Italian Workshop onSpace Situational Awareness

PoliMi Expertise and Contribution to Space Situational Awareness

Michèle Lavagna

Italian Space Agency Headquarter

9 – 10 July 2012, Roma, Italy

Dipartimento di Ingegneria Aerospaziale- Politecnico di Milano

Via La Masa 34, 20156, Milano, Italy

Name Role Email

Michèle Lavagna Associate Professor lavagna@aero.polimi.it

Roberto Armellin Postdoctoral Fellow armellin@aero.polimi.it

Pierluigi Di Lizia Postdoctoral Fellow dilizia@aero.polimi.it

Monica Valli PhD Student valli@aero.polimi.it

Alessandro Morselli PhD Student morselli@aero.polimi.it

Chiara Massimiani PhD Student massimiani@aero.polimi.it

‣ Politecnico di Milano

‣Dinamica Srl

Name Role Email

Michèle Lavagna Partner lavagna@aero.polimi.it

Roberto Armellin Partner armellin@aero.polimi.it

Pierluigi Di Lizia Partner dilizia@aero.polimi.it

Team Members and Roles

Research Areas and Collaborations

‣ Past and ongoing work on both NEO and Space Debris

2005 Participation to ESA/Ariadna study:

‣ Rationales and Curriculum:

• Interval analysis and validated integration techniques

2006 Collaboration with Michigan State University (Berz)

• High order methods: Differential algebra

and Taylor models

• Initially developed for particles

accelerators• Proposed by R. Moore to perform

validated integration of NEO motion

• Extremely useful for global optimization

• Assessment of their accuracy for error and uncertainty propagation in

astrodynamics

Research Areas and Collaborations

20072009

Participation to two ESA/Ariadna studies

• Branch and bound global optimization;

application to MOID computation

• Nonlinear tools for uncertainty propagation

with applications to Apophis

2009 Interest shown by ESA (Granada, 2009) paved

the way to applications in Space Debris sector

• Nonlinear mapping of uncertainties in preliminary orbit determination

• Fast conjunction analysis and impact probability computation

2010

2011

Collaboration with Università di Bologna (Piergentili), Università di Padova

(Francesconi), Università di Roma (Santoni) for Active Debris Removal

2012 • Participation to the ITN “The Asteroid and Space Debris Network” (FP7)

• Collaboration with INAF-IRA: Debris orbit determination with Croce del

Nord radiotelescopes

• Support to the definition of an SSA/NEO architecture in CO-II (Telespazio)

Previous Work and Main Results

‣ Nonlinear tools for uncertainty propagation for NEO and Debris

• NEO/Debris state is Taylor expanded in initial conditions

• Integrations replaced by evaluations of polynomials

Fast Monte Carlo simulation:

Computational time reduced to 1%

• Polynomials are manipulated to obtain time and distance of

close approach as a function of initial conditions

Accurate and fast computation of impact probability

‣ MOID computation

• The use of rigorous global optimizers guarantees that

the exact MOID is computed

• The algorithm is able to handle multiple solutions

• The Taylor expansion of the MOID w.r.t. uncertain

parameters is computed

MOID range including uncertainties

Previous Work and Main Results

‣ Orbit determination

• Uncertainties are taken into account throughout the

orbit determination process

• Subsequent high order propagation improves accuracy

for NEO follow-up

‣ Active Debris Removal

• Robustness analysis to uncertainties on boundary

conditions and model parameters

Nonlinear mapping of uncertainty in NEO state

Finer enclosure of the region to be observed

• Fast nonlinear filtering techniques have been developed

to improve accuracy with additional observations

• Nonlinear optimal feedback control algorithms for

uncertain boundary conditions (noncooperative debris)

• Optimal control laws robust to uncertain model parameters

• Capture mechanisms: docking, net, expanding foam

‣ The implemented algorithms are based on differential algebra (DA)

‣ DA allows semi-analytical, nonlinear, and efficient mapping of uncertainties (e.g.

high order expansion of the flow of ODE)

‣ When nonlinearities play a crucial role

‣ DA enables algorithms that are more accurate than those based on linearizations

‣ DA enables algorithms that are more efficient than classical Monte Carlo

simulation (orders of magnitude) with comparable accuracy

‣ In combination with interval analysis validated propagation and rigorous global

optimization

Algebra ofreal numbers

Algebra ofTaylor polynomial

Implemented Methods

Debris

‣Tool for computing the weekly collision risk between all operative

satellites against a list of all unclassified USSTRATCOM two-line

element (TLE) sets (first guess)

‣Orbital filters for reducing the number of pairs to be analyzed

‣Verified global optimizer for computing the time and distance of closest

approach (TCA and DCA)

‣Analytical and nonlinear mapping of uncertainties on TCA and DCA

‣Efficient algorithms for computation of collision probabilities combining the

Taylor expansion of TCA and DCA and sampling techniques

‣Refinement in more accurate dynamical (numerical) model

‣Methods for nonlinear mapping of observation uncertainties from the

space of observables to phase space

‣High-order filters for accurate orbit determination

Implemented Methods

NEO

‣Algorithms for analyzing NEO trajectories

‣Identification of potentially hazardous objects (PHO) via rigorous

computation of MOID

‣Rigorous computation of the time and distance of closest approach (TCA

and DCA)

‣Analytical and nonlinear mapping of uncertainties on TCA and DCA

‣Highly accurate expansion of the flow to study close approaches, resonant

returns, and for computation of collision probabilities

‣Mapping observation uncertainties from the space of observables to

phase space in preliminary orbit determination

‣High-order filters for accurate orbit determination

Implemented Methods

Potentialities - Limitation

Potentialities

‣Efficient algorithms for the management of uncertainties in orbit determination

and orbit propagation

‣Alternative approach to current ones (independent cross-validation of the result

often pursued by ESA)

‣Inclusion in consolidated tools to extend some capabilities and improve

performances

Limitations

‣Most of the codes is the result of research activity, scientific publications have

been produced

‣DA is implemented in COSY-Infinity (open source), a constraint on computer

language

Funds are needed for software engineering (mandatory) and for DA

implementation in a different working environment (nice to have)

‣ Differential algebra has unexploited potentials in

‣ Debris clouds (post-collision) evolution in arbitrary dynamical model

‣ Enrich TLE with confidence region information

‣ Development of alternatives to TLE and SGP4 for orbital parameters

storage and objects orbit propagation

‣ Expand the flow of ODE with respect to uncertain parameters (e.g.

diameter, spin axis direction, and thermal properties for NEO

propagation) or un-modeled perturbation (unknown, but bounded)

‣ Include information on uncertain parameters (not only initial condition)

in computation of collision probabilities

Unexploited Potentials

‣ Started a collaboration with Medicina Observatory

Contribution to SSA

‣ Current activity: support for target selection for observation with a small

portion of the Croce del Nord

‣ Future goal: orbit determination for the full scale use of re-engineered Croce

del Nord

Radar survey

and follow-up

Medicina

Data processing

Medicina

Orbit determination

and propagation

PoliMi

Catalogue Maintenance

Risk Assessment

PoliMi

Contribution to SSA

‣ TOols for Management of Close Approach Threats (TOMCAT)

• Main goals: accurate impact risk assessment and design of optimal collision

avoidance maneuvers

CA ident. MOID

& IP

Optical & radar

measurements

Improved

ODRisk

Collision

avoidance

UniRM

UniBO

PoliMI

UniRM

UniBO UniRM, UniBO

PoliMI

UniPD PoliMI

‣CO-II SSA Architectural Design (collaboration with Telespazio and INAF- OAB)

• Main goals: consolidated architecture for civilian SSA with programmatic dossier

Req.

analysis

Candidate architectures

identification

Supporting

analysis

Development, deployment,

and operation approach

Active debris removal

‣ Space system design

‣ Pre-phase A studies for debris removal missions

‣ Rendezvous and docking

‣ Robust control algorithms

‣ Facility for 2D algorithms testing: frictionless table

‣ Proposals to MIUR in collaboration with Uni PD, UniBO,

UniNA “Federico II”, Uni RM “La Sapienza”

Active Debris Removal

‣ Catching mechanism

‣ Net system design and testing

‣ Expressed interest by ESA and

contact with Astrium where similar

activities are undergoing

‣ De-orbiting mechanism

‣ Hybrid propulsion for de-orbiting

FOTO e

dettagli