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Reference : UPR8001-DENARZ-001

Workplace : TOULOUSE

Date of publication : Tuesday, September 01, 2020

Type of Contract : FTC Scientist

Contract Period : 12 months

Expected date of employment : 1 December 2020

Proportion of work : Full time

Remuneration : Between 2600 and 3050 euros before taxes according to experience

Desired level of education : PhD

Experience required : Indifferent

Due to the increasing complexity of the orbital environment, spacecraft are increasingly

exposed to the risk of collision with other operational satellites or debris. For instance, since the

collision between the Russian satellite COSMOS 1934 and one debris of COSMOS 926 in December 1991,

no less than eight orbital collisions have been reported between operational satellites, or between satellites

and debris. Collision risk is particularly high in low orbits and different space agencies (CNES, ESA,

NASA) and operators/owners (Airbus Defense and Space (ADS), GMV) have established alert procedures

to assess the risks of collision for controlled satellites, and to authorize avoidance maneuvers if the predicted

risk exceeds some tolerance threshold. These procedures have undergone many changes in recent

years and the field of collision avoidance techniques is currently in full development.

In this context, a first objective is to improve the accuracy, speed and reliability of computation methodologies

for the collision risk in low Earth orbit (LEO) as well as in higher orbits (like GTO or GEO orbit). The

developed methods may concern several encounter situations, such as the case of the so-called short-term

or long-term encounters (depending among other on the relative velocity at the time of closest approach)

or the overall risk for multiple encounters, as well as problems specific to electric orbit raising (EOR). Usually,

the positions and velocities of the involved objects are subject to uncertainties, and represented as

random vectors determined by their probability density functions, which are often approximated as Gaussian

(or Gaussian mixtures). Together with a geometric criterion expressing the minimum allowed distance

between the objects, this modeling entails the formulation of the collision risk assessment problem as a

collision probability calculation. An efficient computation method of such probabilities in the short-term

encounter setting has already been developed based on symbolic-numeric techniques [13]. Extensions of

this method are sought for long-term encounters [3], which involve efficient orbit propagation strategies in

suitable orbital elements and quadrature computations for instance [9, 10, 17, 1, 7, 4, 16]. It is to be noted

that, so far, handling full generality with respect to the dynamics of the objects, the encounter duration, the

potentially high number of objects involved, and the distribution of their initial state, was completely out

of reach. From a theoretical perspective, we proposed a fully general mathematical modeling of the probability of

collision of multiple encounters, in the measure theory framework [2]. This is based on the formulation of

an infinite-dimensional linear programming problem in the cone of nonnegative measures and the so-called

Lasserre hierarchy of relaxations [8], which can be solved in a general convex-optimization-based framework.

The main ingredients of this modeling are: (1) lifting of the nonlinear dynamics into a linear equation of measures via Liouville's equation; (2) stating a linear optimization problem on measures, whose objective

function is exactly the sought probability of collision; (3) practically solving moment problems via a

hierarchy of semi-definite optimization. While this practical numerical way of solving LP problems on measures

is well-known and applicable, in our case, important numerical issues have been identified. Firstly,

the dimension of the general problem is currently prohibitive for existing semi-definite solvers. Secondly,

even simple examples show that numerical results in low dimension do not achieve a good accuracy. These

issues as well as the sometimes partial solutions we provided so far, show that there still is an important

need of cross-fertilization between symbolic-numeric and optimization methods.

A second objective concerns a methodology for computing optimal control strategies for collision risk

avoidance, under probabilistic constraints, while taking into account satellite and mission constraints (EOR,

station-keeping with low-thrust propulsion, limited maneuverability...). Stochastic optimal control strategies

are to be analysed and improved based on existing works [6, 14, 15, 10, 9, 12]. For instance, in certain

cases, probabilistic constraints can be simplified to deterministic ones [11] and the problem can be reduced

to a deterministic convex optimization, which can be then solved by a risk selection approach, for example.

Efficient numerical algorithms are at stake especially when attempting to obtain maneuvers plans for multirisk

avoidance in the context of an electric propulsion (EOR). This induces a complete paradigm shift in the

design of algorithms for calculating maneuvers compared to the more traditional framework of impulsive

maneuvers, as it leads to the formulation of different optimal control problems, which are often solved with

more complex optimization algorithms (for example, using integer mixed nonlinear programming [5]).

See above

- Good knowledge in one or several of the following fields: Astrodynamics, Optimization, Control

Theory, Computer Algebra

- Good programming skills in C, C++ and/or Java; Maple or Mathematica skills is a plus

- Highly self-motivated and willing to learn and work with several of the above listed fields

This work is to be carried out in the ROC Team at LAAS-CNRS, supervised by D. Arzelier and M. Joldes

(ROC, LAAS-CNRS, Toulouse), while closely collaborating with the other research and industry actors of

the R&T project (CNES, Thales Services, TAS).

None

None

Orbital Collision Risk Assessement and Mitigation Strategies (H/F) (TOULOUSE)
https://bit.ly/2Di424D
#Emploi #OffreEmploi #Recrutement

— EmploiCNRS (@EmploiCNRS) Tuesday, 01 September, 20