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Andreas Borggräfe Student of Astronautical Engineering, RWTH Aachen University,

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  1. 2nd International Symposium on Solar Sailing, New York, July 2010 Mission Performance Evaluation for Solar Sails using a Refined SRP Force Model with Variable Optical Coefficients Bernd Dachwald FH Aachen University of Applied Sciences, Hohenstaufenallee 6 52064 Aachen, Germany dachwald@fh-aachen.de Andreas Borggräfe Student of Astronautical Engineering, RWTH Aachen University, Wüllnerstr. 752062 Aachen, Germany andreas.borggraefe@rwth-aachen.de

  2. Outline Motivation SRP Force Models Refined SRP Force Model Global Trajectory Optimization Evolutionary Neurocontrol Mission Performance Evaluation Results Conclusions

  3. 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.

  4. SRP Force Models Solar radiation pressure (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 [5] 4

  5. SRP Force Models Basic SRP force models • The ideal solar sail model • Ideally reflecting sail surface (perfect mirror), only rough approx. of the SRP force • The optical solar sail model (standard model) • real thermo-optical surface with optical coefficients [4], [5] 5


  6. 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] 6

  7. Refined SRP Force Model • 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 • experimentally discovered by using unpolarized solar light on reference sail film • Conclusively: 0.94 [1] Al coated front side [3] 7

  8. standard Refined SRP Force Model • Refined 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) [1] 8

  9. Global Trajectory Optimization 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) [2], [5] 9

  10. Evolutionary Neurocontrol How does InTrance work? Evolutionary Neurocontrol - Neural Networks • 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 [5] 10

  11. Evolutionary Neurocontrol Evolutionary Neurocontrol – Artificial Neural Network coordinates(of S/C and target body) Input layer Output layer steering angles(local optimal thrust direction) [5] 11

  12. Evolutionary Neurocontrol Coding the ANN-parameters onto a string ANN EA 1 2 3 w51 w43 w42 w52 w53 w41 5 4 w65 w64 6 ANN-parameters Individual (string, chromosome) [5] 12

  13. Evolutionary Neurocontrol Evolutionary Neurocontrol – Evolutionary Algorithm Reproduction Selection Recombination/Mutation Winner Loser Evaluation Population [5] 13

  14. Mission Performance Evaluation Chosen 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 14

  15. Results Transfer times of 1996FG3 and Mercury body rendezvous missions 5.2 % 5.3 % 2.3 % 4.9 % • 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 5.8% (5.4%) [1] 15

  16. Results 1996FG3 and Mercury body rendezvous sample trajectories 16

  17. Conclusions • refined SRP model yields shorter transfer timesthan 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 17

  18. Thank you very much for your interest!

  19. 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. 21

  20. Appendix • Simplifications & Assumptions within this study: • 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) [SA] 22

  21. Appendix • Thermo-optical coefficients a1, a2 and a3 • Values of optical coefficients for ideal and standard SRP model [Wright] 23

  22. Refined SRP Force Model • 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) • 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: 0.94 [1] Al coated front side 7

  23. Appendix Refined SRP force model [1] Al coated front side 25

  24. Appendix Refined SRP force model • 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: [1] Cr coated back side Al coated front side 24

  25. Refined SRP Force Model Refined SRP model’s force coefficients a1, a2 and a3 as a function of and h [1] red: standard SRP force model 8

  26. Refined SRP Force Model • Refined SRP model performance • ‘a-bubble’ describes the set of possible acceleration vectors for each SRP model 35° [1] • maximum transversal thrust at about 35° • above 60° the standard model slightly exceeds the performance of the refined model 26

  27. Appendix Evolutionary Neurocontrol – Artificial Neural Networks • 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 [4], [5] 27

  28. Appendix Low-thrust trajectory optimization using evolutionary neurocontrol 28

  29. Mission Performance Evaluation 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) [1], [SA] 15