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Portail > Offres > Offre UPR8001-DENARZ-001 - Evaluation du risque de collision en orbite et stratégies d'évitement (H/F)

Orbital Collision Risk Assessement and Mitigation Strategies (H/F)

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General information

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

Missions

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]).

Activities

See above

Skills

- 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

Work Context

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).

Constraints and risks

None

Additional Information

None

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