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Mission Performance Evaluation for Solar Sails using a Refined SRP Force Model with Variable

Optical Coefficients

Andreas BorggräfeStudent of Astronautical Engineering, RWTH Aachen University, Wüllnerstr. 752062 Aachen, Germanyandreas.borggraefe@rwth-aachen.de

2nd International Symposium on Solar Sailing, New York, July 2010

Bernd DachwaldFH Aachen University of Applied Sciences, Hohenstaufenallee 6

52064 Aachen, Germanydachwald@fh-aachen.de

Outline

Global Trajectory Optimization

SRP Force Models

Mission Performance Evaluation

Conclusions

Motivation

Refined SRP Force Model

Results

Evolutionary Neurocontrol

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Motivation

• Interplanetary mission performance evaluation of the refined SRP force model (Mengali et al., 2006) and comparison to the standard model → mission transfer time?

• Integration of the refined SRP force model into global trajectory optimization tool using evolutionary neurocontrol

• Mengali et. al., 2006 performed a model comparison by a series of interplanetary circle-to-circle body orbit rendezvous missions to Mars and Venus

• Now: Comparison by a series of interplanetary body

rendezvous missions between real orbits → near-Earth asteroid 1996FG3 (eccentricity e = 0.35) → Mercury (semi-major axis a = 0.387)

• Results are compared to the case study by Mengali et al.

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t

[5]

SRP Force Models

• SRP force exerted on a solar sail commonly described by two unit vectors:

sail normal (unit) vector n thrust (unit) vector m

→ sail pitch angle → (thrust) cone angle

→ sail clock angle → sail clock angle

Solar radiation pressure (SRP) force models

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1. The ideal solar sail model

• Ideally reflecting sail surface (perfect mirror), only rough approx. of the SRP force

2. The optical solar sail model (standard model)

• real thermo-optical surface with optical coefficients

[4], [5]

SRP Force Models

22 cosF PA n

Basic SRP force models

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, , const.s

6[1]

SRP Force Models

• summarizing all these force fractions, the SRP force exerted on the solar sail results in

with

• by introducing constant thermo-optical SRP force coefficients

• highly reflective front side (Al) and highly emissive back side (Cr) → (reference sail)

1 2 3( , ), ( , , , , , ), ( , )f b f ba f s a f s B B a f s

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cosmF PA m 2 2

1 2 3cos sina a a

7[1]

3. The refined solar sail model (Mengali et al., 2006)

• introduces dependence of thermo-optical coefficients on the pitch angle , the mean surface roughness (in nm) and the sail temperature

Al coated front side

• experimentally discovered by using unpolarized solar light on reference sail film

• Conclusively:

Refined SRP Force Model

0.94

( ), ( , )

( ) ( , ) ( )

f s f h

f T f r f

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1 2 3, , const.a a a

[3]

hT

8[1]

Refined SRP Force ModelRefined SRP model performance

• ‘force-bubble’ describes the set of possible force vectors for each SRP model as a function of

force-bubbles for:

• ideal SRP model• standard SRP model• refined SRP model

(h = 0, 25 nm)

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standard

mF

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Global Trajectory Optimization

[2], [5]

Motivation for the development of InTrance (Bernd Dachwald, DLR)

(Intelligent Trajectory optimization using neurocontroller evolution)

• Development of an easy-to-use, multi-purpose, low-thrust optimization tool– Users do not need to be experts in astrodynamics or optimal

control theory– No initial guess needed for optimization– Global search behavior

• Preliminary mission analysis shall be possible for a variety of low-thrust problems– Fly-by, rendezvous, orbit-to-orbit transfer, escape, capture– Planetary and interplanetary problems– Multiple-phase problems (e.g. multiple rendezvous/fly-bys, or

GTO to Moon orbit)

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How does InTrance work?

Evolutionary Neurocontrol - Neural Networks

Evolutionary Neurocontrol

[5]

• information processing and intelligence in nervous systems is based on the transmission of stimuli in neurons

• neuron structure is quite simple and uniform

• complexity yields from inter-neural connections (synapses)

• changing the neuron connections = Learning

• idea: adapted neural network to find global optimal trajectory

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Evolutionary Neurocontrol – Artificial Neural Network

Input layer

Output layer

coordinates (of S/C and target body)

steering angles (local optimal thrust direction)

Evolutionary Neurocontrol

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Coding the ANN-parameters onto a string

4γ 5γ

6γ

w41

w51 w42w43

w53

w52

w64 w65

ANN-parameters Individual (string, chromosome)

i1 2 3

4 5

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ANN EA

Evolutionary Neurocontrol

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Evolutionary Neurocontrol – Evolutionary Algorithm

SelectionReproduction

Evaluation

Population

0

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2

5

7

6

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98

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Winner Loser

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108

Recombination/Mutation

i

Evolutionary Neurocontrol

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Mission Performance EvaluationChosen Mission Scenarios

• Two interplanetary body rendezvous missions to Mercury and near-Earth asteroid 1996FG3

• Two solar sails with “low” (ac =0.2 mm/s2) and “medium” (ac = 0.5 mm/s2) performance

• Comparison of standard SRP force model and refined SRP force model (h = 0, 10 and 25 nm)

• launch window from 58000 MJD (09/04/2017) to 58200 MJD (03/23/2018)

• integration step size: 1 d/step

• final target distance: 1000 km

• final relative velocity: 100 m/s

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Results

[1]

Transfer times of 1996FG3 and Mercury body rendezvous missions

• Comparison to case study by Mengali et. al. for Mars (Venus): transfer times for the refined model, h = 0 nm are about smaller with respect to the standard model

5.2 %

4.9 %2.3 %

5.3 %

5.8% (5.4%)

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Results1996FG3 and Mercury body rendezvous sample trajectories

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Conclusions

• refined SRP model yields shorter transfer times than the standard model (good agreement with case study by Mengali et. al. 2006 for Mars and Venus)

• The sail performance grows with decreasing surface roughness of sail’s coating material

• realistic interplanetary missions with large change in eccentricity and semi-major axis show the same difference in transfer time than the Mengali study

• the difference in transfer times between the standard and the refined

SRP model (h = 0 nm) is about 5% with respect to the standard model

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Thank you very much for your interest!

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References

[1] G. Mengali, A. A. Quarta, C. Circi, B. Dachwald: Refined Solar Sail Force Model with Mission Application. Journal of Guidance, Control, and Dynamics, 30(2), 2007.[2] B. Dachwald: Optimization of Interplanetary Solar Sailcraft Trajectories Using Evo-lutionary Neurocontrol. Journal of Guidance, Control, and Dynamics, 27(1), 2004.[3] G. Vulpetti, S. Scaglione: Aurora project: Estimation of the optical sail parameters.

Acta Astronautica, Vol. 44, Nos. 2-4, 1999.[4] J. Wright: Space Sailing, Gordon and Breach Science Publishers, Philadelphia, 1992. [5] B. Dachwald: Low-Thrust Trajectory Optimization and Interplanetary Mission Analysis Using Evolutionary Neurocontrol, Doctoral Thesis, Universität der Bundeswehr München; Fakultät für Luft- und Raumfahrttechnik, 2004.[6] A. Borggräfe: Implementation of a Refined Solar Sail Model with Varying Optical Force Coefficients, Student Research Paper, RWTH Aachen University, 2010.

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[SA]

Simplifications & Assumptions within this study:

Appendix

• The sail film is flat and will not billow under load (rigid surface) • The optical sail film properties will not change with time due to degradation of

the material caused by space environmental effects• Other forms of momentum transport, like solar wind or atmospheric drag are

neglected• Other forms of radiation, like planetary albedo, thermal or cosmic microwave

background are neglected• The sun is approximated as a point source of photonic radiation. In reality,

the sun is a disc of finite angular size and thus the photons are not perfectly parallel on the sail surface. This abberation however is only relevant in close proximity to the sun (r ≤ 0.05 AU)

• Neglection of the Limb-darkened solar disc and decreasing intensity in the outer region

• With regard to the simulation environment provided by InTrance, the change of the sail normal vector n is performed instantaneously (no simulation of sail attitude dynamics)

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[Wright]

Appendix

Thermo-optical coefficients a1, a2 and a3

Values of optical coefficients for ideal and standard SRP model

3a

1a

2a

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3. The refined solar sail model (Mengali et al., 2006)

• force coefficients a1, a2 and a3 are no longer assumed to be constant

• reflectivity and specular reflectivity s depend on the pitch angle and the mean surface roughness h (in nm)

Al coated front side

• Emissivity (front and back) depends on the SET (sail equilibrium temperature) and thus on the pitch angle and the solar distance r

• Thermo-optical coefficients now:

Refined SRP Force Model

0.94

( ), ( , )

( ) ( , ) ( )

f s f h

f SET f r f

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AppendixRefined SRP force model

Al coated front side

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( )f

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[1]

Appendix

• Emissivity (front and back) depends on the SET (sail equilibrium temperature) and thus on the pitch angle and the solar distance r

• Influence of the solar distance r in the SRP force equations is less than 3% for r [0.3, 5.2] AU and can be neglected

• Conclusively:( ), ( , ), ( ) ( , ) ( )f s f h f SET f r f

Al coated front side Cr coated back side

Refined SRP force model

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[1]

Refined SRP Force ModelRefined SRP model’s force coefficients a1, a2 and a3 as a function of and h

red: standard SRP force model

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[1]

Refined SRP Force ModelRefined SRP model performance

• ‘a-bubble’ describes the set of possible acceleration vectors for each SRP model

• maximum transversal thrust at about 35°• above 60° the standard model slightly

exceeds the performance of the refined model

35°

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Evolutionary Neurocontrol – Artificial Neural Networks

[4], [5]

• Alternative computing paradigm to conventional serial digital computing– massively parallel– analog– error-tolerant– adaptive

• Comprise connected primitive information-processing elements, which imitate elemental functions of biological neurons

• Show some features of information processing in real nervous systems– learning from experience– generalization from known

examples to unknown– extraction of relevant information

out of noisy input, which may also contain irrelevant data

Appendix

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Low-thrust trajectory optimization using evolutionary neurocontrol

Appendix

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Mission Performance Evaluation

[1], [SA]

Refined SRP model validation

• Case study by Mengali et. al., 2006: Interplanetary circle-to-circle body orbit rendezvous missions to Mars and Venus for ac [0.12, 5.93] mm/s2

• Comparison of standard and refined SRP force model (h = 0, 10 and 25 nm)

• Two exemplary solar sail performances:

“low” (ac =0.2 mm/s2) and “medium” (ac = 0.5 mm/s2)

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