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
2
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
3
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
5
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
6
Object types and their interactions New launches
Integer PMD ADR Natural decay
•
Payloads
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Rocket bodies
•
MROs
Explosion fragments Collision fragments
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Initial population: LEO* residing objects (Courtesy of ESA)
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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
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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
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Validation of the model against IADC 2013 study
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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).
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Inter-Agency Space Debris Coordination Committee. (2007). IADC Space Debris Mitigation Guidelines, revision 1.
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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
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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
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Kessler, D. J. (1991). Collisional Cascading : the limits of population growth in Low Earth Orbit. Advances in Space Research, 11(12), 63–66.
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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.
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King-Hele, D. G. (1987). Satellite Orbits in an Atmosphere: Theory and Application. Springer Science & Business Media.
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Krisko, P. H. (2011). Proper Implementation of the 1998 NASA Breakup Model. Orbital Debris Quarterly News, 15(4), 4–5.
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National Aeronautics and Space Administration. (2016). Orbital Debris Quarterly News 2016, issue 1 -2.
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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.
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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
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Vallado, D. A. (2013). Fundamentals of Astrodynamics and Applications (4th ed.).
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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
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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
