debris removal

8/20/2019 Debris Removal

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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: [email protected] (J.A.F. Deloo),

[email protected] (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:[email protected]:[email protected]://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:[email protected]:[email protected]://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)

J.A.F. Deloo, E. Mooij / Acta Astronautica 117 (2015) 277 – 295278


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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).

J.A.F. Deloo, E. Mooij / Acta Astronautica 117 (2015) 277 – 295 279


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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/


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.



9/19

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).



10/19

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.



11/19

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.



12/19

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


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


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


ENVISAT in LoS

No obstruction by ENVISAT

Fig. 16. Gaps in the continuous communication window for scenario 1.



13/19

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.


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.


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


ENVISAT in LoS


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).



14/19

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


ENVISAT in LoS


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.



15/19

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


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.



16/19

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


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


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


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



19/19

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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Netherlands (now Airbus Defence and SpaceNetherlands), on re-entry systems and (real-

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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.

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