Adaptive Remediation of the Space Debris ...

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4th International Workshop on Space Debris Modelling ... UN = United Nations .... United Nations Office for Outer Space Affairs. http://doi.org/A/RES/62/217.

ADAPTIVE REMEDIATION OF THE SPACE DEBRIS ENVIRONMENT USING FEEDBACK CONTROL G. L. Somma, H.G. Lewis, C. Colombo

4th International Workshop on Space Debris Modelling and Remediation Paris, 06-08 June 2016

Outline •

Introduction



Research Objectives



The Model – Model description – Object types and their interactions – Feedback controller for the space environment



Validation



Preliminary Results



Conclusions



Future Work

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The space debris problem •

Total number of debris is increasing



Look the problem from a wider prospective



Need to define mitigation strategies able to control the whole population

Credit: NASA, 2016

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Research objectives Analyse debris control strategies 

Define future mitigation measures



Investigate multiple adaptive control strategies

E.g. of research questions

Will it be more effective to act evenly in Low Earth Orbit or have different strategies in certain regions depending on the severity of the problem? Is it better and enough to focus on only one remediation measure (e.g. active debris removal) or use a synergy of multiple ones?

Create a space debris model with a feedback controller 4

Reality vs. Model and Controller

Observed population (telescopes and radars)

* Reality Model

* IADC = Inter-Agency Space Debris Coordination Committee UN = United Nations

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Model description •

Deterministic sources-sink model [Wetherill, 1967] – Intrinsic collision probability [Wetherill, 1967] – Collision rate [Kessler and Cour-Palais, 1978] Simplified Model

Target Model

Launch profile (Courtesy of ESA*)

Mean from 8-yr cycle

8-yr cycle

Explosion profile

Fixed value/year

Lookup table

Collisions type (catastrophic/damaging)

Fixed ratio

Based on energy

Number of fragments: NASA Standard Break-up model [Johnson et al., 2001; Krisko, 2011]

A priori; fixed number

f(m)

Drag: piecewise exponential atmospheric model [King-Hele, 1987; Vallado, 2013]

f(h)

f(h, A, m)

Object types

3

7

Object classes

Circular h

a, e, A, M

Coupled non-linear first-order differential equations

72

5040

Controller

ADR**

ADR, PMD***

* ESA = European Space Agency. ** ADR = Active Debris Removal

*** PMD = Post Mission Disposal

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Object types and their interactions New launches

Integer PMD ADR Natural decay



Payloads



Rocket bodies



MROs

Explosion fragments Collision fragments



Initial population: LEO* residing objects (Courtesy of ESA)



PMD with residual lifetime and level of compliance



Main assumptions: – Circular orbits – No solar cycle and no solar radiation pressure – No other perturbations

* LEO = Low Earth Orbit

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Proportional feedback controller

u (t )  k P e(t )  k P ( NT (t )  NT* ) e(t )  NT (t )  N

* T

Previous work: [White and Lewis, 2014]

k P  0  umax  k   P emax  k P  umax

if

e(t )  0

if

0  e(t )  emax

if

e(t )  emax 8

Validation: Comparison to the IADC 2013 study DAMAGE

Initial

Final pop.

pop..

Intacts Existing fragments

Change %

Final pop.

Difference %

Change %

3410

4540.18

+33.14

4134.42

+21.24

-8.94

13696.99

4978.52

-63.65

4651.46

-66.04

-6.57

0

11060.32

-

13670.37

-

+23.60

17106.99

20579.02

+20.30

22456.25

+31.27

+9.12

67.37

6.31

New fragments Total

Simplified Model

Catastrophic Collisions

63.37

DAMAGE

Simplified Model

Credit: IADC, 2013

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Preliminary results: Analysis with a proportional control law Optimistic scenario •

90% compliance with PMD 25-yr rule



No explosions



PMD starts in 2013, but acts from 2046 (2013+8+25)

ADR •

Starts in 2020



Max 25 removals per year

Synergy of PMD and ADR

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Conclusions •

Simplified model of space debris population – Multi-attitude, multi-species – Fast quantitative results

– Working Proportional controller on ADR



Model assumptions and limitations – Circular bands – No solar cycle, solar activity



Validation of the model against IADC 2013 study



Preliminary results show the potential synergy of PMD and ADR

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Future work Model upgrades: – 7 object types – Area and Mass classes

– Semi-major axis, eccentricity and inclination discretisation

Extend the controller – From Proportional to PID controller – ADR and PMD (residual lifetime, compliance)

Sensitivity analysis: – discretisation values (number and value of height, mass and area bins), – other inputs (initial population, launch traffic) – model behaviour (number of explosions and collisions).

– New features to be included: solar cycle, solar radiation pressure, eccentricity bins.

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References •

Bennett, J. C., & Sang, J. (2011). Modelling the evolution of the low-Earth orbit debris population. In 11th Australian Space Science Conference, Canberra, 26 - 29 September, 2011 (pp. 165–178).



Inter-Agency Space Debris Coordination Committee. (2007). IADC Space Debris Mitigation Guidelines, revision 1.



Inter-Agency Space Debris Coordination Committee Working Group 2. (2013). Stability of the Future LEO Environment, 1–26. http://doi.org/IADC-12-08, Rev. 1



Johnson, N. L., Krisko, P. H., Liou, J.-C., Anz-Meador, P. D. (2001). NASA’s new breakup model of EVOLVE 4.0. Advances in Space Research, 28(9), 1377–1384. http://doi.org/10.1016/S0273-1177(01)00423-9



Kessler, D. J. (1991). Collisional Cascading : the limits of population growth in Low Earth Orbit. Advances in Space Research, 11(12), 63–66.



Kessler, D. J., & Cour-Palais, B. G. (1978). Collision Frequency of Artificial Satellites: The Creation of a Debris Belt. Journal of Geophysical Research, 83(A6), 2637–2646.



King-Hele, D. G. (1987). Satellite Orbits in an Atmosphere: Theory and Application. Springer Science & Business Media.



Krisko, P. H. (2011). Proper Implementation of the 1998 NASA Breakup Model. Orbital Debris Quarterly News, 15(4), 4–5.



National Aeronautics and Space Administration. (2016). Orbital Debris Quarterly News 2016, issue 1 -2.



Rossi, A., Cordelli, A., Farinella, P., & Anselmo, L. (1994). Collisional evolution of the Earth’s orbital debris cloud. Journal of Geophysical Research, 99(E11), 23,195-23,210.



United Nations Office for Outer Space Affairs. (2008). Space Debris mitigation guidelines of the committee on the peaceful uses of outer space. United Nations Office for Outer Space Affairs. http://doi.org/A/RES/62/217



Vallado, D. A. (2013). Fundamentals of Astrodynamics and Applications (4th ed.).



White, A. E., & Lewis, H. G. (2014). An adaptive strategy for active debris removal. Advances in Space Research, 53(8), 1195–1206. http://doi.org/10.1016/j.asr.2014.01.021



Wetherill, G. W. (1967). Collisions in the Asteroid Belt, 2429.

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Thank you for your attention Merci de votre attention

Gian Luigi Somma [email protected] Astronautics research group, Faculty of Engineering and the Environment, University of Southampton, United Kingdom

Acknowledgements •

ESA Space Debris Office



Part of this research was funded by the Doctoral Training Partnership through the EPSRC Grant EP/M50662X/1