# Dr Roberto Armellin

### Biography

Roberto Armellin obtained an MSc in Aerospace Engineering in 2003 from Politecnico di Milano with a thesis project on the optimisation of formation flying reconfiguration manoeuvres. Space trajectory optimisation was the main focus of his PhD studies (2004-2007) aimed at the multidisciplinary optimisation of aero-assisted manoeuvres.

From 2007 to 2013 he was a postdoctoral research fellow at Politecnico di Milano, working mainly on the development of algorithms and tools for space situational awareness (SSA). This included: Space objects observation; uncertainty propagation; orbit determination; conjunction identification and collision probability computation; and end-of-life disposal optimisation. In 2008, he co-founded Dinamica, an Italian firm active in the field of astrodynamics.

In 2013, Roberto became a lecturer of Astronautics at the University of Southampton, where he continued his research activity in the field of SSA and participated in the teaching activity of the Astronautics group, both at undergraduate and graduate level. In 2015, he joined the Universidad de la Rioja with a two-year Marie Curie Intra-European Individual Fellowship. The fellowship was focused on the implementation of innovative orbit propagation techniques for applications in SSA. Since 2017, he has been a full-time Senior Lecturer in Spacecraft Dynamics at Surrey Space Centre where he is now leading the astrodynamics group.

### Research

### Research interests

Current research interests include:

- Development of efficient methods for short-term and long-term orbit propagation (with application to catalogue propagation, debris environment modelling, end-of-life disposal, formation flying design)
- High order methods for uncertainty propagation with applications to space surveillance and tracking (propagation of sets in highly nonlinear dynamical systems, orbit determination and state estimation for limited and/or inaccurate measures; collision probability computation, re-entry prediction)
- Optimisation of observation strategies and sensor network optimisation for space debris• Optimal control theory with applications to space trajectories optimization (low-thrust transfer, perturbation-assisted end-of-life disposal optimization)
- Bounded motion design and control for formation flying and rendezvous and docking missions.

Roberto has extensive collaboration links with universities and research institutions worldwide including:

- Politecnico di Milano
- Universidad de La Rioja
- University of Southampton
- Michigan State University
- University of Arizona
- Beihang University

He has been PI or co-I in projects funded by the European Space Agency, European Commission, EOARD, DSTL, and Italian Space Agency.

### My teaching

- EEE3039 Space Dynamics and Missions.
- EEEM009 Advanced Guidance Navigation and Control.
- Supervisor of PhD and MSc students carrying out projects in astrodynamics.
- Industrial tutor for undergraduate industrial placement year.
- Personal tutor for undergraduate students.

### My publications

### Publications

of entire sets of initial conditions in the phase space and their associated phase space densities based on Differential

Algebra (DA) techniques. Secondly, this DA density propagator is applied to a DA-enabled implementation of Semi-Analytical

(SA) averaged dynamics, combining for the first time the power of the SA and DA techniques.

While the DA-based method for the propagation of densities introduced in this paper is independent of the dynamical system

under consideration, the particular combination of DA techniques with SA equations yields a fast and accurate method to

propagate large clouds of initial conditions and their associated probability density functions very efficiently for long time.

This enables the study of the long-term behavior of particles subjected to the given dynamics.

To demonstrate the effectiveness of the proposed method, the evolution of a cloud of high area-to-mass objects in Medium

Earth Orbit is reproduced considering the effects of solar radiation pressure, the Earth?s oblateness and luni-solar perturbations.

The computational efficiency is demonstrated by propagating 10; 000 random samples taking snapshots of their state

and density at evenly spaced intervals throughout the integration. The total time required for a propagation for 16 years in the

dynamics is on the order of tens of seconds on a common desktop PC.

in celestial mechanics based on differential

algebra is presented. The arbitrary order

Taylor expansion of the flow of ordinary differential

equations with respect to the initial condition

delivered by differential algebra is exploited to

implement an accurate and computationally efficient

Monte Carlo algorithm, in which thousands

of pointwise integrations are substituted

by polynomial evaluations. The algorithm is applied

to study the close encounter of asteroid

Apophis with our planet in 2029. To this aim,

we first compute the high order Taylor expansion

of Apophis? close encounter distance from

the Earth by means of map inversion and composition;

then we run the proposed Monte Carlo

algorithm to perform the statistical analysis.

objects (either spacecraft or space debris) orbiting around the Earth is presented.

The method is based on the computation of the minimum distance between two

evolving orbits by means of a rigorous global optimizer. Analytical solutions of

artificial satellite motion are utilized to account for perturbative effects of Earth?s

zonal harmonics, atmospheric drag, and third body. It is shown that the method can

effectively compute the intersection between perturbed orbits and hence identify

pairs of space objects on potentially colliding orbits. Test cases considering sunsynchronous,

low perigee and earth-synchronous orbits are presented to assess the

performances of the method.

space trajectory design. A remarkable example is represented by the

Lambert?s problem, where the conic arc linking two fixed positions in

space in a given time is to be characterized in the frame of the two-

body problem. However, a certain level of approximation always affects

the dynamical models adopted to design the nominal trajectory of a

spacecraft. Dynamical perturbations usually act on the spacecraft in

real scenarios, deviating it from the desired nominal trajectory. Conse-

quently, the boundary conditions assumed for the nominal solutions are

usually affected by uncertainties and errors. Suitable techniques must

be developed to quickly compute correction maneuvers to compensate

for such errors in practical applications. This work proposes differential

algebra as a valuable tool to face the previous problem. An algorithm is

presented, which is able to deliver the arbitrary order Taylor expansion

of the solution of a two-point boundary value problem about an available

nominal solution. The mere evaluation of the resulting polynomials en-

ables the design of the desired correction maneuvers. The performances

of the algorithm are assessed by addressing typical applications in the

field of spacecraft dynamics, such as the simple Lambert?s problem and

the station keeping of a spacecraft around a nominal halo orbit.

linear approximations, whose accuracy drops off

rapidly in highly nonlinear dynamics. A high

order optimal control strategy is proposed in this

work, based on the use of differential algebraic

techniques. In the frame of orbital mechanics,

differential algebra allows the dependency of the

spacecraft state on initial conditions and environmental parameters to be represented by high

order Taylor polynomials. The resulting polynomials can be manipulated to obtain the high order expansion of the solution of two-point boundary value problems. Based on the reduction of

the optimal control problem to an equivalent two-point boundary value problem, differential algebra is used in this work to compute the high order

expansion of the solution of the optimal control

problem about a reference trajectory. New optimal control laws for displaced initial states are

then obtained by the mere evaluation of polynomials.

all resident space objects larger than 1 cm this rises to an estimated minimum of 500,000 objects. Latest

generation sensor networks will be able to detect small-size objects, producing millions of observations per day. Due

to observability constraints it is likely that long gaps between observations will occur for small objects. This requires

to determine the space object (SO) orbit and to accurately describe the associated uncertainty when observations are

acquired on a single arc. The aim of this work is to revisit the classical least squares method taking advantage of the

high order Taylor expansions enabled by differential algebra. In particular, the high order expansion of the residuals

with respect to the state is used to implement an arbitrary order least squares solver, avoiding the typical approximations

of differential correction methods. In addition, the same expansions are used to accurately characterize the

confidence region of the solution, going beyond the classical Gaussian distributions. The properties and performances

of the proposed method are discussed using optical observations of objects in LEO, HEO, and GEO.

accomplish specific mission goals with limited on-board resources. A multi-agent architecture is here selected to

cope with flexibility and reliability requirements typical for a system that must be operative in a hostile and not

completely known environment such the space environment is. A distributed versus a central architecture is here

preferred, and the communication protocol and negotiation mechanisms are investigated. The CSP problem is solved

both by applying to the STN scheme a Shortest Path algorithm and a Maximum Weighted Cliques technique for the

resources management. The applicative scenario here proposed consists of an Earth spacecraft formation devoted to

accomplish both single and globally shared activities by exploiting both local and global resources. Reconfiguration

maneuvers are included, to be accomplished by an electric propulsion module. That kind of operations make the set

of temporal constraints to be satisfied by the final schedule more complex as the search mechanism has to cope with

a nested optimal control problem. A dedicated light and fast algorithm to solve the control problem for the

reconfiguration maneuvers has been developed. Preliminary results according to the formation flying application are

discussed.

have supplied us with the possibility of developing an environment called

MathATESAT embedding in Mathematica, which is not linked to a Poisson series processor.

MathATESAT implements all the necessary tools to carry out high accuracy analytical

or semi-analytical theories in order to analyze the quantitative and qualitative behavior

of a dynamic system.

The debris environment predictions are affected by many sources of error, including low-accuracy ephemerides and propagators. This, together with the inherent unpredictability of e.g. solar activity or debris attitude, raises doubts about the ADR target-lists that are produced. Target selection is considered highly important, as removal of non-relevant objects will unnecessarily increase the overall mission cost [1].

One of the primary factors that should be used in ADR target selection is the accumulated collision probability of every object [2]. To this end, a conjunction detection algorithm, based on the ?smart sieve? method, has been developed and utilised with an example snapshot of the public two-line element catalogue. Another algorithm was then applied to the identified conjunctions to estimate the maximum and true probabilities of collisions taking place.

Two target-lists were produced based on the ranking of the objects according to the probability they will take part in any collision over the simulated time window. These probabilities were computed using the maximum probability approach, which is time-invariant, and estimates of the true collision probability that were computed with covariance information.

The top-priority targets are compared, and the impacts of the data accuracy and its decay highlighted. General conclusions regarding the importance of Space Surveillance and Tracking for the purpose of ADR are drawn and a deterministic method for ADR target selection, which could reduce the number of ADR missions to be performed, is proposed

is expressed in polynomial form of minimum order to satisfy a set of 17 boundary constraints,

depending on 2 parameters: time-of-flight and initial thrust magnitude. The consequent

control acceleration is expressed in terms of differential algebraic (DA) variables,

expanded around the point of the domain along the nominal trajectory followed at the retargeting

epoch. The DA representation of objective and constraints give additional information

about their sensitivity to variations of optimization variables, exploited to find the

desired fuel minimum solution (if it exists) with a very light computational effort, avoiding

less robust processes.

fairly recently that we have come to appreciate that these impacts by asteroids and comets (often called Near Earth

Objects, or NEO) pose a significant hazard to life and property. Although the probability of the Earth being struck by a

large NEO is extremely small, the consequences of such a collision are so catastrophic that it is adviseable to assess the

nature of the threat and prepare to deal with it.

One of the major issues in determining whether an asteroid can be dangerous for the Earth is given by the uncertainties

in the determination of its position and velocity. Important studies arose from the previous issue, which dealt with the

problem of getting accurate uncertainty estimates of the state of orbiting objects by means of several approaches, among

which statistical theory has showed important results [1,2,3]. Recently, several tools and techniques have been

developed for the robust prediction of Earth close encounters and for the identification of possible impacts of NEO with

the Earth [4,5,6]. However, these methods might suffer from being either not sufficiently accurate when relying on

simplifications (e.g., linear approximations) or computationally intensive when based on several integration runs (e.g.,

the Monte Carlo approach). Moreover, the standard integration schemes are affected by numerical integration errors,

which might unacceptably accumulate during the integration, especially when long term integrations are performed.

The resulting inaccuracies might strongly affect the validity of the results, precluding the use of such integrators.

The necessity of solving these problems brought about a strong interest in self validated integration methods [7], which

are based on the use of interval analysis. Interval analysis was originally formalized by Moore in 1966 [8]. The main

idea beneath this theory is the substitution of real numbers with intervals of real numbers; consequently, interval

arithmetic and analysis are developed in order to operate on the set of interval numbers in place of the classical analysis

of real numbers. This turned out to be an effective tool for error and uncertainty propagation, as both the numerical

errors and the uncertainties can be bounded by means of intervals, which are rigorously propagated in the computation

by operating on them using interval analysis.

Unfortunately, the naïve appli

simulations [4]. The linear assumption simplifies the problem, but fails to characterize trajectory statistics when the

system is highly nonlinear or when mapped over a long time period. On the other hand, Monte Carlo simulations

provide true trajectory statistics, but are computationally intensive. The tools currently used for the robust detection and

prediction of planetary encounters and potential impacts with Near Earth Objects (NEO) are based on these two

techinques [5?7], and thus suffer the same limitations. A different approach to orbit uncertainty propagation has been

discussed by Junkins et al. [8,9], in which the effect of the coordinate system on the propagated statistics is thoroughly

analyzed; however, the propagation method was based on the linear assumption and the system nonlinearity was not

incorporated in the mapping. An alternate way to analyze trajectory statistics by incorporating higher-order Taylor

series terms that describe localized nonlinear motion was proposed by Park and Scheeres [10]. Their appoach is based

on proving the integral invariance of the probability density function via solutions of the Fokker?Planck equations for

diffusionless systems, and by combining this result with the nonlinear state propagation to derive an analytic

representation of the nonlinear uncertainty propagation. This method is limited to systems derived from a single

potential.

Differential algebraic (DA) techniques are proposed as a valuable tool to develop alternative approaches to tackle the

previous tasks. Differential algebra provides the tools to compute the derivatives of functions within a computer

environment [11?13]. More specifically, by substituting the classical implementation of real algebra with the

implementation of a new algebra of Taylor polynomials, any function f of v variables is expanded into its Taylor series

up to an arbitrary order n. This has an important consequence when the numerical integration of an ordinary differential

equation (ODE) is performed by means of an arbitrary integration scheme. Any explicit integration scheme is based on

algebraic operations, involving the evaluations of the ODE right hand side at several integration points. Therefore,

carrying out all the evaluation in the DA framework allows differential algebra to compute the arbitrary order expansion

of the flow of a general ODE initial val

several space missions which involve either in orbit assembly of numerous modules or serving/refueling

operations; both around Earth and interplanetary scenarios, manned and unmanned vehicles may ask

for such a technique. In order to obtain the nal docking interface conditions, translational and attitude

constraints must be satis ed during a rendezvous and docking maneuver; therefore, the control scheme

has to simultaneously tune the relative position and velocity between the two satellites and adjust the

chaser spacecraft's orientation with respect to the target port. Since dynamic equations which describe

the relative satellites pose are nonlinear, many nonlinear control methodologies have been investigated

during last decade: Terui has shown the e ectiveness of the sliding mode control technique to control

both position and attitude for proximity

ight around a tumbling target; Kim et al. have proposed

nonlinear backstepping control method to solve the spacecraft slew manoeuvre problem. One of the

highly promising and rapidly emerging methodologies for designing nonlinear controllers is the state-

dependent Riccati equation (SDRE) approach, originally proposed by Pearson and Burghart and then

described in details by Cloutier, Hammett and Beeler. This approach manipulates the governing dynamic

equations into a pseudo-linear non-unique (SDC parameterization) form in which system matrices are

given as a function of the current state and minimizes a quadratic-like performance index. Then, a sub-

optimal control law is obtained by online solution of Algebraic Riccati Equation (ARE). Even if the SDRE

method represents a valid option to solve the nonlinear control problem related to ARD manoeuvring, it

is prone to high computational costs due to the online solution of ARE. In this paper, a new approximated

SDRE solution to solve ARD manoeuvring problem based on the di erential algebra (DA) exploitation

is proposed. Di erential algebraic techniques allow for the e cient computation of the arbitrary order

Taylor expansion of a su ciently continuous multivariate function in a computer environment with a xed

resource demand. A DA-based algorithm is here presented to compute a high order Taylor expansion of

the SDRE solution with respect to the state vectors around a reference trajectory. The computation of

the next SDRE solution is then reduced to the mere evaluation of

NEO and debris segments, have to face the

challenging problem of accurately managing uncertainties

in highly nonlinear dynamical environments.

The uncertainties affect all the

main phases necessary for the successful realization

of the program; i.e., orbital determination,

ephemeris prediction, collision probability computation,

and collision avoidancemaneuver planning

and execution. Since the amount of data

that must be processed is huge, efficient methods

for the management of uncertainties are required.

Differential algebraic (DA) techniques

can represent a valuable tool to address this tasks.

Differential algebra supplies the tools to compute

the derivatives of functions within a computer

environment. This technique allows for the efficient

computation of high-order expansions of

the flow of ordinary differential equations (with

respect to initial conditions and/or model parameters)

and the approximation of the solution manifold

of implicit equations in Taylor series. These

two features constitute the building blocks of a

set new algorithms for the nonlinear and efficient

management of uncertainties. Applications to

1) angles-only preliminary orbit determination 2)

propagation of orbital dynamics 3) nonlinear filtering

4) space conjunction prediction 5) robust

optimal control are presented to prove the efficiency

of DA based algorithms.

transfer by means of a Taylor Model based global optimizer is presented.

Although a planet-to-planet transfer represents the simplest case of in-

terplanetary transfer, its formulation and solution is a challenging task

as far as the rigorous global optimum is sought. A customized ephemeris

function is derived from JPL DE405 to allow the Taylor Model evalu-

ation of planets? positions and velocities. Furthermore, the validated

solution of Lambert?s problem is addressed for the rigorous computa-

tion of transfer fuel consumption. The optimization problem, which

consists in finding the optimal launch and transfer time to minimize the

required fuel mass, is complex due to the abundance of local minima and

relatively high search space dimension. Its rigorous solution by means

of COSY-GO is presented considering Earth?Mars and Earth?Venus

transfers as test cases.

of the Jet Propulsion Laboratory and was announced in October 2006. The competition objective was to find the

global optimal low-thrust trajectory, maximizing a complex objective function over a huge search space. The

problem was a multiple asteroid rendezvous: a trajectory had to be designed for a low-thrust spacecraft which

departs from the Earth and subsequently performs a rendezvous with one asteroid chosen within each of four

defined groups of asteroids. In this paper we present the results obtained by the Aerospace Engineering Department

of Politecnico di Milano. The problem has been approached by means of a two-phase solution process. The first

phase aims at determining a preliminary solution close to the global optimum that is refined in the second phase

through a local optimization. In this work the two-phase approach is presented together with the obtained solution.

to maximize the payload launch-mass ratio while achieving the primary mission goals. A certain level

of approximation always characterizes the dynamical models adopted to perform the design process. Furthermore the state identification is usually affected by navigation errors. Thus, after the nominal optimal

solution is computed, a control strategy that assures the execution of mission goals in the real scenario

must be implemented. In this frame differential algebraic techniques are here proposed as an effective alternative tool to design the guidance law. By using differential algebra the final state dependency on initial

conditions, environmental and control parameters is represented by high order Taylor series expansions.

The mission constraints can then be solved to high order using a so-called high order partial inversion of

the polynomial relationship for every admissible uncertainty. The control strategy is eventually reduced to

a simple function evaluation. The performances of the proposed methods are assessed by two examples of

space mission trajectory design: a continuous propelled Earth-Mars transfer and an aerocapture maneuver

at Mars.

value problems with two-point nonlinear boundary conditions. The proposed scheme

is a linear multi-point method of sixth-order accuracy successfully used in uid

dynamics and here implemented for the rst time in astrodynamics applications.

It is an optimal scheme since a discretization molecule made up of just four grid

points assures an h6 order of accuracy. This kind of discretization allows to attain

an accuracy beyond the rst Dahlquist's stability barrier and simultaneously has

a simple formulation and numerical e ciency. Astrodynamics applications concern

the computation of libration point halo orbits, in the restricted three- and four-body

models, and the design of an optimal control strategy for a low thrust libration point

mission.

to the high sensitivity of the final state to variations of the initial velocity. In this work two

different solvers based on high order Taylor expansions and an analytical solution of the J2

problem are presented. In addition, an iteration-less procedure is developed to refine the

solutions in a dynamical model that includes J2 ? J4 perturbations. The properties of the

proposed approached are tested against transfers with hundreds of revolutions including those

required to solve the Global Trajectory Optimisation Competition 9.

prediction of rocket bodies in eccentric orbits

based on TLE data, Mathematical Problems in Engineering 2017 7309637 Hindawi Publishing Corporation

impact risks to the Earth's surface when they re-enter the Earth's at-

mosphere. To mitigate these risks, re-entry prediction of GTO rocket

bodies is required. In this paper, the re-entry prediction of rocket bod-

ies in eccentric orbits based on only Two-Line Element (TLE) data

and using only ballistic coefficient (BC) estimation is assessed. The

TLEs are preprocessed to filter out outliers and the BC is estimated

using only semi-major axis data. The BC estimation and re-entry pre-

diction accuracy are analyzed by performing predictions for 101 rocket

bodies initially in GTO and comparing with the actual re-entry epoch

at different times before re-entry. Predictions using a single and mul-

tiple BC estimates and using state estimation by orbit determination

are quantitatively compared with each other for the 101 upper stages.

and challenging task in astrodynamics. In this work, a semi-analytical approach based on

high-order Taylor expansions of Poincaré maps is developed. Entire families of periodic orbits,

parameterized by the energy and the polar component of the angular momentum, are computed

under arbitrary order zonal harmonic perturbations, thus enabling the straightforward

design of missions with prescribed properties. The same technique is then proven effective in

determining quasi-periodic orbits that are in bounded relative motion for long time and with

very large aperture. Finally, an illustrative example on how to frame the design of bounded

relative orbits with prescribed properties as an optimization problem is presented.

Therefore, automated Mission Planning systems are being designed, allowing for operators

to simply specify their intentions on a high level. In this paper, we propose an auto-

mated Mission Planning System based on the ants' foraging mechanism and apply it to

two different mission planning problems, from an Earth Imaging and a Data Relay mission,

investigating the system's ability to be generalised. We compare the planning process for

the two problems and generalise on the type of planning problems the system can address.

and impact probability computation on the first resonant returns of Near Earth Objects is presented in this paper. Starting from the results of an orbit determination

process, we use a diferential algebra based automatic domain pruning to estimate

resonances and automatically propagate in time the regions of the initial uncertainty

set that include the resonant return of interest. The result is a list of polynomial state

vectors, each mapping specific regions of the uncertainty set from the observation

epoch to the resonant return. Then, we employ a Monte Carlo importance sampling

technique on the generated subsets for impact probability computation. We assess the

performance of the proposed approach on the case of asteroid (99942) Apophis. A

sensitivity analysis on the main parameters of the technique is carried out, providing

guidelines for their selection. We finally compare the results of the proposed method

to standard and advanced orbital sampling techniques.

and complexity over the last years. EO missions are

becoming more capable and more agile, carrying highresolution

sensors that need to frequently be steered at

different directions depending on the mission goals. In this

paper we discuss the Coverage Planning problem Disaster

Monitoring Constellation (DMC3) mission deals with. It is

an Earth Imaging mission from Surrey Satellite Technology

Ltd (SSTL). The combinatorial optimization problem of

determining a not only feasible but optimal sequence of the

spacecraft attitude in order to image the total of a target area

is NP-hard. We propose an automated planning system for

DMC3, employing a self-organizing software architecture

and a nature inspired optimization algorithm, Ant Colony

Optimization. The advantages of the system are discussed

and some key results are shown.

a fundamental part of our daily life. Small debris between 1 and 10 cm are currently too small to be cataloged and are

only detectable for a limited amount of time when surveying the sky. The very-short arc nature of the observations

makes it very difficult to perform precise orbit determination with only one passage of the object over the observing

station. For this reason the problem of data association becomes relevant: one has to find more observations of the same

resident space object to precisely determine its orbit. This paper is going to illustrate a novel approach that exploits

Differential Algebra to handle the data association problem in a completely analytical way. The paper presents an

algorithm that uses the Subset Simulation to find correlated observations starting from the solution to the Initial Orbit

Determination problem. Due to the different capabilities of the observatories, several observing strategies are currently

being used. The algorithm is thus tested for different strategies against a well known approach from literature. Then,

the performance of the data association method is tested on some real observations obtained in two consecutive nights.

Finally, preliminary results for data association without Initial Orbit Determination are shown

motion is a key topic in celestial mechanics and astrodynamics, e.g. to study

the stability of orbits or design bounded relative trajectories. The high-order

transfer map (HOTM) method enables efficient mapping of perturbed Kep-

lerian orbits using the high-order Taylor expansion of a Poincaré or strobo-scopic map. The HOTM is only accurate close to the expansion point and

therefore the number of revolutions for which the map is accurate tends to

be limited. The proper selection of coordinates is of key importance for im-

proving the performance of the HOTM method. In this paper, we investigate

the use of different element sets for expressing the high-order map in order

to find the coordinates that perform best in terms of accuracy. A new set of

elements is introduced that enables extremely accurate mapping of the state,

even for high eccentricities and higher-order zonal perturbations. Finally, the

high-order map is shown to be very useful for the determination and study of fixed points and center manifolds of Poincaré maps.

ground population. Predictions are particularly difficult for objects in highlyelliptical

orbits, and important for objects with components that can survive

re-entry, e.g. rocket bodies (R/Bs). This paper presents a methodology to

filter two-line element sets (TLEs) to facilitate accurate re-entry prediction

of such objects. Difficulties in using TLEs for precise analyses are highlighted

and a set of filters that identifies erroneous element sets is developed. The

filter settings are optimised using an artificially generated TLE time series.

Optimisation results are verified on real TLEs by analysing the automatically

found outliers for exemplar R/Bs. Based on a study of 96 historical

re-entries, it is shown that TLE filtering is necessary on all orbital elements

that are being used in a given analysis in order to avoid considerably inaccurate

results.

of operational satellites whose services have become

a fundamental part of our daily life. Small debris

between 1 and 10 cm are currently too small to be cataloged

and are only detectable for a limited amount of

time when surveying the sky. The very-short arc nature

of the observations makes it very difficult to perform precise

orbit determination with only one passage of the object

over the observing station. For this reason the problem

of data association becomes relevant: one has to find

more observations of the same resident space object to

precisely determine its orbit. This paper focuses on multitarget

tracking, which is part of the data association problem

and deals with the challenge of jointly estimating the

number of observed targets and their states from sensor

data. We propose a new method that builds on the admissible

region approach and exploits differential algebra

to efficiently estimate uncertainty ranges to discriminate

between correlated and uncorrelated observations. The

multi-target tracking problem is formulated with two different

mathematical conditions: as initial-value problem

and as boundary-value problem. The first one allows us

to define the constraints as a six-dimensional region at a

single epoch for each observation, while the second one,

instead, allows us to consider the two-by-two comparison

as a Lamberts problem thus constraining the position

vectors at the two epochs. The efficiency and success rate

of the two formulations is then evaluated.

(RGT) orbits in a high fidelity dynamical model, including non-conservative

forces and accurate Earth orientation parameters, is introduced. The method is

based on the use of high-order expansion of Poincaré maps to propagate forward in

time regions of the phase space for one, or more, repeat cycles. This map provides

the means to efficiently study the effect that an impulse, applied at the Poincaré

section crossing, produces on the ground-track pattern, thus enabling highly accurate

design and control. The approach is applied to the design and control of

missions like TerraSAR-X, Landsat-8, SPOT-7, IRS-P6, and UoSAT-12.

cheaper launch opportunities and wider spectrum of EO applications. Along with an exponential

growth of the ground based users that can access Low Earth Orbit (LEO) spacecraft

data, this growing community represents an important demand for Data Relay missions. LEO

spacecraft have short visibility windows to the Ground Stations (GS) which limit their throughput.

Data Relay missions are comprised of spacecraft at higher altitude orbits (Geostationary

Orbits) acting as relays of data among LEO spacecraft and GS. Those missions are then able

to offer more frequent data downlink opportunities to the LEO spacecraft thus increasing

the volume of the data reaching the ground and improving the responsiveness between users?

requests and downlink operations. Ground based Mission Planning Systems (MPS) are commonly

managing such complex missions, representing a large operational cost. In this paper,

we propose the application of a Swarm Intelligence algorithm to the design of an automated

MPS for Data Relay missions. Automated MPS have the potential of saving operational costs

while leaving the high level decisions to human operators. This paper represents the first time

that an Ant Colony Optimization (ACO) algorithm is applied to this type of scheduling problem.

This family of algorithms is generally found to offer good level of efficiency and scalability. In

this work, we compare our approach against an algorithm popular in literature, called Squeaky

Wheel Optimization (SWO) and show how our ACO algorithm outperforms it.

Uncertainty propagation has been addressed extensively in space missions around the Earth, but much less for missions around small solar system bodies. Small bodies usually have irregular and weak gravity and our knowledge of their gravity, rotation speed and surrounding space environment is largely uncertain. These characteristics make the orbit propagation around these small bodies a challenging task.

Focusing on the uncertainty of the small body's gravity, this paper applies the differential algebra (DA) technique to study the orbit propagation problem, and addresses its efficiency for a given the required accuracy. Different from traditional studies that focus on the uncertainty of the initial state, this study assumes an exact initial state and studies the influences that gravity model uncertainties have on the orbit. Taking the asteroid Steins as an example, the accuracy and the efficiency of the DA approach are firstly validated by comparison with the traditional Monte Carlo method. Then, the effects of gravity uncertainties on different types of orbits (prograde, retrograde and polar) are studied. The retrograde motion is found to be more robust to the gravity uncertainty than the prograde ones. For near polar orbits, the impact of gravity uncertainty on orbital motion depends significantly on the initial position, and it reaches the maximum if the initial position is near the polar regions. Moreover, short-term effects are found to play an important role in orbit deviation as a result of the gravity uncertainty. These discoveries can help mission designers assess the posed risk and design appropriate mission orbits.

Missions involving multiple spacecraft have been in the spotlight during the last years due to the number of scientific and engineering advantages they offer. They are crucial in the context of Earth monitoring, disaster management and data relay missions which provide

a way of addressing the increasing demand of the volume of data produced on-board daily. The spacecraft are equipped with complex instruments of many capabilities and

diverse constraints which exponentially increase the possible state of the constellation at each moment. Hence, their management has become too complex for human operators to handle. To this end, automated mission planning systems are designed and implemented; the operator defines a goal on a higher level, i.e. submits an imaging request, and the

system is responsible for determining the activities to achieve it, taking into account the mission's capabilities and constraints. The main challenge when designing such systems lies in finding methods that reliably produce optimal or near optimal solutions while also satisfying certain scalability and responsiveness system requirements.

In this work, we consider two different target missions and propose a ground-based space mission planning framework to address their planning problems. A coverage planning problem for the Disaster Monitoring Constellation 3 mission from Surrey Satellite Technology Limited is solved; an Earth imaging mission consisting of 3 agile spacecraft, that is expected to image 1 million square km each day. We also address the planning problem of a data relay mission, where Geostationary spacecraft act as relays of data among low Earth orbit spacecraft and ground stations. The

flexible LEO spacecraft requests have different priorities and are far more than the GEO spacecraft can accommodate, resulting in an oversubscribed scheduling problem. Both problems are of very high computational complexity for exact methods to be efficient. We explore the potential of a stochastic algorithm that is based on the ants' foraging mechanism, Ant Colony Optimisation. Applying this nature-inspired technique to the two planning problems, we manage to achieve optimisation of their schedules while coordinating the constellation's spacecraft. In order to further investigate the capabilities of the method,

we introduce and analyse the stability of a non-linear system that models the long-term ACO dynamics in directed graph environments. The analysis provided insights that have proved helpful in increasing the algorithm's efficiency. The performance of the designed system is validated by comparing our results with a Squeaky Wheel Optimisation approach, a method widely used in recent years in the space mission planning field.

a fundamental part of our daily life. Small debris between 1 and 10 cm are currently too small to be cataloged and

are only detectable for a limited amount of time. Indeed, when performing survey campaigns, the selected schedule

and/or visibility constraints often result in short-arc observations with long observing gaps, which do not allow for

precise orbit determination during a single passage of the object over an observing station. For this reason the problem

of data association becomes relevant: one has to find more observations of the same resident space object to precisely

determine its orbit. This paper compares different methods that build on the concept of Admissible Region and

attributable to solve the problem of correlating sparse observations. The comparison is carried out on real optical

observations obtained by the ZimSMART telescope on consecutive nights.

Feedback-driven Control Laws and State-dependent Parameters, Aerospace Research Central

important with the development of high specific impulse, low-thrust engines. Closed-loop

feedback-driven (CLFD) control laws can be used to solve these trajectory design problems

with minimal computational cost and offer potential for autonomous guidance. However,

they have user-defined parameters which limit their optimality. In this work, an actor-critic

reinforcement learning framework is proposed to make the parameters of the Lyapunov-based

Q-law state-dependent, ensuring the controller can adapt as the dynamics evolve during a

transfer. The proposed framework should be independent of the particular CLFD control

law and provides improved solutions for mission analysis. There is also potential for future

on-board autonomous use, as trajectories are closed-form and can be generated without an

initial guess. The current results focus on GTO-GEO transfers in Keplerian dynamics and

later with eclipse and J2 effects. Both time-optimal and mass-optimal transfers are presented,

and the stability to uncertainties in orbit determination are discussed. The task of handling

orbit perturbations is left to future work.