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Active debris removal: Aspects of trajectories, communication
and illumination during final approach
J.A.F. Deloo, E. Mooijn
Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 1, 2629 HS Delft, The Netherlands
a r t i c l e i n f o
Article history:
Received 18 April 2015
Received in revised form
1 July 2015
Accepted 3 August 2015
Available online 15 August 2015
keyword:
Active debris removal
Final approach
Passive safety
Communication blockage
Illumination
E.deorbit
a b s t r a c t
The aim of this research is to investigate a debris-remediation technique where a chaser
performs a rendezvous with the debris, establishes a rigid-link connection, and actively
de-orbits the debris. ESA's satellite Envisat has been used as a design case. The research
assessed passive safety aspects of the final-approach manoeuvres by analysing the
resulting trajectories after thrust inhibit. Next, the research explored the possibility for
continuous ground communication by considering the chain of European space tracking
(ESTRACK) ground stations (located mainly in Europe). Furthermore, obstruction of the
communication signal by the target was studied. Last, the research studies the illumina-
tion conditions encountered by the chaser, where obscuration of the Sun by the target was
taken into account. Each of these elements are studied for the final approach only. In the
topic of passive safety, the results confirm that manoeuvres on H-bar are passively unsafe,
and indicate this also for the fly-around manoeuvres along the natural orbital motion. It
can be concluded from the communication analysis that the maximum duration of the
uninterrupted window varies between 22 and 32 min, using the chain of core ESTRACK
ground stations. However, the study on communication blockage shows that frequent
communication gaps can occur, with the longest gaps being in the order of one minute in
duration. In the field of illumination, it can be concluded that correct target illumination
and sensor visibility cannot be guaranteed. Furthermore, the average solar-array area
available during final approach varies between 35% and 75%, due to both incorrect
pointing of the solar array by the chaser and obscuration by the target.
& 2015 IAA. Published by Elsevier Ltd. All rights reserved.
1. Introduction
Recent studies on the instability of the debris popula-
tion in low-Earth orbit (LEO) have shown that the envir-
onment has reached a point where collisions among
existing debris will result in the population to increase,
even without any new launches [1]. This scenario is called
the Kessler syndrome. Studies show that it is required to
remove five large objects per year from highly populated
orbits (e.g., LEO) to stabilise the projected growth [2,3].
These studies assume active mitigation measures for new
launches on top of the removal of five large objects.
However, not all new launches comply with these end-
of-life strategies, and because there are still break-ups
every year the growth prediction is a dynamic feature.
More recent studies show that at least five to ten large
objects should be removed per year [4,5]. Because the
natural orbital decay of defunct objects alone will not be
sufficient, active debris removal (ADR) has to be used.
Such active removal can be achieved in different ways.
One way would be to hook up to a (passive) target with a
Contents lists available at ScienceDirect
jo urnal hom epa ge: www.elsevier.com/locate/actaastro
Acta Astronautica
http://dx.doi.org/10.1016/j.actaastro.2015.08.001
0094-5765/& 2015 IAA. Published by Elsevier Ltd. All rights reserved.
n Corresponding author. Tel.: +31 15 278 9115.
E-mail addresses: jonathandeloo@gmail.com (J.A.F. Deloo),
e.mooij@tudelft.nl (E. Mooij).
Acta Astronautica 117 (2015) 277–295
http://www.sciencedirect.com/science/journal/00945765http://www.elsevier.com/locate/actaastrohttp://dx.doi.org/10.1016/j.actaastro.2015.08.001mailto:jonathandeloo@gmail.commailto:e.mooij@tudelft.nlhttp://dx.doi.org/10.1016/j.actaastro.2015.08.001http://dx.doi.org/10.1016/j.actaastro.2015.08.001http://dx.doi.org/10.1016/j.actaastro.2015.08.001http://dx.doi.org/10.1016/j.actaastro.2015.08.001mailto:e.mooij@tudelft.nlmailto:jonathandeloo@gmail.comhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.actaastro.2015.08.001&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.actaastro.2015.08.001&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.actaastro.2015.08.001&domain=pdfhttp://dx.doi.org/10.1016/j.actaastro.2015.08.001http://dx.doi.org/10.1016/j.actaastro.2015.08.001http://dx.doi.org/10.1016/j.actaastro.2015.08.001http://www.elsevier.com/locate/actaastrohttp://www.sciencedirect.com/science/journal/00945765
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tether by harpoon or net [6], and either passively (with an
electrodynamic tether that induces a Lorenz force by
interacting with the Earth's magnetic field [7]) or actively
(by pulling with a dedicated propulsion unit or actual
spacecraft [8,9]) remove the target from orbit such that it
will enter the atmosphere. Another option could be that of
a rendezvous of an active chaser spacecraft with the target,
dock to it, and use the chaser's propulsion system to forcethe combination to deorbit and move towards the
atmosphere.
An ADR study, named e.deorbit, has been carried out at
the European Space Agency (ESA) to investigate the
possibility for an ADR mission using a chase and catch
approach. The e.deorbit mission aims at removing a single,
large, non-operational satellite from LEO and is intended
for launch in 2021 [10]. In that research a rigid-link
connection has been considered between the chaser and
the target. Such a mission faces major challenges in the
rendezvous, capture and de-orbit phase of the mission.
The rendezvous mission is typically divided into a
number of main phases. After launch and injection of thechaser into the orbital plane of the target, the orbit phase
angle will be reduced to bring the chaser roughly in the
vicinity of the target. With relative navigation, the far-
range rendezvous guidance will transfer the chaser from
the phasing orbit to a first aim point in close vicinity of the
target. The close-range rendezvous consists of two sub-
phases, notably the final approach to the capture point and
the closing phase to acquire the final-approach line.
Finally, the actual docking takes place by establishing a
structural connection. The main focus of this paper will be
on the final-approach phase up to, but not including, the
docking to the target.
Fehse [11] describes a number of challenges for an ADR mission, among others absolute and relative navigation
including the required sensors during the rendezvous, as
well as the capture process and structural connection
between chaser and target. The main challenge comes
from the fact that the target is uncooperative. The rendez-
vous with uncooperative objects requires flexible guidance
strategies to cope with variable target motions. To avoid a
catastrophic collision between the chaser and the target,
passive safety measures must be incorporated in the
trajectory design. Proper communication and illumination
conditions, or rather lack thereof, only contribute to the
complications.
Communication conditions for a non-cooperative ren-dezvous mission in LEO are expected to be very
demanding for orbit control. To begin with, the commu-
nication windows in LEO are relatively short. Per ground
station a communication window of roughly 10 min may
be expected. The lack of communication with the chaser
during the final approach would require high on-board
autonomy of the chaser, which is undesired in a novel
mission that implements many immature technologies.
Therefore, it would be beneficial to have continuouscontact with the spacecraft during the final approach,
such that the rendezvous can be humanly supervised. This
can be envisaged by using a chain of ground stations. For
rigid-link connections, the distances between the chaser
and target will be small during the final approach to allow
for capturing the target. As a result, the communication
signal may be obstructed from reaching the ground
stations.
The illumination conditions in LEO can be quite chal-
lenging for rendezvous, not only for navigation sensors
that require visible light, but also for power supply of the
chaser. Due to the short orbital period (90–100 min), the
Sun direction changes quickly in time. Also, a large part of the orbit is eclipsed (except for orbits near the dawn–dusk
region). The navigation system must be able to cope with
these conditions. The small distance required between the
chaser and target during the final approach also impacts
the energy that can be produced by the solar array,
because it cannot be guaranteed that the solar array is
able to receive Sunlight, as it may be obscured from the
Sun by the target. At the same time, the power require-
ments during the final approach may become high due to
the use of a robotic arm, navigation sensors and artificial
lighting.
This research addresses the challenges identified above,
which can be classed in three categories: final approach,communication and illumination. The structure of this
paper is as follows. First, in Section 2 the models and
definitions adopted in the research are summarised.
Section 3 describes the methodology of the research. The
results of the research are presented in Sections 4, 5, and 6,
respectively. Section 4 deals with the final approach,
Section 5 with communication, and Section 6 with illumi-
nation. Finally, Section 7 summarises the conclusions of
the research.
2. Denitions and models
The research has been performed in the framework of ESA's e.deorbit feasibility study and therefore the
Nomenclature
Roman Symbols
r Position vector (m)
[ x, y, z ] Position vector components (m)
t Time (s) V Velocity (m/s)
½ _ x; _ y; _ z Velocity vector components (m/s)
Greek Symbols
α Azimuth (rad)
γ Acceleration vector ðm=s2Þ
½γ x; γ y; γ z Acceleration vector components ðm=s2Þ
Δ x Change of quantity x (-)
ϵ Spacecraft elevation angle (rad)θ Elevation (rad)
ω Mean motion (rad/s)
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definitions of the research have been mainly determined
by these study parameters. The models for the spacecraft
have also been based on the mission covered by this study.
The definitions and models of the research are des-
cribed below.
2.1. Requirements
A number of relevant requirements related to rendez-
vous, communication and illumination aspects are listed in
Table 1. These requirements come from the e.deorbit
Phase A mission requirements document (MRD) [10].
2.2. Relative orbital motion
The local vertical, local horizontal (LVLH)-frame is a
commonly used reference frame in the field of relative
orbital motion. The origin of the LVLH-frame is generally
the centre of mass (CoM) of the (target) spacecraft. The
LVLH-frame is illustrated in Fig. 1(a), where r and V
represent the in-orbit position and velocity vector, respec-
tively. The axes of the LVLH-frame are defined as follows:
the þ z -axis towards the CoM of the Earth, the þ y-axisopposite to the direction of the orbit angular momentum
vector, and the þ x-axis completes right-handed coordi-
nate system, roughly in the direction of the orbital velocity.
The x-, y- and z -axes are commonly denoted by V-bar,
H-bar and R-bar, respectively. The orientation of a vector in
the LVLH-frame will be defined by the azimuth angle, α ,and elevation angle, θ . The azimuth defines the directionof the vector projected on the XY -plane. The azimuth is
measured from 0 to 360 1C starting from the þ x-axis
towards the þ y-axis. The elevation represents the angle
between the vector and the XY-plane. The elevation is
measured from 90 to 90 1C and is positive towards theþ z -axis. The azimuth and elevation angles are illustrated
in Fig. 1(b) for a vector V .
2.2.1. Hill' s Equations of relative motion
The Equations of Hill, rediscovered by Clohessy and
Wilthsire for the application to space rendezvous, are used
to describe relative motion between the chaser and the
target. The differential equations of Hill expressed in the
LVLH-frame are shown in Eq. (1) [12,13]:
€ x2ω_ z ¼ γ x ð1Þ
€ yþω2 y ¼ γ y ð2Þ
Fig. 1. Local vertical, local horizontal reference frame. (a) Definition of the LVLH-frame with respect to Earth. (b) Definition of azimuth (α ) and elevation (θ ).
Table 1
E.deorbit phase-A requirements relevant for the research [10].
Req. ID Statement
R-MIS-
100
The chaser shall rendezvous to a parking point at 100 m (TBC) of the target in along-track direction
G-MIS-
085
A target angular velocity of 51/s around no single fixed axis shall be considered as a worst case scenario
R-TTC-020
The communication link shall be maintained during all safety critical mission phases without any critical functionality. Note: no directivesteerable antenna should be used
R-TTC-
030
The TTCa subsystem, in particular the antenna coverage and accommodation, shall be able to cope with the target in near vicinity/contact
R-TTC-
060
The TTC subsystem shall interface with the ESA network of ground stations, as defined in the ESTRACK facilities manual
R-GNC-
030
The chaser spacecraft shall be able to perform relative navigation with respect to the target object during the full target orbit anytime of
the year (TBC). Note: relative navigation should also be possible during eclipse
R-PWR-
010
The power subsystem shall provide sufficient power for the spacecraft systems and payload instrument during all modes and mission
phases
a Telemetry, tracking and command (TTC).
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€
z þ2ω_
x3ω
2
z ¼ γ z ð3ÞIn Eq. (1), x, y and z (and the derivatives) represent thechaser's motion in the LVLH-frame. γ represents the
inertial acceleration applied to the chaser in this frame,
and ω represents the mean motion of the target orbit. TheEquations of Hill will be used to determine the required
thrust during the forced-motion manoeuvres (hold points,
straight-line forced motion and forced fly-around man-
oeuvres). Given the related states and their derivatives for
these manoeuvres, substituting them in Eq. (1) gives the
required thrust acceleration. The differential equations of
Hill can be solved analytically by assuming constant input
accelerations, yielding the so-called Clohessy-Wiltshire
solution (CW-solution) [13]. This solution will be used to
simulate the free-drift motions.
2.3. Vehicle models
The spacecraft considered in the rendezvous are ESA's
Envisat and a deorbitation spacecraft. Envisat is Europe's
largest satellite (78 tonnes) in orbit, but inactive since
April 2012. Envisat will serve as target. The deorbitation
spacecraft is a conceptual chaser conceived during the e.
deorbit study, weighing about 1500 kg [14]. In Fig. 2 both
spacecraft are illustrated during rendezvous just before
clamping of the chaser onto the target. The body-fixed
reference frame of the target and the chaser are alsodepicted in these figures and are denoted by the t -frame
and c -frame, respectively. The origin of these reference
frames is in the CoM of the corresponding spacecraft.
2.4. Envisat attitude
To cope with the uncertainty in Envisat's future attitude
motion three different attitude scenarios are investigated,
in line with those studied in the context of e.deorbit. The(hypothetical) attitude scenarios are summarised in
Table 2. Here, the target is rotating around a spin axis,
with a (maximum) rate of 51/s (cf. req. G-MIS-085,
Table 1), and the spin axis in its turn is precessing around
the angular momentum vector as an additional perturba-
tion. The spin axis coincides with the þ z -axis of the t -
frame, an assumption made by the team studying the
attitude motion of Envisat [15]. The attitude scenarios are
illustrated in Fig. 3. It is noted that these scenarios
represent fictive scenarios and that these rotations do
not necessarily correspond to resulting torque-free mo-
tions.
2.5. Envisat orbit propagation
Envisat's future orbit is propagated from the High-
Precision Orbit Propagator (HPOP) in Satellite Tool Kit
(STK). The current orbit of Envisat is estimated using the
two-line element (TLE) of 24 July 20141:
1 27386U 02009A 14205.17227990 .00000017 00000-0
19997-4 0 3065
2 27386 098.3806 269.6083 0 001267 110.6854 275.0601
14.37721203648893
This corresponds to a semi-major axis of 7144 km andan eccentricity of 0.001 (giving a perigee and apogee
altitude of 757 and 775 km, respectively). The orbit incli-
nation is 98.41. This orbit is propagated with the default
HPOP settings. A pressure coefficient of 1 and an area-to-
mass ratio of 0.01 m2/kg have been assumed for Envisat for
the computation of the solar-radiation pressure. For the
computation of the drag the same area-to-mass ratio has
been assumed, with a drag coefficient of 2.2. For 2021, it is
found that the altitude of Envisat varies around 740 km.
2.6. Hold points and keep-out sphere
Irrespective of the attitude scenario, the starting point
for the final approach is defined by requirement R-MIS-
100 in Table 1. This requirement defines a hold point at
100 m on V-bar, and will be denoted by S 1. The end of the
rendezvous is a hold point stationary with respect to the
clamping location at a distance of 3 m. This hold point is
denoted by S f , during which the clamping mechanism
attaches to the target. A nominal duration of 300 s is
assumed for this phase. Note that S f is, strictly speaking,
not necessarily a hold point since, in the case of precession
of the target spin axis, this point is moving in the LVLH-
Fig. 2. Spacecraft models and body-fixed reference frames of Envisat and
e.deorbit's deorbitation spacecraft [14].
Table 2
Scenarios for Envisat's motion [15].
Scenario Spin
axis
Reference
axis
Spin
rate
(1/s)
Angle
between spin
axis and
reference axis
(deg)
Precession
rate of spin
axis around
reference axis
(1/s)
# 1 þ z -
axis
of t -
frame
Angular
momentum
5.0 0 –
# 2 5.0 45 0.15
# 3 5.0 90 0.15
1
Two-Line Element Sets Current Data, NORAD, http://www.celestrak.com/NORAD/elements/
J.A.F. Deloo, E. Mooij / Acta Astronautica 117 (2015) 277 – 295280
http://www.celestrak.com/NORAD/elements/http://www.celestrak.com/NORAD/elements/http://www.celestrak.com/NORAD/elements/http://www.celestrak.com/NORAD/elements/
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frame. Besides the hold points, a (KOS) is defined around
the CoM of Envisat. Considering that the outermost part of
Envisat's solar panel extends to about 20 m from the CoM,the radius of the KOS is defined to be 50 m. Within this
sphere only forced motion manoeuvres and hold points are
allowed. Furthermore, a maximum closing rate of 5 cm/s is
adopted within this sphere, which leads to a 20-min durationof this phase.
Fig. 3. Envisat attitude scenarios illustrated. Generated with STK [16]. (a) Scenario 1. (b) Scenario 2. (c) Scenario 3.
Fig. 4. The chaser's antenna configuration. (a) Antenna 1. (b) Antenna 2.
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2.7. Chaser attitude
Within the KOS the chaser is assumed to be target
pointing, with the negative x-axis of its body-fixed frame
pointing towards the target. Also, the chaser is assumed to
rotate along with the rotational motion of the target. In
target-pointing mode this implies a rotation of 51/s around
the x-axis of the c -frame. This attitude means that theclamping mechanism of the chaser points to the target,
and that residual motion between clamping mechanism
and the clamping point is nullified, if the chaser is aligned
with the target spin axis.
2.8. Chaser antenna configuration
The placement of the antennas on the chaser is illu-
strated in Fig. 4. Note that in this figure the antennas are
separated by the width of the chaser. In the configuration
that is assessed by the distance between the antennas is
halved to be able to cope with chaser designs that are
smaller than the current one.
2.9. Solar-array configuration of the chaser
The solar-array area of the chaser is equal to 3.2 m2 [14].
Three different solar-array configurations are assessed. The
configurations are shown in Fig. 5. Two fixed configurations
and a one degree-of-freedom pointing configuration are
considered.
3. Methodology
As mentioned earlier, the research is divided into threetopics: rendezvous, communication and illumination. This
section describes the methodology that is used to provide
an answer to the related challenges.
3.1. Final approach
To assess possible final-approach strategies the hold-
points and KOS defined in Section 2.6 are adopted. The
approach towards the target is started from hold point S 1.
It is assumed that from this point on the goal of the chaser
is consecutively to: (i) align with the target spin axis on
the KOS, (ii) point towards the target and spin up to match
the angular motion with the target, while following thespin axis, (iii) approach the target while following the spin
axis, and (iv) remain stationary with respect to the
clamping point.
This strategy allows to match the rotation the chaser
with the rotation of Envisat, so that no residual motion
exists between the clamping mechanisms and the clamp-
ing location. Moreover, this strategy avoids Envisat's main
appendage: the solar array. The passive safety of the
resulting final approach is assessed from the free-driftmotion (using the CW-equations) by investigating the
behaviour after thrust inhibit anywhere during the final
approach. Furthermore, aspects of the feasibility of the
final approach are assessed by analysing the thrust
profiles.
3.2. Communication
To assess the communication conditions during the
rendezvous of the chaser with Envisat, first the optimal
communication window during the rendezvous is identi-
fied. Next obstruction of the communication signal during
this optimal communication window is assessed. It is
noted that no actual antenna design is incorporated.
Basically, everything forward of the chaser can be “seen”,
i.e., effectively defining a semi-beam angle of 901.
3.2.1. Identification of the optimal communication window
Requirement R-TTC-020 in Table 1 states that a con-
tinuous communication link is to be maintained during
the mission-critical phases. Requirement R-TTC-060
demands communication via de ESTRACK network of
ground stations. To comply with these requirements, the
optimal communication window is defined as the longest-
duration uninterrupted communication window that canbe obtained using the ESTRACK network. There is a chain
of ESTRACK ground stations located in Europe and South
America, which are used to determine the duration of the
Fig. 5. The chaser's solar-array configurations. (a) Nominal fixed configuration. (b) Alternative fixed configuration. (c) One degree-of-freedom pointingconfiguration.
Table 3
Considered ESTRACK ground stations.
Core network Augmented network
Kiruna (Europe) Svalbard (Europe)
Redu (Europe) Santiago (South America)
Villafranca (Europe)
Santa Maria (Europe)
Maspalomas (Europe)
Kourou (South America)
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uninterrupted communication window. The stations that
are considered are listed in Table 3.
For details on the exact locations of ground stations one
is referred to the ESTRACK facilities manual [17]. The
optimal communication windows are identified for the
ESTRACK network assuming minimum elevation angles,
ϵmin, of 51 and 101, respectively.
STK's Access Tool is used to determine the availablecommunication windows with the individual ground sta-
tions in the year 2021. The data will then be post-
processed to identify overlap between the individual
communication windows and subsequently the longest-
duration uninterrupted communication window. Note that
the optimal communication windows are independent of
the attitude scenario of Envisat and that Envisat's orbit
requires to be propagated to 2021.
3.2.2. Assessment of the severity of antenna obstruction by
Envisat
The severity of the obstruction by Envisat is assessed by
placing a nadir-pointing antenna on the chaser. This an-tenna has a (FoV) just wide enough to contain the entire
Earth in its conical (FoV) at the considered altitude. The
percentage of the antenna's (FoV) that is obstructed by
Envisat is determined using STK's Obscuration Tool. This
is done for the entire length of the uninterrupted commu-
nication window. The severity of the communication
blockage by Envisat depends on the attitude scenario of
Envisat and will therefore be individually assessed for each
scenario.
3.2.3. Assessment of gaps in the continuous communication
window
The next step is to analyse whether the obstruction byEnvisat results in gaps in the continuous communication
window. For this purpose it is assessed whether Envisat is
obstructing the LOS from the antennas to the ground
stations. Hereto, STK's Obscuration Tool is used. The
attitude of the chaser is simulated using a realistic antenna
configuration. The assumptions with respect to chaser
attitude and antenna configuration have been presented
in Section 2.7 and 2.8, respectively.
3.3. Illumination
To assess the illumination conditions during the ren-
dezvous of the chaser with Envisat, first the expected
illumination conditions are determined. Next, solar-panel
obscuration by Envisat is assessed.
3.3.1. Expected illumination conditionsUsing STK, the illumination conditions in 2021 are
extracted for the propagated orbit of Envisat. For commu-
nication purposes the final approach to Envisat is con-
strained above Europe, since here the ESTRACK network is
available. Therefore, the illumination conditions have only
been considered for this part of the orbit. A pass over
Europe is defined by every orbit that has a descending
node between 0 and 601 in longitude from Greenwich.
The portions of the orbits from the descending node to 1/4
of an orbital period before the descending node are
defined as passes over Europe. The ground tracks of the
orbits that satisfy these conditions are enclosed by the
dashed lines as shown in Fig. 6. In this figure the blobsrepresent the range of the core ESTRACK ground stations
(ϵmin¼101) for a spacecraft at Envisat's orbital altitude.
3.3.2. Solar-panel obscuration
Solar-panel obscuration is only assessed for the final
phase of the rendezvous within the KOS, where the
chaser's attitude is simulated. The KOS is defined in
Section 2.6. The solar-array configurations presented in
Section 2.9 have been assessed using STK's Solar Panel
Tool. In the analysis, both self-obscuration as well as
obscuration by Envisat is taken into account.
4. Final-approach results
In Fig. 7 the approach strategy defined in Section 3.1 is
illustrated for the three scenarios. The figure shows the
final approach of the chaser with the target in the LVLH-
frame. The approach starts from S 1 (¼(100,0,0) m) and
ends in S f (3 m relative to the clamping location). The KOS
is represented by the dotted lines, and has a 50-m radius.
Fig. 6. Pass over Europe (defined by every portion of orbit enclosed by the dashed lines). Generated with STK [16].
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In Fig. 7(a) a complete trajectory is shown for the final-approach phase of scenario 1. The final approach starts
with the chaser moving from V-bar to H-bar with a
straight-line forced motion FM 1. Hereafter, the chaser
maintains a hold point on H-bar at SK 1, where it can
acquire the required attitude (i.e., it can point its clamping
mechanism towards the target and rotate along with the
target). After hold point SK 1, the chaser approaches the
target along H-bar (i.e., along the target spin axis) with a
straight-line forced motion FM 2. Finally, the chaser ends
in hold point SK 2, where it has time to clamp onto the
target.
An example of a complete sequence of manoeuvres for
scenario 2 is shown in Fig. 7(b) for a fly-around directionagainst the natural orbital motion. Note that the circle on
the KOS, drawn to aid visualisation, represents the projec-
tion of the spin axis during a full revolution of precession.
The scenario starts with the transfer to H-bar with the
straight-line forced motion, FM 1. On H-bar the hold point,
SK 1, is established. Hereafter, the chaser aligns with the
spin axis with FM 2. Next, the spin axis is followed with
the constant-range forced-motion fly-around, FMFA 1. This
allows the chaser to acquire the required attitude to be
able to proceed with the closing forced-motion fly-around,
CFMFA 1. Finally, the clamping location is followed at a
distance of 3 m with FMFA 2. It is noted that FMFA 2 is
almost not visible in this figure due to the small radius of this fly-around.
The rendezvous strategy for scenario 3 is summarisedin Fig. 7(c). Assumptions have to be made regarding the
catching up with the spin axis. It is assumed that the catch
up is done with a fly-around having an angular velocity of
0.31/s, which is double that of the precession rate (in the
orbital plane of the chaser). In the case shown in Fig. 7(c)
the initial conditions are such that the fly-around lasts for
2701. This is illustrated by FMFA 1. Hereafter, the spin axis
is followed with FMFA 2 (0.151/s) to allow the chaser to
acquire the desired attitude. Next, the target is approached
while following the spin axis with CFMFA 1. The final
manoeuvre, FMFA 3, hovers 3 m above the clamping
location to allow for clamping.
4.1. Passive safety
It can be seen from Fig. 7 that the final approach con-
sists of straight-line forced-motion manoeuvres and for-
ced-motion fly-around manoeuvres. Two manoeuvres in
particular have been found passively unsafe after thrust
inhibit. These include fly-around manoeuvres along the
natural orbital motion for some fly-around angles and
manoeuvres along H-bar. In the case that trajectories
contain such passively unsafe forced-motion manoeuvres,
the usual way of risk mitigation is to improve the failure
tolerance of the GNC-system. The characteristics of the
passively unsafe manoeuvres that have been identified arediscussed next.
Fig. 7. Final approach from S 1 (¼(100,0,0) m) to S f (3 m relative to the clamping location). (a) Scenario 1. (b) Scenario 2. (c) Scenario 3.
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4.1.1. Forced-motion fly-around along the natural orbital
motion
The free-drift trajectories after thrust inhibit during a
forced-motion fly-around along the natural orbital motion
are illustrated in Fig. 8. The free-drift trajectories are
shown for a fly-around angular rate of 0.151/s, and for
failures at fly-around angles of 0, 45, 90 and 1351, res-
pectively. For failures at angles of 180, 225, 270 and 3151,
the same trajectories are obtained, but mirrored around
the x- and z -axes.
In Fig. 8(a), the fly-around, FMFA 1, is inhibited just after
it has been initiated. This results in a free-drift trajectory, FD
1, where the chaser comes back to its initial position. Fig. 8
(b)–(d) all show similar behaviour, but on a different scale.
In all cases the free-drift trajectories first move away fromthe KOS, but loop back to KOS after one orbital revolution.
−1000100200300400500
−150
−100
−50
0
50
100
150
V−bar (m)
R − b a r ( m )
KOS
FM 1
SK 1
FMFA 1
FD 1
−800−600−400−2000200400
−150
−100
−50
0
50
100
V−bar (m)
R − b a r ( m )
KOS
FM 1
SK 1
FMFA 1
FD 1
−1000−5000500
−150
−100
−50
0
50
100
V−bar (m)
R − b a r ( m )
KOS
FM 1
SK 1
FMFA 1
FD 1
−1000−800−600−400−2000200
−150
−100
−50
0
50
100
V−bar (m)
R − b a r ( m )
KOS
FM 1
SK 1
FMFA 1
FD 1
Fig. 8. Free-drift trajectories after thrust inhibit during a forced-motion fly-around along the natural orbital motion (Fly-around angular velocity ¼0.151/s).
(a) Thrust inhibit at a fly-around angle of 01. (b) Thrust inhibit at a fly-around angle of 451. (c) Thrust inhibit at a fly-around angle of 901. (d) Thrust inhibit
at a fly-around angle of 1351.
Fig. 9. Critical fail angles for a fly-around along the natural orbital motion
(Fly-around radius¼50 m).
−100−50050−50
0
50
V−bar (m)
H − b a r ( m )
KOS
FM 1
SK 1
FD 1 in KOS
Fig. 10. Free-drift trajectory after thrust inhibit on H-bar (hold point at
50 m).
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For different angular rates of the fly-around the same type
of trajectories is obtained. The question is whether the
chaser enters the KOS for specific fly-around angles of
failure. This is shown in Fig. 9, where the range of critical
fly-around angles for which the free-drift trajectory enters
the KOS is shown for different angular rates. The figure
shows that the range of critical fly-around angles is higher
for low-angular-velocity fly-around manoeuvres. For exam-ple, in the case of a fly-around with an angular rate of 0.15 1/s,
critical fly-around angles are found around 40, 180, 220 and
3501, respectively.
4.1.2. Manoeuvres on H-bar
The free-drift trajectory of the chaser in the case of
thrust inhibit during a hold point on H-bar is illustrated in
Fig. 10. The figure shows that the chaser drifts along H-bar
after thrust inhibit. As a result the chaser and the target
will collide, a lack of passive safety that is well known
from the literature [18]. It can be found analytically from
the CW-solution that the chaser will cross the orbital plane
for the first time (i.e., collide with the target) after 1/4 of an orbital period. After one orbital revolution the chaser
will have returned to its initial position. Considering the
geometrical extension of both vehicles, the collision is
expected a little before 1/4 of an orbital period. Every
subsequent crossing of the orbital plane is an integer times
1/2 orbital period later. Similar behaviour is observed for
any manoeuvre along H-bar. In case the chaser has an
initial velocity towards the target at thrust inhibit, the time
before collision is reduced.
4.2. Thrust profiles
Typical manoeuvres that require continuous thrusting
are hold points, straight-line forced motions and forced
fly-around manoeuvres. The required thrust for the man-oeuvres can be found by inserting the equations of motion
for these manoeuvres in the Hill equations, Eq. (1) [19].
The continuous-thrust manoeuvres are assumed to be
initiated and terminated by impulsive shots. Fig. 11 sum-
marises the results for scenario 3. Scenarios 1 and 2 are
not presented here, but similar conclusions concerning the
thrust profiles and resulting accelerations can be drawn.
Fig. 11 (a) shows the magnitude of thrust acceleration
required. The figure shows a high variation in thrust
acceleration between the different manoeuvres. It can be
observed that FMFA 1 requires the largest thrust accelera-
tion. This is attributed to the higher angular velocity of this
fly-around compared to the other fly-around manoeuvres.The required thrust acceleration during FMFA 1 is about
2.2 103 m/s2. This is within the thrusting capabilities of
the 22-N attitude thrusters of the chaser.
Fig. 11 (b) illustrates the magnitude of the impulsive
shots required. The labels on top of the bars represent the
manoeuvre that is initialised with the corresponding
impulsive ΔV. It can be observed that the highest
0 1000 2000 3000 40000
0.5
1
1.5
2
2.5x 10
Time (s)
T h r u s t a c c e l e r a t i o n ( m / s
2 )
Acceleration
FM 1
SK 1
FMFA 1
FMFA 2CFMFA 1
FMFA 3
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
∆V1
∆V2
∆V3
∆V4
∆V5
∆V6
∆ V ( m / s )
FM 1 SK 1
FMFA 1
FMFA 2
CFMFA 1FMFA 3
0 500 1000 1500 2000 2500 3000 35000
90
180
270
360
Time (s)
A z i m u t h ( ° )
0 500 1000 1500 2000 2500 3000 3500−90
−45
0
45
90
E l e v a t i o n ( ° )
Azimuth
Elevation
FM 1
SK 1
FMFA 1
FMFA 2
CFMFA 1
FMFA 3
−100−50050
−60
−40
−20
0
20
40
60
V−bar (m)
R − b a r ( m )
KOS
FM 1SK 1
FMFA 1
FMFA 2
CFMFA 1
FMFA 3
Fig. 11. Required thrust acceleration for manoeuvres in scenario 3. (a) Magnitude of thrust acceleration. (b) Magnitude of impulsive shots. (c) Direction of thrust acceleration in the LVLH-frame (azimuth and elevation). (d) Representation of thrust acceleration and impulsive shots in the LVLH-frame.
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impulsive ΔV is 0.26 m/s, required to initialise FMFA 1.
Using the relation ΔV ¼ γ Δt , the time to deliver thisimpulsive shot with 22-N attitude thrusters is found to
be almost 10 s. Compared to the duration of the man-
oeuvres, this is small and the impulsive-shot assumption is
considered to be reasonable.
The direction of the required thrust during the final
approach is depicted in Fig. 11(c) and (d). In Fig. 11(d) thegrey arrows represent continuous thrust-acceleration,
whereas the black arrows are impulsive shots. The figures
show that the required thrust acceleration is always
towards the target. This is a good result as it means that
thrusters must be fired away from the target. For the
impulsive shots this is not always the case: ΔV 2 and ΔV 6require thrusting towards the target. Since ΔV 2 is applied
at a large distance from the target this is not expected to
be a problem. On the other hand, ΔV 6 applied at a closedistance and may interfere the target.
For the phase within the KOS, the required acceleration
components in the c -frame have been computed, assum-
ing a rotating and target-pointing chaser, as defined in
Section 2.7. The result is shown in Fig. 12. It can be
observed that thrust-acceleration components in the c -
frame are highly variable, especially during CFMFA 1. The
y- and z -components show an oscillating behaviour, with a
period corresponding to the rotation period of the chaser.
Such a thrusting strategy requires throttleable attitude
thrusters.
5. Communication results
5.1. Longest-duration communication windows
The longest-duration uninterrupted communication
windows are summarised in Table 4 for minimum eleva-
tion angles, ϵmin, of 51 and 101. For the identification of these communication windows the orbit propagated until
year 2021 has been used. It is noted that for this study it is
assumed that continuous communication is required
when the chaser is inside the keep-out sphere. Duration
of this phase is 20 min (see, for instance, Fig. 12 for
scenario 3). The results of Table 4 are compliant with that.
The ground track of the longest-duration pass over thecore ESTRACK stations is shown in Fig. 13 for ϵmin¼101.The spacecraft moves from north to south on this ground
track. The blobs in this figure represent the range for
communication of the different ground stations. The
duration of the uninterrupted communication window
that is obtained for this pass is 1337 sð722 minÞ. Com-
munication windows that are within 5% in duration of this
Table 4
Summary of optimal communication windows.
ESTRACK network ϵmin(deg)
Maximum
communication time
(s)
Occurrence
(within 5%)
Core 10 1337 (E2 2 min) At least daily
Core 5 1938 (E32 min) Every 1 or 2
days
CoreþAugme nted 10 1474 (E24 min) At least daily
CoreþAugmented 5 204 4 (E34 min) Every 1 or 2
days
Fig. 13. Ground track of the longest-duration uninterrupted communication windows with the ESTRACK network (core ESTRACK network, ϵmin¼101).Generated with STK [16].
0 500 1000 1500−8
−6
−4
−2
0
2
4
6x 10
Time after entering KOS (s)
T h r
u s t a c c e l e r a t i o n ( m / s 2 )
CFMFA 1
FMFA 3
Fig. 12. Thrust acceleration components in the c -frame for the phase
within the KOS.
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optimal window (i.e., larger than 1270 s) can be expected
to occur at least daily. It is noted that in this case the
uninterrupted communication window does not include
the Kourou ground station in South America.
Table 4 indicates that the maximum uninterrupted
communication window is greatly increased ð732 minÞ
if minimum elevation angles, ϵmin¼51, are assumed. The
reason for this increase is mainly due to the fact that inthis case the Kourou station can be included. In the case
that the augmented ESTRACK stations are also considered,
the uninterrupted communication window is increased by
2 min due to the inclusion of the Svalbard station. The
augmented station in Santiago cannot be included in the
continuous communication window (even if ϵmin¼51).There is a small gap of approximately 30 s after being
out of range for communication with Kourou and before
being in range for communication with Santiago. If San-
tiago would be included though, a window of roughly
2600 s ð743 minÞ would be obtained.
Fig. 13 shows that the ground track passes close to
zenith for most stations. Also, the ground track passesthrough multiple blobs at the same time. The result is an
overlap of the individual communication windows as
shown in Fig. 14. In the considered mission, overlap
between the individual windows is a desired quality. In
this case, if Envisat is obstructing communication with one
of the ground stations, the chances are higher that another
ground station is able to maintain the continuous com-
munication link. In the communication windows where
Kourou is included the overlap is worse. Antenna obstruc-
tion and the resulting communication gaps are discussed
in the next sections.
5.2. Obstruction of communication antennas
In this section first the severity of antenna obstruction
is determined and subsequently the consequence of
obstruction in terms of communication gaps is assessed
for the communication window with the core ESTRACK
network (ϵmin¼101).
5.2.1. Severity of antenna obstruction
The severity of antenna FoV obstruction by Envisat is
assessed using a nadir-pointing antenna. The rendezvous
of the chaser with Envisat is simulated such that the end of
the final hold point S f coincides with the end of theuninterrupted communication window, i.e., the end of
the communication window corresponds with clamping
of the target. Any required margin to cover uncertainties is
taken into account in the duration of the hold point, S f ,
0 500 1000 15000
10
20
30
40
50
Time after first contact (s)
D i s t a n c e t o t a r g e t ( m )
0 500 1000 15000
10
20
30
40
50
Time after first contact (s)
A n t e n n a F O V o b s t r u c t i o n ( % )
Scenario 1
Scenario 2
Scenario 3
Fig. 15. Distance to target and FoV obstruction. (a) Distance to target during uninterrupted communication window (core ESTRACK network, ϵmin ¼ 101).(b) Antenna FoV obstruction by Envisat for nadir-pointing antenna.
0 500 1000 1500
Kiruna
Redu
Santiago
Santa Maria
Maspalomas
Time after first contact (s)
Fig. 14. Overlap of the individual windows in the uninterrupted com-
munication window (core ESTRACK network, ϵmin¼101).
0 500 1000 1500
Kiruna
Redu
Villafranca
Santa Maria
Maspalomas
Time after first contact (s)
ENVISAT in LoS
No obstruction by ENVISAT
Fig. 16. Gaps in the continuous communication window for scenario 1.
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assigned to clamping onto target, which is 300 s in dura-
tion. For the communication window with the core
ESTRACK network (ϵmin¼101), the distance to the targetduring contact with the stations is shown in Fig. 15(a). This
applies to all attitude scenarios of Envisat, since the
rendezvous strategies have all been defined to move
towards the target with a velocity of 5 cm/s within the
KOS. The time at which the distance to target, defined tobe along the trajectory, starts to decrease corresponds with
entering the KOS. It can be observed that the distance to
the target stops decreasing around 1000 s after first con-
tact. This represents the hold point S f at 3 m from the
clamping point. The FoV obstruction of the nadir-pointing
antenna is shown in Fig. 15(b) for the worst-case
approaches for the three scenarios.
A number of aspects can directly be observed from
Fig. 15(b). For all scenarios, FoV obstruction only starts
after about 600 s after first contact with the Kiruna ground
station (distance to target: 725 m). The percentage of
obstruction then increases until about 1000 s after first
contact, after which it stagnates. This stagnation is due tothe fact that the distance between the chaser and target is
constant after around 1000 s (see Fig. 15(a)). A second
observation that is made is the oscillation in the percen-
tage of obstruction. This is explained by the fact that
Envisat is rotating with respect to the nadir-pointing
sensor. Last, it is observed that scenarios 2 and 3 represent
the critical scenarios with high FoV obstruction. For these
scenarios, the approach to the target can be from above (as
seen from ground). As a result much more obstruction is
obtained, since the entire body of Envisat could be in the
antenna FoV. On the other hand, for scenario 1, by
definition, the chaser approaches the target from the side
(as seen from the ground). In this case, only the outergeometrical extension of the target can obstruct the
antenna FoV, explaining the low obstruction. The resulting
communication gaps in the uninterrupted communication
windows are presented next.
5.2.2. Communication gaps for scenario 1
In scenario 1 the chaser approaches the target from the
side with respect to the Earth and thus obstruction of the
communication signal is not expected to be significant.
The trajectory in Fig. 7(a) has been simulated and the
resulting obstruction in this case is shown in Fig. 16.
The number of gaps found is limited. On top of that the
duration of all the gaps is less than 5 s. During these gaps
communication is also established with other ground
stations. Therefore, there is no threat of losing commu-
nication with the chaser in the whole course of the final
approach for this scenario.
5.2.3. Communication gaps for scenario 2
A worst-case approach with respect to obstruction of
the communication signal is obtained when the chaser is
above the XY-plane of the LVLH-frame in the final part of
the approach. In this case Envisat is in between the chaser
and the ground stations, when the distance between
Envisat and the chaser is small. In Fig. 17(a) such an
approach is shown for scenario 2 and it is used to find
results for the communication analysis. From Fig. 15 it can
be seen that the FoV obstruction of the nadir-pointing
antenna goes up to 40% for scenario 2. The resulting gaps
in the uninterrupted communication window are shownin Fig. 17(b).
It can directly be observed from Fig. 17(b) that the
number of gaps and the length of the gaps is greatly
increased compared to scenario 1. The main gap occurs for
the communication window with Santa Maria. This gap is
just over 1 min in duration. Next to this major gap, multi-
ple smaller gaps occur during the communication window
with Villafranca, Santa Maria and Maspalomas. These gaps
are all smaller than 15 s. Inspection of the results has
shown that the two final gaps (75 s each) in the com-
munication window with Maspalomas represent the only
cases where no other station is available for communica-
tion. During all other gaps there is at least one station inLoS to maintain the continuous communication link.
However, quick alternation between stations is required
to maintain the continuous link. In any case requirement
R-TTC-020 is violated due to the loss of the communication
link at the end of the window with Maspalomas.
5.2.4. Communication gaps for scenario 3
In scenario 3 the chaser can approach from anywhere
in the plane of the orbit. For the same reasons as for
−100−50
050−50
0
50
−50
0
50
V − b a r ( m )
H − b a r ( m )
R − b a r ( m )
KOS
FM 1
SK 1
FM 2
FMFA 1
CFMFA 1
FMFA 2
0 500 1000 1500
Kiruna
Redu
Villafranca
Santa Maria
Maspalomas
Time after first contact (s)
ENVISAT in LoS
No obstruction by ENVISAT
Fig.17. Gaps in the continuous communication window for scenario 2. (a) Worst-case approach for scenario 2 with respect to communication. (b) Nominalscenario 2 (approach from H-bar).
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scenario 2, a worst-case approach with respect to obstruc-
tion of the communication signal is obtained when the
chaser is above the XY-plane of the LVLH-frame in the final
part of the approach. Such an approach is shown in Fig. 18
(a). It can be seen from Fig. 15(b) that the FoV obstruction
of the nadir-pointing antenna amounts up to 40%. This
indicates that significant gaps may occur in the continuous
communication window. The resulting gaps are shown inFig. 18(b).
The most striking result is the long gap that occurs
during the communication window with Maspalomas.
This gap is about 1 min in duration. During the gap, the
Santa Maria and Villafranca station also have short
obstruction periods. This makes it challenging to maintain
the continuous communication link, as a quick alternation
between stations is required. Furthermore, two gaps of
around 5 s each are found near the end of the commu-
nication window with Maspalomas. During these gaps no
other stations are in range, which means that the com-
munication link will be lost.
6. Illumination results
The position of the Sun with respect to the target and
chaser in 2021 has been extracted during all passes over
Europe in 2021. The resulting azimuth and elevation of the
Sun in the LVLH-frame are summarised in Table 5. The
azimuth and elevation in the LVLH-frame have been
defined in Fig. 1(b). Fig. 19 illustrates the mean target-
Sun vector in the LVLH-frame. The results indicate that the
Sun is always more or less coming from H-bar. Also the
maximum elevation angle is above Earth horizon and thus
no eclipses are to be expected.
The expected illumination conditions in 2021 haveconsequences for the (visual) navigation sensors and the
target illumination during the final approach. It should
also not to be forgotten that this phase and subsequent
capture operations need to be monitored by ground via
cameras on the chaser. These may be subject to possible
blinding as well and may therefore need artificial illumi-
nation. However, at this moment nothing is known yetabout the chosen sensor configuration and monitoring
loops by ground control. Therefore, only a global analysis
has been done to see to what extent artificial lighting
would be required.
The incoming Sunlight is coming from approximately
H-bar. Therefore, an out-of-plane approach from this
side is preferred. In this case the Sunlight will namely be
coming from behind the chaser. Since the visual sensors
for relative navigation will be pointing towards the target,
there is no risk of being blinded by the Sun. Also, the target
face that is approached will be illuminated by the Sun and
there is no risk of solar-array obscuration. However, the
risk of the chaser creating a shadow on the target exists.An out-of-plane approach from þH-bar represents the
Table 5
Azimuth and elevation of Sun in LVLH.
Azimuth, α (deg) Elevation, θ (deg)
Mean Min Max STD Mean Min Max STD
281.03 236.22 301.93 16.42 20.96 40.58 15.72 13.29
−100−50050
−50
0
50
V−bar (m)
R −
b a r ( m )
KOS
FM 1
SK 1
FMFA 1
FMFA 2
CFMFA 1
FMFA 3
0 500 1000 1500
Kiruna
Redu
Villafranca
Santa Maria
Maspalomas
Time after first contact (s)
ENVISAT in LoS
No obstruction by ENVISAT
Fig. 18. Gaps in the continuous communication window for scenario 3. (a) Worst-case approach for scenario 3 with respect to communication. (b) Over-
view of gaps.
−X
−Y
−Z
Z
Y
X
Fig. 19. Mean target-Sun vector and schematic for Sun elevation at sun-
rise or sunset.
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worst case. In this case the Sun is behind the target from
the chaser point-of-view. This means that the visual
sensors will have a high risk of being blinded. Moreover,
artificial light is required as the target face that is
approached will not be illuminated. Finally, the chaser
solar array risks being obscured by the target.
Since the approach strategy is variable due to the
uncertain attitude dynamics of Envisat, favourable ligh-ting conditions cannot be guaranteed during the final
approach. The chaser must therefore be designed to cope
with all lighting conditions to cope with requirement R-
GNC-030.
6.1. Available solar-array area
The available solar-array area is assessed at the epoch
for which the longest-duration communication window is
obtained with the core ESTRACK network (ϵmin¼101).Since the variation in illumination conditions in 2021 is
limited, as shown in Table 5, this will give a fair indication
of the solar-array obscuration that can be expected. Thevariation of the Sun vector during the epoch of the optimal
communication window is shown in Fig. 20(a), where t irepresents roughly the beginning of the uninterrupted
communication window and t f roughly the end of the
uninterrupted communication window. t 1 and t 2 represent
two intermediate times. Note that the available solar-array
area has been computed for the three solar-array config-
urations presented in Section 2.9. It is also emphasised
that the chaser is simulated to be target pointing and
rotating with the target, as defined in Section 2.7. A 5 cm/s
closing rate has been adopted within the KOS for all
scenarios. The distance to the target is then represented
by Fig. 20(b).
6.1.1. Envisat attitude scenario 1
As discussed above an approach from H-bar is pre-
ferred over an approach from þH-bar, when considering
the illumination conditions. Approaching the target from
H-bar namely results in the Sun coming from behind,
meaning that there is no threat of solar-array obscuration
by Envisat. Approaching from þH-bar represents thus the
worst case for this scenario regarding the illumination
conditions. Such an approach is shown in Fig. 21 and is
considered to find the worst-case results for solar-array
obscuration. In Fig. 22 the available solar-array area is
shown for the three array configurations. A number of
observations are discussed below.
In Fig. 22(a) and (c) strong periodic oscillations in the
available solar-array area are observed. These oscillationsrepresent the chaser's inability to point the array as a
result of the forced rotation along with Envisat. The period
of the oscillation is thus related to the rotation rate of the
chaser. The phenomenon of poor pointing as a result of a
forced rotation along with the target is depicted concep-
tually in Fig. 23. The upper left figure shows the situation
where the chaser solar array is parallel to the incoming
rays of Sun. Even in the case that the solar array has one
degree-of-freedom around its longitudinal axis, no Sun
rays would hit the array. The upper right figure shows the
situation later in time, after the target and chaser have
rotated by about 451. It can be seen that the solar array
then starts to receive Sunlight. However, the array is stillnot working at full capacity. The bottom figure shows the
ideal case where the solar array is perpendicular to the
incoming Sunlight.
−X
−Y
tf
ti
t2
t1
−Z
Z
Y
X
0 500 1000 15000
10
20
30
40
50
Time after entering KOS (s)
D i s t a n c e t o t a r g e t ( m )
Fig. 20. Target-Sun vector and distance to target within KOS. (a) Target-Sun vector in LVLH-frame during optimal uninterrupted communication windowwith core ESTRACK network (ϵmin ¼ 101). (b) Distance to target as a function of time after entering KOS.
−100−50050−50
0
50
V−bar (m)
H −
b a r ( m )
KOS
FM 1
SK 1
FM 2
SK 2
Fig. 21. Worst-case approach for scenario 1 with respect to illumination.
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No periodic oscillations are visible in Fig. 22(b). This is dueto the fact that the rotation of the solar array is such that the
incidence angle of the Sunlight on the solar array is not
impacted. This phenomenon is illustrated in Fig. 24. In this
figure the chaser is shown for various orientations during a
full revolution. From the observer's point of view, the chaser
solar-array area remains constant during the revolution. This
illustrates that a rotation does not necessarily lead to a
fluctuation in available solar-array area.
An observation that can be made for all configurations
is a strong decrease in the average area starting 800 s after
entering the KOS. This is equal to a distance of 10 m from
the target as can be seen from Fig. 20(b). This sudden
decrease in solar-array area is attributed to the obscurationby Envisat. This phenomenon is illustrated in Fig. 25. This
figure shows that as the chaser approaches the target it
gets more obscured. In Fig. 22(b) and (c) a number of
sudden pits in the real-time available area are observed
around 500 s, leading to a small decrease in the mean
available area. This is also attributed to obscuration by
Envisat.
The overall average solar-array area available during
the approach is summarised in Table 6. It is observed that
the alternative fixed configuration is competing well with
the pointing solar-array configuration. The difference in
available solar-array area is only about 5%. On the contrary,
the nominal fixed configuration performs poorly and has50% less solar-array area available on average.
6.1.2. Envisat attitude scenarios 2 and 3For scenarios 2 and 3 the same illumination phenom-
ena are observed. The resulting average solar-array area
available for worst-case approaches is summarised in
Table 7.
It is noted that, in scenarios 2 and 3, the nominal fixed
configuration performs better than the alternative fixed
configuration. This is a result of the fly-around approach
required for these scenarios. However, similarly to sce-
nario 1, it is found that the pointing solar-array configura-
tion performs best, but the fixed solar-array configurations
can come close in performance. It can be concluded that if
the orientation of the fixed array is carefully chosen, the
performance can be close to the pointing array.
7. Conclusions
Due to the uncertain attitude of Envisat, three different
rotation scenarios have been considered for Envisat. An
approach along H-bar is required for the first scenario. This
approach along H-bar requires continuous thrusting
towards the target. It is well known that an approach
along H-bar is passively unsafe: in case of thrust inhibit
the chaser drifts along H-bar towards the target. The exact
time until collision depends on the initial relative position
and velocity at the moment of thrust inhibit.
For the two other scenarios forced fly-around motionshave been investigated. Forced fly-around motions against
0 500 1000 15000
20
40
60
80
100
Time after entering KOS (s)
A v a i l a b l e s o l a
r p a n e l a r e a ( % )
0 500 1000 15000
20
40
60
80
100
Time after entering KOS (s)
A v a i l a b l e s o l a
r p a n e l a r e a ( % )
0 500 1000 15000
20
40
60
80
100
Time after entering KOS (s)
A v a i l a b l e s o l a r p a n e
l a r e a ( % )
Fig. 22. Available chaser solar-array area for Envisat attitude scenario 1. (a) Nominal fixed array configuration. (b) Alternative fixed array configuration. (c)
Pointing array configuration.
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the natural orbital motion are in general passively safe,
while those along the natural orbital motion are generallypassively unsafe. For the latter, free-drift trajectories after
thrust inhibit either loop back to the KOS after one orbital
period or move towards the target initially for a specific
range of failure angles. Therefore, fly-around manoeuvres
against the natural orbital motion are preferred.
In terms of feasibility of the final-approach strategies, it
was found that the attitude thrusters of 22 N each are
sufficient to provide the required thrust in this phase.
However, owing to the forced rotation of the chaser along
with the rotation of Envisat, the required thrust level inthe body-fixed frame of the chaser is quickly oscillating.
This leads to complicated thrust profiles for the individual
attitude thrusters.
For ground communication during the final approach a
continuous communication window of 22 min has been
identified, if only the core ESTRACK network is considered
and minimum elevation angles of 101 are assumed. In the
case that minimum elevation angles of 51 are assumed, the
window is increased to approximately 32 min. The main
reason for the increase is the fact that the ground station
at Kourou can be included. If the augmented ESTRACK
network stations are also considered, then the commu-
nication windows are increased by 2 min due to theinclusion of the Svalbard ground station. The 22-min
Fig. 23. Poor chaser solar-array pointing due to attitude matching with target. (a) Solar array parallel to incoming rays of Sun. (b) Solar array at 7451 angle
to incoming rays of Sun. (c) Solar array perpendicular to incoming rays of Sun.
Fig. 24. Constant solar-array area during full revolution from the obser-
ver's point of view.
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communication window is sufficient for the flight in the
keep-out sphere, currently assumed to be 20 min.
Communication blockage by Envisat has been assessed
for the core ESTRACK network with minimum elevation
angles of 101. Obstruction by Envisat starts at a distance of
25 m from the target and becomes only significant for a
distance of 5 m or less. As a result of this obstruction
significant gaps occur near the end of the continuous
communication window, if worst-case approaches that
end the rendezvous on top of Envisat are considered.
Maximum gaps of about 1 min have been found during
the communication window with Santa Maria or Maspa-
lomas. Also, multiple smaller gaps ð710Þ of less than 15 s
with various ground stations (mainly Villafranca, Santa
Maria and Maspalomas) have been found. Even though the
overlap between the individual communication windows
is good, the number of gaps will make it challenging to
maintain the continuous communication link, since quickswitching between stations would be required. For an
approach purely from out of the orbital plane no signifi-
cant gaps are present in the communication window.
Because during the final approach with the target a
continuous communication window is required, given this
constraint the corresponding illumination conditions dur-
ing this part of the orbit (epoch 2021) have been investi-
gated. No eclipses are expected and the Sunlight will come
from approximately the H-bar direction on average, i.e.,
from out of the orbital plane. Favourable illumination
conditions are thus obtained for approaches from H-bar. In this case there is a low risk of sensor blinding and
Fig. 25. Chaser solar-array obscuration by target illustrated. (a) No obscuration of solar array. (b) Partly obscured solar array. (c) Full obscuration of
solar array.
Table 6Average solar-array area available during
scenario 1.
Configuration Available area (%)
Nominal fixed 24.8
Alternative fixed 69.9
Pointing 75.2
Table 7Average solar-array area available during
scenarios 2 and 3.
Configuration Available area
(%)
Scenario 2
Nominal fixed 45.0
Alternative
fixed
39.0
Pointing 63.7
Scenario 3
Nominal fixed 57.5
Alternative
fixed
39.9
Pointing 72.4
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solar-array obscuration. However, since the chaser must be
prepared for rendezvous from any direction due to the
uncertain attitude of Envisat, one cannot design the re-
ndezvous for favourable illumination conditions. Worst-
case conditions dictate that artificial light is requi-
red and light-independent navigation sensors must be
available.
To assess obscuration of the chaser solar array by thetarget, three solar-array configurations have been consid-
ered (two fixed and a one degree-of-freedom pointing).
From the results it can be concluded that obscuration of
the solar array only becomes relevant for a distance
smaller than 10 m from the target. Before this distance,
the available solar-array area is mainly determined by the
ability of the chaser to point the solar array towards the
Sun. Since the chaser is required to rotate along with the
rotation of Envisat, pointing of the solar array is restricted
and strong oscillations occur in the available solar-array
area. On average the pointing solar array performs better,
but the fixed solar-array configurations can come quite
close. For the three rotation scenarios of Envisat theaverage area available for the pointing solar array varies
between 64% and 75%. For the fixed arrays this varies
between 25% and 70%. It can be concluded that if the
orientation of the fixed array is carefully chosen, the
performance can be close to the pointing array. The use
of a pointing solar array during the final-approach phase is
challenging, because the chaser rotates along with Envisat.
As a result a quick rotation of the solar array is required to
point correctly. It is therefore more convenient to fix the
solar array at an efficient angle before the final approach.
Acknowledgements
The authors would like to thank the Systems and
Concurrent Engineering section at ESA/ESTEC for provid-
ing resources to the research in the form of support,
accommodation and software licences. Furthermore, the
Guidance, Navigation and Control Section at ESA/ESTEC is
thanked for their additional support. Last, a special thanks
to ESA's e.deorbit team, and in particular Tiago Soares, for
the continuous input and support during the research.
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J.A.F. Deloo received his BSc and MSc inAerospace Engineering with honours fromDelft University of Technology in 2012 and2015, respectively. Throughout his studies hedeveloped a strong affection for space-debrisrelated topics. During his MSc he worked asan intern at Airbus Defence and Space in LesMureaux, France (former Astrium), on devel-oping a simulator for non-cooperative ren-dezvous. For his MSc thesis he analysed
various challenging aspects of the e.deorbitmission at ESA/ESTEC.
E. Mooij received his MSc and PhD in Aero-space Engineering from Delft University of Technology, The Netherlands, in 1991 and
1998, respectively. From 1995 until mid2007 he was working for Dutch Space, The
Netherlands (now Airbus Defence and SpaceNetherlands), on re-entry systems and (real-
time) simulator development. Currently, he isan Assistant Professor at the Faculty of Aero-
space Engineering, Delft University of Tech-nology. His research interests include re-entry systems, space-debris removal, trajec-tory optimization, guidance and control sys-
tem design, and design methods and data-analysis techniques. He is anassociate fellow of the American Institute of Aeronautics and Astro-nautics.
J.A.F. Deloo, E. Mooij / Acta Astronautica 117 (2015) 277 – 295 295
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