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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”
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