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