation
capability but not available cluster of pseudolites in the DIAA lab, so that all tests including
phase observables (i.e. the ones required in this specific case) should be carried out outside
the lab with the wireless configuration remarkably fitting this constraint.
Figure 8. The two link manipulator equipped with Septentrio receivers and the set of aeronautical
grade antennas at the shoulder, elbow and end effector joints
Figure 9. The set-up equipped with the three GARMIN wireless units (the unit at the elbow has been
rotated in vertical position just to better show the motor shaft and gear). The board in the foreground is
the uncoupling section to PC, while the two green PCBs are the motor drivers
In order to gain experience on the hardware as well as to test the implementation of the
ambiguity-solving code, a set up using a tripod has been used for static measurements,
exploring different baseline lengths and different baseline orientation with respect to the
direction of the impinging signal from satellites. The same set-up can be used to evaluate the
possible multipath, and the relevance of the antennas’ altitude with respect to the local
ground.
Figure 10. The tripod used for preliminary static tests
4. FINAL REMARKS
The paper highlights the possibility to use GNSS signal (the phase of) to navigate space
manipulators during in-orbit servicing. The main advantage deals with the capability to take
into account flexibility effects, which can be really important due to specific characteristics of
space hardware. A short description of the experimental test-bed prepared in the labs of the
Aero/Astro Engineering Dept. at the Università di Roma La Sapienza is provided. Further
steps in the research project do include the identification of performing RTK techniques and
the evaluation of the accuracy actually achievable during manipulator manoeuvres, taking into
accountalso the multipath effects.
ACKNOWLEDGEMENTS Activities related to this research program have been partly carried out in the frame of a
MIUR/PRIN program on the navigation applications in aerospace engineering.
The Septentrio receiver used in the experimental set-up has been acquired from the Italian
dealer (Arvatech) on the basis of a specific educational contract.
REFERENCES Casonato G, Palmerini GB (2004) Visual Techniques Applied to the ATV/ISS Rendez-Vous
Monitoring”, Proceedings of the IEEE Aerospace Conference, Big Sky (MT, USA), paper 1526
Kaplan ED, Hegarty CJ Eds (2006) Understanding GPS: Principles and Applications, 2nd ed., Artech
House, Norwood (MA, USA)
Palmerini GB, Gasbarri P, Toglia C (2009) Determination of kinematic state of an orbiting multibody
using GNSS signals, Acta Astronautica 64: 1109-1122
Strange G, Borre K (1997) Linear Algebra, Geodesy and GPS, Wellesley-Cambridge Press, Wellesley
(MA, USA)
Toglia C, Sabatini M, Gasbarri P, Palmerini GB (2009) Optimal Manoeuvring of a Flexible Space
Manipulator for a Class of Objectives, 59th Congress of the International Astronautical
Federation, Daejeon (South Korea), paper IAC-09-C2.3.3
Van Graas F, Braasch M (1992) GPS Interferometric Attitude and Heading Determination Initial
Flight Test Results, NAVIGATION: Journal of The Institute of Navigation 38 (4): 297-316
Wilson JR (2007) Satellite hopes ride on Orbital Express, Aerospace America, February 2007, 30-35
Wilson JR (2008) Orbital Express Rendezvous and Renewal, Aerospace America, March 2008, 38-43.
Teunissen PJG (1993) Least-squares estimation of the integer GPS ambiguities, General Meeting of
the Internationale Association of Geodesy (invited lecture), Beijing 1993
Top Related