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73rd International Astronautical Congress (IAC), Paris, France, 18-22 September 2022.

Copyright ©2022 by the International Astronautical Federation (IAF). All rights reserved.

IAC–22–B4, 5A-C4.8

Space Mobility Optimization and Concurrent Engineering for Modular

Micro-Propulsion Systems with 360 by IENAI SPACE

Giuseppe Di Pasqualea,b,∗, Daniel Per´ez Grandea, Manuel Sanjurjo-Rivob

aIENAI SPACE, Av. Gregorio Peces Barba, 1, 28919, Legan´es, Spain, giuseppe.dipasquale@ienai.space

bDepartment of Aerospace and Bioengineering, Universidad Carlos III de Madrid, Av. De la Universidad, 30,

28911, Legan´es, Spain, msanjurj@ing.uc3m.es

∗Corresponding author

Abstract

Space propulsion oﬀers many beneﬁts, such as an increased satellite mobility and lifetime or higher sustain-

ability through decommissioning and collision avoidance, being recognized as an enabling technology. However,

propulsion is still struggling to keep up with other subsystems advancements, due to diﬃculties in miniaturizing

the technologies, while satisfying the extremely tight requirements typical of small satellites. IENAI SPACE is

working on solving this problem with ATHENA™, a high-eﬃciency micro-propulsion system based on a micro-

fabricated electrospray technology. The system follows a deeply modular and customizable philosophy, with the

ambitious goal of providing a tailored solution for satellites ranging from picosats to nanosatellites. However,

a modular system, while oﬀering great ﬂexibility and adaptability for any potential mission, adds complexity

at the design stage and the need for a framework capable of generating realistic and optimized solutions. This

task is particularly intricate for propulsion since the system design is strongly coupled with orbital dynamics

and subject to complex constraints coming from other subsystems and operations. 360™is an advanced mission

analysis tool developed by IENAI SPACE, conceived to solve this problem, exploiting the critical advantage

of a fully integrated mission optimization/system design philosophy for spacecrafts equipped with a modu-

lar propulsion system. The software is based on a genetic algorithm coupled with a feedback control law for

multi-revolution low-thrust maneuvers optimization. A rapid estimation of near-optimal propulsive transfers

covering the whole mission, concurrently with optimized thruster conﬁgurations is provided at an early stage

of the mission design, enabling quick exploration of a wide design space for the propulsion system itself, its re-

quirements, and the impact on the other subsystems and operations. Additionally, the framework can perform

concurrent engineering with correlated subsystems, such as the EPS and ADCS, yielding global solutions that

are optimized at a spacecraft/mission level, drawing the highest beneﬁts from the use of propulsion. Complex

operational constraints, such as eclipses, visibility and pointing needs, are included as well, ensuring realism

and balance of the solutions obtained. Designers are given the power to iterate rapidly and eﬀectively a vast

and multi-domain design space, comprising variables from several subsystems and to obtain solutions optimized

with respect to multiple objectives. The joint optimization of maneuvers and subsystems and the resulting

preliminary trade-oﬀs allow for improved mission and system-budget management from early iterations up to

detailed design phases, providing a clear insight of the impact of a tailored propulsion system on the whole

architecture and mission.

Keywords: electric propulsion, trajectory optimization, concurrent design

Nomenclature

asemi-major axis

Eelectrical energy

g0gravitational acceleration at sea level

Isp speciﬁc impulse

iinclination

mppropellant mass

mps propulsion system wet mass

mupayload mass

m0initial total mass

nnumber of thruster heads

Ppower

QQ-law quotient

Tthrust

Vvolume

Wasemi-major axis Q-law weight

Wiinclination Q-law weight

βdbattery capacity

IAC-22, B4, 5A-C4.8 Page 1 of 14

73rd International Astronautical Congress (IAC), Paris, France, 18-22 September 2022.

Copyright ©2022 by the International Astronautical Federation (IAF). All rights reserved.

∆tgeneric time interval

∆VDelta-V

Π mission phase

σdsolar panels conﬁguration

fvectorial objective function

gvectorial constraint function

ucontrol vector

xdesign vector

ystate vector

Acronyms/Abbreviations

ADCS Attitude Control and Determination System

ATHENA Adaptable THruster based on Electrospray

for NAno/micro-satellites

EPS Electrical Power System

FEEP Field Emission Electric Propulsion

GA Genetic Algorithm

GIE Gridded Ion Engine

GVE Gauss Variational Equations

HET Hall Eﬀect Thruster

MDO Multi-Disciplinary Optimization

MEPT Magnetically Enhanced Plasma Thruster

PCL Predeﬁned Control Law

1. Introduction

From the advent of CubeSats as a mean to provide

students with hands-on experience on a real space mis-

sion project lifecycle, small satellites have evolved into

a proﬁtable business, sustaining an ecosystem of hun-

dreds of commercial and governmental players. In fact,

CubeSats oﬀer a competitive, although still comple-

mentary, alternative to bigger platforms [1], even sur-

passing their performance in some cases, as for exam-

ple with high-temporal coverage distributed systems,

i.e. constellations and mega-constellations.

Additionally, compared to the large legacy counter-

part, CubeSats are cheaper and faster to develop due

to the substantial adoption of commercial-oﬀ-the-shelf

(COTS) components, agile management approach and

the ﬁne balancing of time, cost, risk, mission lifetime

and reliability. The latter has seen an increase over

the past few years [2], thanks to the advancement and

miniaturization of many critical technologies, such as

for example, electronics, solar cells, batteries and imag-

ing and communication systems. These technological

breakthroughs have been enablers for an abundance of

CubeSat-based missions: from commercial Earth ob-

servation and communication constellations [3,4,5,6],

up to scientiﬁc interplanetary missions [7,8,9].

However, not all technological disciplines seem to

move at the same development rate for small satellites.

Particularly, propulsion appears to be lagging behind,

as it can be seen from the market adoption for

CubeSats (below 8% [10]), whereas for larger satellites

(mass above 100 kg), the adoption goes well above

70%, even just considering Starlink and OneWeb

constellations and the satellites in the GEO ring.

The high adoption on larger satellites is evidently

related to the many beneﬁts oﬀered by propulsion,

such as increased lifetime, access to lower altitude and

station-keeping, capabilities which impact directly the

quality and economic return of the mission. On top

of this, propulsion allows for de-orbiting and collision

avoidance maneuvers: these are critical constituents

for mitigating the everyday more urgent space debris

problem and guaranteeing access to a safe and sus-

tainable near-Earth environment.

The reasons for this low adoption in the small satel-

lites class can be attributed to two main factors:

ﬁrstly, the technological diﬃculty of miniaturizing the

systems while retaining good eﬃciencies. Secondly,

the presence of exceedingly tight constraints from

the platforms, mainly in terms of mass, power and

volume. The combination of these two aspects leads

to high-footprint and low-performance propulsion

solutions which are unappealing to small satellite

manufacturers, hence, explaining the low market

adoption in this class range.

Due to the mass and volume constraints, in fact,

chemical propulsion technologies are mainly limited

in terms of ∆Vdeliverable. Electric propulsion

systems, on the other hand, suﬀer mostly from the

power constraints and the diﬃculties in the process of

miniaturization, intrinsic to many technologies, which

ultimately impact their performance and operations.

Besides, most commercial propulsion solutions follow

a plug-and-play philosophy, which is convenient for

decreasing integration costs. However, this approach

oﬀers no ﬂexibility and adaptability to the above-

mentioned constraints, due to the design being ﬁxed

a priori. A sub-optimal propulsion solution might

usually lead to compromising the initial objectives or

even the feasibility of the mission, whereas a tailored

design could enable the pursuit of more demanding,

ambitious and proﬁtable mission goals.

Within this context, IENAI SPACE is developing

the Adaptable THruster based on Electrospray for

NAno/micro-satellites (ATHENA), a novel, high-

eﬃciency and “deeply” modular propulsion system

for small satellites. ATHENA™is based on a

micro-fabricated electrospray thruster, which is an

electrostatic propulsion technology capable of reaching

outstanding eﬃciencies at low powers ([11] reports up

to 65%) due to the physical mechanisms behind its

functioning and the advanced propellants employed.

Additionally, ATHENA™follows a “deeply” modular

IAC-22, B4, 5A-C4.8 Page 2 of 14

73rd International Astronautical Congress (IAC), Paris, France, 18-22 September 2022.

Copyright ©2022 by the International Astronautical Federation (IAF). All rights reserved.

approach, which diﬀerentiates from the typical “clus-

tering” of other providers, by reducing the size of the

repeating elementary unit from 1U or even more (for

commercially available solutions), down to a fraction

of a 1U for ATHENA™. This allows tuning the perfor-

mance and the physical characteristics of the system

in a much ﬁner way, allowing to adapt the thruster

to the platform and match as closely as possible the

requirements and constraints of any potential mission,

while minimizing the excess footprint on the platform.

However, a modular propulsion system brings ad-

ditional complexity in the mission design, since the

properties of the thruster are strongly coupled to the

orbital and attitude dynamics [12], the behaviour

of other subsystems and it is subject to intricate

operational constraints.

For this reason, IENAI SPACE is complementing

ATHENA™with 360™, an innovative space mobility

analysis software tool speciﬁcally conceived for the

generation of optimized design solutions of ATHENA™

with respect to user-deﬁned objectives. The tool

embeds all the above-mentioned couplings and con-

straints, ultimately providing realistic and balanced

solutions for each case.

This paper intends to present the methodology

behind 360™, addressing the problem of design and

optimization of a modular electric propulsion system

for small satellites. This problem is highly coupled

with the search of optimal low-thrust trajectories

and the sizing of related subsystems, and lends

itself to a multi-objective approach for preliminary

phase analysis. Hence, this design problem can be

characterized as a multi-objective Multi-Disciplinary

Optimization (MDO) one, considering that the design

variables aﬀect several disciplines, with couplings and

inter-dependencies between the various domains.

Literature provides some examples of MDO method-

ologies applied to both spacecraft design and the

aspects related to maneuvering and mission planning.

Isaji et al. [13] proposed a methodology based on

Augmented Lagrangian Coordination approach for the

problem of mission planning and spacecraft design,

showing fast convergence rates for the case study

presented. Taylor and de Weck [14], developed an

integrated design optimization applied to the problem

of design of an Earth-Moon cargo supply chain. They

demonstrated that a concurrent approach improves

the system design if compared to a traditional network

design optimization. A multidisciplinary tool for

mission and system design of lunar space tugs was

presented by Rimani et al. [15], with highlight on

the coupling of electric propulsion design and the

other subsystems. Beauregard et al. [16] carried

out a study on the concurrent optimization of the

mission architecture and the system design for a lunar

lander, highlighting the coupling of the two aspects

with respect to the solutions obtained. Budianto and

Olds [17] applied Collaborative Optimization to the

problem of constellation design, including the aspects

related to spacecraft design and the launch manifest

logistics. Crisp et al. [18], proposed an integrated

design methodology for constellations, including the

problem of deployment maneuvers and using a genetic

algorithm-based approach. They demonstrated the

capability of this approach to explore eﬀectively vast

design-spaces over several realistic examples.

The problem addressed in this paper, shares some

features with the above-mentioned works, however,

it diﬀerentiates by focusing on the optimization of a

highly modular and custom propulsion system and by

emphasizing the coupling with trajectory optimization

and the design of other subsystems.

In the following sections, the technical methodology

and framework developed will be presented, showing

the application to the design of a modular propulsion

system jointly with the optimization of low-thrust

maneuvers. Furthermore, the paper will explore the

application of the above-mentioned framework to a

more complex problem, such as the concurrent design

of several subsystems of a spacecraft alongside the

optimization of its operations.

2. Problem statement

The MDO problem introduced in Sec. 1 can be de-

scribed in the following standard mathematical nota-

tion:

mininimze f(x,y)

with respect to x,y

subject to ˙

y(x,y)

g(x,y)≥0

x∗∈X,

(1)

where fis the objective function, gthe inequality con-

straints vector and xand yare respectively the design

and state vectors. x∗is the optimal design vector that

is researched and Xis the set of feasible design solu-

tions.

2.1 Objective function

The objective function fcan be vectorial, as mul-

tiple conﬂicting objectives are typically explored at

early design stages. Additionally, objectives can be

expressed both at discipline and system-level, as it will

be detailed in the following.

The objective function is formulated as a vector f∈

IAC-22, B4, 5A-C4.8 Page 3 of 14

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Copyright ©2022 by the International Astronautical Federation (IAF). All rights reserved.

Rnf, where nfis the number of objectives. These ob-

jectives can be related to the entire mission, speciﬁc

phases only, the whole spacecraft or a speciﬁc subsys-

tem or assembly. More speciﬁcally:

•Subsystem physical or cost properties such as mass

and volume.

•Spacecraft physical or cost properties.

•Discipline-speciﬁc properties, such as for example

the ∆Vfor propulsion.

•Duration of speciﬁc phases/maneuvers.

•Operations eﬀort, such as the cumulative ﬁring

time over a given duration.

An example of objective is the following:

f=−mu

m0

,−Vu

V0

,∆ttot|ΠT

,(2)

where mu/m0and Vu/V0are respectively the mass and

volume fraction of the payload (to be maximized, hence

the minus sign) and ∆ttot|Πis the total cumulative

maneuvering time for a given phase Π, which should

be minimized. The latter is deﬁned by:

∆ttot|Π=X

c

∆t(c), c ∈[1, .. . , Ca]∪Π (3)

where ∆t(c)represents the time elapsed in each ﬁring

arc, assuming a total number of Cacontinuous ﬁring

arcs during a given phase Π.

The payload mass fraction can be written as:

mu

m0

= 1 −X

k

msubsytemk

m0

−mp

m0

,(4)

where msubsytem is the mass of a generic subsystem. In

this form, the design and selection of a given subsystem

or set of subsystems can be accounted for by including

them in the summation, whereas the rest of the ﬁxed

subsystems can be seen as part of the payload.

The mp/m0term represents the propellant fraction,

which can be expressed using Tsiolkovsky rocket equa-

tion:

mp

m0

= 1 −e−∆V

Ispg0.(5)

For the payload volume fraction, a similar relation-

ship can be written:

Vu

V0

= 1 −X

k

Vsubsytemk

V0

.(6)

Please note that an alternative formulation is pos-

sible: in fact, the “payload” could be ﬁxed and the

total mass of the system could be let free. In that case,

however, it would be more convenient to use m0as an

objective, which ultimately would impact the launch

cost. However, a variable payload and subsystems ap-

proach is preferred, since it allows for focusing more on

an in-depth exploration of the spacecraft design.

2.2 Design variables

The design vector x∈Rnxminimal set for the

problem includes parameters of the propulsion system

(e.g. operative set-points, size of physical elements),

alongside variables related to the maneuvers, (control

history, coasting/thrusting arcs sequence), where nxis

the number of design variables.

In a more general form, the design vector can include

variables from other subsystems as well, such as,

for example, parameters related to Electrical Power

System (EPS) and Attitude Control and Determi-

nation System (ADCS). The two above-mentioned

subsystems, in particular, are strongly coupled to

the propulsion system and the guidance adopted,

and an integrated optimization approach allows for

improved exploration and identiﬁcation of favorable

design solutions at system-level [18]. Additionally, the

elements of the design vector can be both continuous

and discrete, hence characterizing the problem as a

hybrid one.

3. Methodology

The methodology and framework developed to solve

the problem described in Sec. 2 are presented in the

following. The problem being treated entails multiple

objectives and constraints, and can include a hybrid

set of design variables. Thus, an ideal solving method-

ology and framework should be ﬂexible, robust, fast

and capable of searching for optimal solutions in a vast

design space.

Classical gradient-based solutions, such as direct, indi-

rect methods and dynamic programming can yield op-

timal solutions rather quickly, but struggle to meet the

ﬂexibility and robustness requirements, due to prac-

tical diﬃculties intrinsic to their implementation, or

dimensionality issues [19].

An alternative is heuristic solvers, which, on the

other hand, do not require gradient information and

search the design space using random processes and

stochastic rules. Therefore, they are more ﬂexible and

robust, although require many function evaluations

with consequent drawbacks in computation speed.

Evolutionary algorithms (EA) are one of the most com-

mon heuristic solvers. The ﬂexibility and robustness of

IAC-22, B4, 5A-C4.8 Page 4 of 14

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Copyright ©2022 by the International Astronautical Federation (IAF). All rights reserved.

these methods rely on the fact that they do not require

an initial guess, they are less prone to convergence is-

sues and, additionally, are more likely to ﬁnd a global

optimum, given that enough resources are allocated.

Thus, the approach proposed is based on an EA, and

more speciﬁcally, on a genetic algorithm (GA) coupled

with a predeﬁned control law. A feedback or prede-

ﬁned control law (PCL) is a representation of a low-

thrust trajectory that allows parametrizing the guid-

ance, reducing the number of optimization variables

and usually improving the convergence, albeit at the

cost of optimality. Several PCL have been developed

[20,21,22], however, the choice has fallen on the Q-

law algorithm developed by Petropoulos [23], which,

has great convergence and optimality properties.

Fig. 1 reports an example of an extended design

structure matrix [24] for the problem and the method-

ology at hand, highlighting the various disciplines, their

coupling and the high-level algorithm employed.

Fundamentally, the genetic algorithm (identiﬁed as

“Optimizer” in the ﬁgure) calls a high-ﬁdelity propa-

gator coupled to the Q-law, hence ﬁnding the controls:

this way, the genetic algorithm can tune the parameters

of the PCL modifying the properties of the low-thrust

maneuver, while selecting suitable perspective design

variables for each domain in the diagonal. Fig. 1 em-

phasizes the coupling between the trajectory domain

and the other disciplines: for example, the guidance

laws (attitude quaternion qproﬁles over time) obtained

with the Q-law, impact the power generated on-board,

since it aﬀects the instantaneous incidence angle of the

solar panels with the Sun. Note that Fig. 1 is an ex-

ample of a model, more detailed models would show

a more intricate web of couplings between every disci-

pline and potentially additional disciplines as well. For

example, thrust misalignment in the propulsion system

would cause a continuous accumulation of momentum

in the ADCS, or there might be thermal, electrical and

EMI coupling eﬀects between various subsystems, dur-

ing thruster operation.

3.1 Dynamics

The orbital dynamics is described using Gauss Vari-

ational Equations (GVE) system in a singular-free

modiﬁed equinoctial elements formulation:

˙

ym=A(ym)(p+u) + b,(7)

where ymis the state vector containing the modi-

ﬁed equinoctial elements, as deﬁned in [25], pis the

non-Keplerian accelerations vector expressed in radial-

circumferential-angular momentum direction frame,

and uthe controls, expressed in the same frame. The

matrix Aand the vector bare deﬁned in [26].

Any perturbation can be included in this formula-

tion, in case the analysis requires the level of detail.

The inclusion of models with various levels of ﬁdelity

allows for balancing realism and computation speed on

a case base. For example, gravity can be modeled with

a simpliﬁed J2formulation:

pJ2=

−3J2µRe

2

2r4

(1−12(hsin L−kcos L)2

(1+h2+k2)2)

−12J2µRe

2

2r4

(hsin L−kcos L)(hcos L+ksin L)

(1+h2+k2)2

−6J2µRe

2

2r4

(hsin L−kcos L)(1−h2−k2)

(1+h2+k2)2

,(8)

where Reis the Earth equatorial radius, J2the ﬁrst

zonal harmonic and rthe orbital radius vector mag-

nitude. Or alternatively, it can be expressed using

the more computational intensive, albeit higher ﬁdelity,

spherical harmonics potential representation [27]. An-

other example of perturbation, especially relevant in

LEO, is atmospheric drag modeling, which is captured

by the following relation:

Fdrag =−1

2ρ CDAram v2

rel

vrel

||vrel|| ,(9)

in which, ρis the density and vrel is the relative iner-

tial velocity vector of the satellite with respect to an

Earth co-rotating atmosphere. Various density models

are available, ranging from the simpliﬁed U.S. stan-

dard atmosphere 1976, up to NRLMSISE-00 [28], in

which solar activity and geomagnetic indexes, F10.7

and ap, are obtained from historical data or through

future prediction models. Other state-of-the-art per-

turbations can be included as well in the same way,

but no further detail is provided here for conciseness.

The GVE system in Eq. (7) is completed by two

scalar diﬀerential equations. The ﬁrst one describes

the evolution of the mass over time due to the ejection

of propellant mass through the thruster:

˙m=−||u(t)||

c,(10)

where mis the mass of the spacecraft and cis the

eﬀective exhaust speed of the thruster, related to the

Isp by the gravitational acceleration at sea level g0.

The second equation represents the electrical energy

stored in the satellite’s batteries over time:

˙

E=X

i

Pi(t),(11)

where Eis the electrical energy stored on-board and

Pi(t) is the instantaneous power of the i-th subsystem,

with the convention of positive Pfor generation and

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Fig. 1: Extended design structure matrix highlighting relations between the disciplines considered.

negative for consumption. The full state vector is then

deﬁned as:

y= (ym, m, E)T.(12)

Attitude dynamics could be included in the formula-

tion as well. However, in this case, the attitude quater-

nions qare obtained directly from the Q-law-derived

thrust angles, and the remaining states, angular veloc-

ity (ω) and acceleration ( ˙ω), are obtained by means of

numerical derivation. These can be then used to im-

pose various kinds of attitude-related constraints with-

out slowing down the computation.

Within the propagator, it is possible to enable the

detection of a plurality of events, ranging from eclipses,

which are computed with a cylindrical approximation,

up to ground station visibility-related events. These

events enable the enforcement of complex operational

constraints that concur into increasing the ﬁdelity and

realism of the solutions obtained.

3.2 Predeﬁned control law

The trajectory controls uare obtained through the

Q-law algorithm developed by Petropoulos [23]. The

quotient Qis deﬁned as a candidate Lyapunov function

which adheres to the classical form dependent on the

error of the osculating elements œ with respect to the

target ones œt:

Q=X

œ

WœSœœ−œt

˙œxx 2

,(13)

where Wœare some scalar weights, Sœis a scaling

factor and the denominator ˙œxx represents the maxi-

mum rate of change of each orbital element over thrust

direction and true anomaly. The controls udirection

is obtained so that the derivative of the quotient ˙

Qis

as negative as possible at each instant:

u=arg minu∇œQ·˙

y.(14)

This guarantees Lypaunov stability, and drives Qto

zero as fast as possible.

A coasting mechanism is embedded as well by deﬁn-

ing a “thrust eﬀectivity” parameter:

ηa=˙

Qn

minθ˙

Qn

,(15)

where the instantaneous most negative rate of Q,˙

Qn,

is divided by its minimum along the true anomaly θ. In

its simplest form, the thrust can be set to zero when-

ever the ηais below a given threshold ηthr.

This formulation presents no convergence issues and

does not require an initial guess. However, the algo-

rithm yields solutions as a function of the weights Wœ

and are typically sub-optimal. The genetic algorithm

can be used to ﬁne-tune these weights, increasing the

optimality of the solutions obtained.

3.3 Heuristic solver

The heuristic solver selected is the multi-objective

genetic algorithm NSGA-II [29]. This algorithm re-

lies on non-dominated sorting, crowding distance and

sorting which mitigates the problematic of other multi-

objective GA, like lack of elitism and high computa-

tional complexity, in fact achieving a time complexity

of O(MN 2) where Mis the number of objectives and N

the size of the population. Fig. 2 shows a schematic of

the NSGA-II main loop: an initial population Rtof size

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2Nis formed by parent individuals Ztand oﬀspring in-

dividuals Qt, the latter generated through binary tour-

nament selection, recombination and mutation. The

population is sorted according to non-domination, cre-

ating a non-dominated set F1, followed by other sets,

ordered by their domination ranking.

Non-dominated

sorting

Crowding

distance

sorting

F1

F2

F3

Zt

Qt

Rt

Zt+1

Rejected

Fig. 2: Schematic of NSGA-2, edited from [29]

The highest-ranking Nsolutions are then selected as

parents of the new population Zt+1, and new oﬀspring

individuals are generated, repeating the process until

convergence or a stopping condition is reached.

In order to cope with the high number of function

evaluations necessary to obtain x∗, the GA is deployed

on a cloud computing platform. The platform oﬀers

the possibility to use a large number of cores, hence

enabling the possibility of performing evaluation calls

in parallel, increasing signiﬁcantly the computation

speed.

4. Analysis

In order to demonstrate the capabilities of the

methodology described in the previous section, an ex-

ample of a realistic mission is presented. The exam-

ple will be explored using several test cases, in which

the design variables are varied with the intent of high-

lighting the ﬂexibility and robustness features of the

framework.

The mission considered is a LEO constellation com-

posed of 6U CubeSats whose properties are based on

[30] and the relevant parameters are reported in Ta-

ble 1. The propulsion system fulﬁlls three main func-

tions:

•Deployment of the constellation through plane

spacing and in-plane phasing.

•Maintenance of the constellation structure and ge-

ometry over time.

•Collision avoidance maneuvers.

Property Value Unit

Spacecraft mass 8 kg

Surface area 0.03 m2

Form factor 6 U

Nominal altitude 650 km

Nominal eccentricity 0.003 -

Nominal inclination 97.73 °

Plane spacing (∆Ω) 5 °

Table 1: Platform and mission properties.

Before going into the details of the test cases,

some preliminary considerations are made. First, the

methodology versatility allows to consider both contin-

uous and discrete design variables. Continuous vari-

ables can be intrinsic (e.g. a voltage set-point chosen

within a given range) or the approximation of a dis-

crete variable, typical of early stage iterations. The

latter can be deﬁned, for example, through analytical

relations or data ﬁtting of available discrete solutions,

as shown in Fig. 3: in this case, a linear ﬁt is chosen to

correlate the battery capacity (βd) and mass, although

more complex multi-variable models can be used.

0.2 0.3 0.4 0.5 0.6 0.7

Mass (kg)

20

30

40

50

60

70

80

Capacity (Wh)

Optim-30

Optim-40

Optim-80

BP4

BPX

iEPS A

iEPS B

iEPS C

Fig. 3: Battery capacity (βd) versus subsystem mass

[31,32,33].

Discrete variables, on the other hand, can be used

when a preliminary down-selection has been already

carried out, resulting in a ﬁnite number of perspective

solutions to choose between, or for some cases where

a continuous approach is impossible (for example the

selection of the number of heads of ATHENA™is in-

trinsically discrete).

For the purpose of showcasing the capabilities of the

IAC-22, B4, 5A-C4.8 Page 7 of 14

73rd International Astronautical Congress (IAC), Paris, France, 18-22 September 2022.

Copyright ©2022 by the International Astronautical Federation (IAF). All rights reserved.

tool, a hybrid approach is used for the EPS, using the

continuous relation for the battery sizing, and a dis-

crete set of conﬁgurations for the solar panels. Fig. 4

shows the three discrete solutions considered for the

cases presented σd∈[0,1,2]: the mass of the panel is a

function of the size, the number of cells and the hinge

mechanism, if any.

Fig. 4: Solar panels conﬁgurations (σd) considered:

body-ﬁxed (left), 3U (x2) deployable (center), 6U

(x2) deployable (right).

Secondly, a model for ATHENA™is introduced:

the model relates the design variables of ATHENA™,

namely, the number of thruster heads (n), the voltage

set-point (vp) and the propellant mass (mp), to system

cost (cps), physical (mps ,Vps) and performance met-

rics (T,Isp,P) through a set of experimentally-derived

scaling laws:

T, Isp, P =f1(n, vp)

mps, Vps , cps =f2(n, mp)

with n∈[2,4,6,8] .

(16)

For the cases presented, a 1U version of ATHENA™

is considered. Due to torque-balance and beam neu-

trality constraints, this ﬁxes the number of heads to

the discrete set reported in Eq. (16). Some examples

of conﬁgurations are shown in Fig. 5. The voltage is

Fig. 5: Examples of ATHENA™thrusters with diﬀer-

ent thruster heads and propellant mass: n= 4 (left),

n= 6 (center), n= 8 (right). Propellant mass in-

creasing from left to right.

ﬁxed to the highest eﬃciency point for this case, but

it can be explored in a broader analysis. Addition-

ally, with the aim of highlighting the advantages of a

modular system, a set of propulsion systems based on

real COTS products is considered as well, with their

properties reported in Table 2. Performance models

for each of them are derived from data-sheets and rele-

vant publications, in order to allow the GA to optimize

their performance in each case. Speciﬁcally, some sys-

tems’ performance scales with power (used as a design

variable), whereas for others multiple variables can be

tuned to select the operational point on a 2D perfor-

mance map.

Finally, in an eﬀort to keep the example short,

the cases will focus on the deployment maneuver ex-

clusively, which, however, represents a rather exten-

sive and complete example [40,26], although any kind

of maneuver can be accounted in the analysis, cov-

ering the whole mission. This maneuver consists in

ﬁnding the optimal injection altitude and inclination

and performing the most eﬃcient transfer between the

found injection point and the operational orbit, which,

through the exploitation of the J2dynamics, allows to

eﬀectively obtain the ∆Ω indicated in Table 1. Only

one satellite of the constellation needs to be studied

since it is assumed that all the satellites will perform

the same maneuvers.

For each case presented in the following, the design

vector will be explicitly shown. The objective function

considered in all the cases is:

f=∆tdpl,−mu

m0T

,(17)

where ∆tdpl is the deployment time, and the con-

straints vector is:

g=

∆tdpl −∆tdpl|max

SOCmin −SOC(t)

mp−mp|max

≤0,(18)

where the deployment time is imposed to be lower

than a maximum ∆tdpl|max. The SOC is the State

of Charge of the batteries, which has to be above a

given minimum value at any time. The last constraint

makes sure that the maximum embarked propellant

mp|max is not exceeded.

4.1 Modular propulsion system

In the ﬁrst case, the EPS properties are ﬁxed (βd=

50 Wh, σd= 1), and the methodology is focused on

optimizing the low-thrust transfer, by tuning the Q-law

weights (Wa, Wi) and the injection point (ainj, iinj )

and on ﬁnding the best design of a modular ATHENA™

thruster (namely deﬁning the best number of heads

nand the propellant needed mp) for each case. The

design vector can be expressed as:

x=ainj , iinj ,Wi

Wa

, nT

.(19)

IAC-22, B4, 5A-C4.8 Page 8 of 14

73rd International Astronautical Congress (IAC), Paris, France, 18-22 September 2022.

Copyright ©2022 by the International Astronautical Federation (IAF). All rights reserved.

System Thrust Speciﬁc impulse Wet mass Propellant Power References

T (mN) Isp (s) mps (kg) mp(kg) PP RO (W)

FEEP 0.05 - 0.42 2000 - 6000 0.9 0.22 20 - 40 [34]

MEPT 0.3 - 0.8 300 - 600 2.5 0.56 30 - 60 [35]

GIE 0.3 - 1.2 300 - 2600 1.84 0.84 34 - 66 [36,37]

HET 2.2 - 2.8 700 - 890 1.9 0.1 50 - 65 [38]

ATHENA™0.1 - 0.43 ≤1650 - - <12 [39]

Table 2: Propulsion systems, their nominal performance and properties.

The propellant mass cancels in Eq. (19), since, the

value is obtained automatically from the trajectory

optimization. The variables are based on the model

in Fig. 1, neglecting the ADCS conﬁguration vari-

able γd, and using the relations ainj =a0−∆aand

iinj =i0−∆i, where a0and i0are the nominal alti-

tude and inclination.

Fig. 6 shows a Pareto-optimal front of the objectives

described in Eq. (17) for the 5°Ω spacing maneuver.

Each point represents the combination of a unique

thruster design solution and a low-thrust transfer

maneuver. Please note that the payload fraction

accounts for what remains when removing the mass of

both the propulsion system and the, in this case ﬁxed,

EPS, as in Eq. (4).

Four families of solutions can be recognized, each

corresponding to thruster designs with a given num-

ber of thruster heads n. It is evident that faster de-

ployments are obtained with higher n, hence heavier,

although higher thrust, propulsion system solutions.

75 100 125 150 175 200

Deployment time (days)

74.0

74.5

75.0

75.5

76.0

Payload fraction (%)

Number of thruster heads (n)

2

4

6

8

Fig. 6: Pareto-optimal front for a spacing maneuver

of ∆Ω = 5°for diﬀerent thruster heads and a ﬁxed

EPS.

550

600

650

ainj (km)

75 100 125 150 175 200

Deployment time (days)

98.0

98.2

iinj (°)

Number of thruster heads (n)

2

4

6

8

Fig. 7: Optimal injection altitude (top) and inclina-

tion (bottom) versus deployment time. Operational

elements are shown as dashed grey lines.

Additionally, Fig. 7 shows the optimal ainj and iinj ,

highlighting the nin the color bar. As observed in pre-

vious works [40], the deployment speed increases as the

injection orbit is further away from the operational one,

allowing to generate larger J2drifts. However, when

factoring a modular propulsion system, it appears that

the high-nsolutions allow performing larger maneuvers

more eﬃciently, including bigger variations of inclina-

tion, compared to low-n. The mass of the propulsion

system increases as well, since the propellant needed

grows as larger and faster maneuvers are performed.

Fig. 8 shows a detail of the thrust (top) and battery

SOC (bottom) over time for one of the solutions found.

The plot highlights the triggering of the constraint

when the thruster is shut oﬀ to guarantee that the

state of charge is kept above the minimum enforced

by Eq. (18).

Finally, the COTS propulsion system from Table 2

are considered in the analysis to perform the same ma-

neuver, optimizing the operational point for each of

them. Fig. 9 shows the payload fraction versus deploy-

IAC-22, B4, 5A-C4.8 Page 9 of 14

73rd International Astronautical Congress (IAC), Paris, France, 18-22 September 2022.

Copyright ©2022 by the International Astronautical Federation (IAF). All rights reserved.

ment time for all the propulsion systems. It is evident

that, since the COTS thruster have a ﬁxed mass, only

single-point solutions can be found, corresponding to

the minimum deployment time for each maneuver and

the given constraints. On the other hand, a modu-

lar propulsion system like ATHENA™, allows to ﬁnd a

proper Pareto front, which translates into greater ﬂex-

ibility and exploration breadth for the mission design-

ers.

Additionally, by analyzing the propellant used by

each thruster, it is noticeable that the remaining

propellant goes from about 10% for the HET to

nearly 80% for the FEEP, with the other thrusters

in between. All the ATHENA™’s solutions, on the

other hand, are designed for complete fuel depletion

(although accounting for some reserve). In other

0.0

0.2

0.4

Thrust (mN)

292 294 296 298 300

Hours since t0

60

80

100

SOC (%)

SOCmin

Fig. 8: Thrust (top) and battery state of charge (bot-

tom) over time for one of the solutions of Fig. 6

60 80 100 120 140 160 180 200

Deployment time (days)

55

60

65

70

75

Payload fraction (%)

GIE

HET

MEPT

FEEP

ATHENA

Fig. 9: Pareto-optimal front from Fig. 6, with optimal

point for propulsion systems described in Table 2.

words, the propellant embarked is exactly the amount

necessary for the maneuvers to be carried out. This

aspect contributes to achieving the lightest solutions

among all the other systems.

4.2 Concurrent subsystem optimization

In this case the EPS properties are added to the

design vector of Eq. (19), leading to:

x=ainj , iinj ,Wi

Wa

, n, σd, βdT

.(20)

The genetic algorithm is now allowed to explore solar

panels’ conﬁgurations σdand the battery capacity βd

alongside the maneuver and thruster design and oper-

ational point variables.

The Pareto front in Fig. 10 shows that a concurrent

subsystem optimization approach generates a new set

of improved solutions. In fact, the front obtained in the

previous case (reported with semi-transparent mark-

ers) appears to be dominated by newly found, both in

terms of payload fraction and deployment speed.

75 100 125 150 175 200

Deployment time (days)

72

74

76

78

Payload fraction (%)

Number of thruster heads (n)

2

4

6

8

Fig. 10: Pareto-optimal front for a spacing maneuver

of ∆Ω = 5°for diﬀerent thruster heads and EPS.

Front from Fig. 6 shown with semi-transparent

markers.

By applying the concurrent optimization to the

thrusters from Table 2, it is possible to obtain Fig. 11,

where all the Pareto fronts for each product are shown

with diﬀerent colors and markers.

This time, proper fronts are obtained for all systems,

although it is evident that this depends only on the

EPS optimization. ATHENA™, however, presents a

much more spread Pareto front, namely a larger pool

IAC-22, B4, 5A-C4.8 Page 10 of 14

73rd International Astronautical Congress (IAC), Paris, France, 18-22 September 2022.

Copyright ©2022 by the International Astronautical Federation (IAF). All rights reserved.

60 80 100 120 140 160 180

Deployment time (days)

50

55

60

65

70

75

80

Payload fraction (%)

GIE

HET

MEPT

FEEP

ATHENA

Fig. 11: Pareto-optimal front for a spacing maneuver

of ∆Ω = 5°for diﬀerent thruster heads.

60 80 100 120 140 160 180

Deployment time (days)

0

10

20

30

40

50

60

Thruster power (W)

GIE

HET

MEPT

FEEP

ATHENA

Fig. 12: Thruster power versus deployment time for

various propulsion systems.

of optimal options to select. This demonstrates, once

again, that a modular system allows for far greater

ﬂexibility at the design stage.

Fig. 12 to Fig. 14, show the impact of the con-

current optimization on the power-related design vari-

ables. Speciﬁcally, Fig. 12 shows the optimal thruster

power for diﬀerent deployment duration and for each

propulsion system considered. It can be seen that, as

the deployment time is shortened, the power consumed

by the thrusters increases, with a consequent increase

in thrust.

Consequently, Fig. 13 and Fig. 14 show that the EPS

needs to increase in terms of power generation and bat-

tery capacity, as the thruster requires more power.

60 80 100 120 140 160 180

Deployment time (days)

0

1

2

Solar panels conﬁguration

GIE

HET

MEPT

FEEP

ATHENA

Fig. 13: Optimal solar panel conﬁgurations versus de-

ployment time, for various propulsion systems.

60 80 100 120 140 160 180

Deployment time (days)

20

40

60

80

Battery capacity (Wh)

GIE

HET

MEPT

FEEP

ATHENA

Fig. 14: Battery capacity versus deployment time, for

various propulsion systems.

It is interesting as well to notice that ATHENA™

requires smaller battery capacities (although also the

largest solar panel conﬁguration is explored), thanks to

the higher eﬃciency, and lower power required.

Finally, it appears that the possibility of tuning

the EPS allowed to obtain some solutions for the

GIE which are faster than ATHENA™, even though

in Fig. 9, the GIE was slower. Ultimately, this shows

that a concurrent approach can be convenient also for

non-modular propulsion solutions.

IAC-22, B4, 5A-C4.8 Page 11 of 14

73rd International Astronautical Congress (IAC), Paris, France, 18-22 September 2022.

Copyright ©2022 by the International Astronautical Federation (IAF). All rights reserved.

5. Conclusions

This paper presents the methodology at the core

of IENAI SPACE’s cutting-edge space mobility anal-

ysis tool, 360™. The methodology proposed shows the

capability of solving hybrid multi-disciplinary multi-

objective optimization problems, with application to

the concurrent design of space systems and in particu-

lar the propulsion system, the coupled subsystems and

associated low-thrust maneuvers.

The framework is applied to the design of a modular

propulsion system, showing the capability of producing

well-spread Pareto fronts, oﬀering far greater ﬂexibility

and exploration of candidate solutions, if compared to

non-modular systems.

The following conclusions are summarized:

•The methodology presented is versatile and robust

enough to handle multiple hybrid design variables,

complex design and operational constraints and

multiple contrasting optimization objectives eﬀec-

tively.

•Concurrent design and optimization of propul-

sion system, maneuvers and the coupled subsys-

tems allows obtaining solutions that are signiﬁ-

cantly improved at system-level in comparison to

subsystem-level optimization.

•A modular propulsion system enables the achieve-

ment of a lower footprint (in terms of physical and

cost properties) and larger sets of optimal solu-

tions. This ultimately translates into greater ﬂex-

ibility for the mission designers and ease of meet-

ing mission requirements and goals, compared to

non-modular products.

Acknowledgments

This project has received funding from the “Co-

munidad de Madrid” under “Ayudas destinadas a

la realizaci´on de doctorados industriales” program

IND2020/TIC-17317.

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