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 giovanni.palmerini@uniroma1.it

Paolo Gasbarri

DIAA Dipartimento di Ingegneria Aerospaziale e Astronautica/ Università di Roma La Sapienza/Italy Ph.+39.06.44585324 Fax+39.06.44585670 paolo.gasbarri@uniroma1.it

Riccardo Monti

DIAA Dipartimento di Ingegneria Aerospaziale e Astronautica/ Università di Roma La Sapienza/Italy Ph.+39.06.44585324 Fax+39.06.44585670 riccardo.monti@uniroma1.it

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.

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Palmerini GB, Gasbarri P, Toglia C (2009) Determination of kinematic state of an orbiting multibody

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(MA, USA)

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