[10] “3rd Global Trajectory Optimisation Competition,” Politecnico di Torino, [http://www2.polito.it/eventi/gtoc3/. Accessed 6 November 2009]. [11] “4th Global Trajectory Optimisation Competition,” Centre National D’Etudes Spatiales, [http://cct.cnes.fr/cct02/gtoc4/index.htm. Accessed 6 November 2009]. [12] Sims, J.A., Flanagan, S.N., “Preliminary Design of Low-Thrust Interplanetary Mission,” AAS 99-338, AAS/AIAA Astrodynamics Specialist Conference, Girdwood, Alaska, 16-19 August 1999. [13] Sims, J.A., Finlayson, P.A., Rinderle, E.A., Vavrina, M.A., Kowalkowski, T.D., “Implementation of a Low-Thrust Trajectory Optimization Algorithm <strong>for</strong> Preliminary Design”, AIAA 2006-6746, AIAA/AAS Astrodynamics Specialist Conference, 21-24 August 2006, Keystone, CO. [14] Ranieri, C.L., Ocampo, C.A., “Optimization of Roundtrip, Time-Constrained Finite Burn Trajectories via an Indirect Method,” Journal of Guidance, Control, <strong>and</strong> Dynamics, Vol. 28, No. 2, March-April 2005, pp. 306-314. [15] Kluever, C.A., “Optimal Low-Thrust Interplanetary Trajectories by Direct Method Techniques,” Journal of the Astronautical Sciences, Vol. 45, No. 3, July-Sept. 1997, pp. 247-262. [16] Dewell, L., Menon, P., “Low-Thrust Orbit Transfer Optimization Using Genetic Search,” AIAA Guidance, Navigation, <strong>and</strong> Control Conference <strong>and</strong> Exhibit, AIAA, Reston, VA, 1999, pp. 1109-1111. [17] Betts, J.T., “Survey of Numerical Methods <strong>for</strong> Trajectory Optimization”, Journal of Guidance, Control, <strong>and</strong> Dynamics, Vol. 21, No. 2, March-April 1998 pp. 193-207. [18] Betts, J.T., “Optimal Interplanetary Orbit Transfers by Direct Transcription,” Journal of the Astronautical Sciences, Vol. 42, No. 3, July-Sept. 1994, pp. 247-268. [19] Coverstone-Carroll, V., Williams, S.N., “Optimal Low-Thrust Trajectories using Differential Inclusion Concept,” Journal of the Astronautical Sciences, Vol. 42, No. 4, Oct.-Dec. 1994, pp. 379-393. 181
[20] Hargraves, C. R., <strong>and</strong> Paris, S.W., “Direct Trajectory Optimization Using Nonlinear Programming <strong>and</strong> Collocation,” Journal of Guidance, Control, <strong>and</strong> Dynamics, Vol. 10, No. 4, 1987, pp. 338–342. [21] Tang, S., <strong>and</strong> Conway, B. A., “Optimization of Low-Thrust Interplanetary Trajectories Using Collocation <strong>and</strong> Nonlinear Programming,” Journal of Guidance, Control, <strong>and</strong> Dynamics, Vol. 18, No. 3, 1995, pp. 599–604. [22] Lantoine, G., Russell, R.P., “A Hybrid Differential Dynamic Programming Algorithm <strong>for</strong> Robust Low-Thrust Optimization,” AIAA 2008-6615, AIAA/AAS Astrodynamics Specialist Conference <strong>and</strong> Exhibit, Honolulu, Hawaii, 18-21 August 2008. [23] Lantoine, G., Russell, R.P., “A Fast Second-Order Algorithm For Preliminary Design of Low-Thrust Trajectories,” IAC-08-C1.2.5, 59th International Astronautical Congress, Glasgow, Scotl<strong>and</strong>, 29 September – 3 October 2008. [24] Lantoine, G., Russell, R.P., “The Stark Model: An Exact, Closed-Form Approach to Low-Thrust Trajectory Optimization,” 21st International Symposium on Space Flight Dynamics, Toulouse, France, 28 September – 2 October 2009. [25] Gao, Y., Kluever, C.A., “Low-Thrust Interplanetary Orbit Transfers Using Hybrid Trajectory Optimization Method with Multiple Shooting”, AIAA 2004-5088, AIAA/AAS Astrodynamics Specialist Conference <strong>and</strong> Exhibit, August 2004, Providence, RI. [26] Ranieri, C.L., Ocampo, C.A., “Optimizing Finite-Burn, Round-Trip Trajectories with Isp Constraints <strong>and</strong> Mass Discontinuities” Journal of Guidance, Control, <strong>and</strong> Dynamics, Vol. 28, No. 4, July-August 2005, pp. 775-781. [27] Russell, R., “Primer Vector Theory Applied to Global Low-Thrust Trade Studies,” AAS 06-156, 16th AAS/AIAA Space Flight Mechanics Conference, Tampa, Florida, 22-26 January 2006. [28] Gill, P.E., Murray, W., Saunders, W.A., “User’s Guide <strong>for</strong> SNOPT Version 7: A FORTRAN Package <strong>for</strong> Large-Scale Nonlinear Programming,” University of Cali<strong>for</strong>nia, San Diego, 16 June 2008. 182
- Page 1 and 2:
DESIGN SPACE PRUNING HEURISTICS AND
- Page 3 and 4:
“The mediocre teacher tells. The
- Page 5 and 6:
I am thankful for all of my friends
- Page 7 and 8:
2.5 Small Sample Problem...........
- Page 9 and 10:
LIST OF TABLES Table 1 Ten best ast
- Page 11 and 12:
LIST OF FIGURES Figure 1 Mars round
- Page 13 and 14:
Figure 35: Low-thrust optima as a f
- Page 15 and 16:
LIST OF SYMBOLS AND ABBREVIATIONS A
- Page 17 and 18:
σBXB υ φ ω Ω Sample standard d
- Page 19 and 20:
optimization scheme to locate a bro
- Page 21 and 22:
provide clues to the nature of the
- Page 23 and 24:
additional constraints and objectiv
- Page 25 and 26:
Pontryagin’s Minimum Principle, w
- Page 27 and 28:
improved accuracy (as compared to d
- Page 29 and 30:
Figure 2: Trajectory structure of t
- Page 31 and 32:
flyby problems with numerous interm
- Page 33 and 34:
Gravity assists are modeled as inst
- Page 35 and 36:
Prior to the LTTT effort, the prima
- Page 37 and 38:
the shape of the trajectory and ana
- Page 39 and 40:
draws upon the theory of niche and
- Page 41 and 42:
the sequence of encounter bodies, t
- Page 43 and 44:
1.2.2 Evolutionary Neurocontrollers
- Page 45 and 46:
Figure 6: Converting an evolutionar
- Page 47 and 48:
which find good solutions but can n
- Page 49 and 50:
functions. In this problem, only im
- Page 51 and 52:
As aforementioned, branch-and-bound
- Page 53 and 54:
consuming, user-intensive, and ofte
- Page 55 and 56:
asteroid tour mission design proble
- Page 57 and 58:
CHAPTER II DEVELOPMENT OF METHODOLO
- Page 59 and 60:
Kˆ ĥ i ν ê v r ω Ĵ Ω nˆ Î
- Page 61 and 62:
Finally, both the eccentricity of a
- Page 63 and 64:
maximum possible number of revoluti
- Page 65 and 66:
outer loop: a genetic algorithm and
- Page 67 and 68:
2.3.2 Branch-and-Bound The branch-a
- Page 69 and 70:
The order in which the branches are
- Page 71 and 72:
approach performs best, followed by
- Page 73 and 74:
Figure 16: Effect of number of segm
- Page 75 and 76:
Within the sample problem, MALTO wa
- Page 77 and 78:
Table 2: Orbital elements of astero
- Page 79 and 80:
final mass. The correlation coeffic
- Page 81 and 82:
Maximum Final Mass (kg) 1500 1250 L
- Page 83 and 84:
The next approach is to compare the
- Page 85 and 86:
Final Mass (kg) 950 900 850 800 750
- Page 87 and 88:
pruning metric must be calculated f
- Page 89 and 90:
educed-size problem. Furthermore, t
- Page 91 and 92:
aBiB < 25%, and 15% for Leg 1, Leg
- Page 93 and 94:
Earth departure date and three time
- Page 95 and 96:
algorithm, which determines the opt
- Page 97 and 98:
is calculated using the same specif
- Page 99 and 100:
metrics which were calculated in th
- Page 101 and 102:
sorted by final mass. All of the se
- Page 103 and 104:
impulse optima. Figure 35 plots the
- Page 105 and 106:
CHAPTER III OVERVIEW OF METHODOLOGY
- Page 107 and 108:
(1) All asteroid sequences are rank
- Page 109 and 110:
two-impulse optimum solutions. Ther
- Page 111 and 112:
identifying another metric that cou
- Page 113 and 114:
CHAPTER IV VALIDATION OF METHODOLOG
- Page 115 and 116:
Table 8 lists the 10 best asteroid
- Page 117 and 118:
In order to further validate the pr
- Page 119 and 120:
impulse ∆V). The first iteration
- Page 121 and 122:
Because the impulsive multiplier ha
- Page 123 and 124:
Table 12: Effectiveness of the meth
- Page 125 and 126:
function calls to MALTO were requir
- Page 127 and 128:
order of 0.8 (assuming a final mass
- Page 129 and 130:
Table 16: Design variables for gene
- Page 131 and 132:
known solution to 1621 kg. Based on
- Page 133 and 134:
MBfB (kg) #1, #63, and #16, respect
- Page 135 and 136:
problem (Table 17). Additionally, t
- Page 137 and 138:
≤ Inclination (deg) 60 50 40 30 2
- Page 139 and 140:
order to have a benchmark with whic
- Page 141 and 142:
Of the remaining sequences, the 1 s
- Page 143 and 144:
Table 22: Settings for the genetic
- Page 145 and 146:
120 Impulsive Solutions Low-Thrust
- Page 147 and 148:
of exactly four weeks. As a benchma
- Page 149 and 150: Objective Function (kg/yr) 120 100
- Page 151 and 152: these two problems, the best known
- Page 153 and 154: asteroid sequences would be require
- Page 155 and 156: Table 27: Best known solutions rema
- Page 157 and 158: Table 29: Best known solutions rema
- Page 159 and 160: good solutions exist in the design
- Page 161 and 162: heuristics chosen were based on the
- Page 163 and 164: problem, the best set of solutions
- Page 165 and 166: Finally, for each set of inner loop
- Page 167 and 168: solutions from the GTOC2 competitio
- Page 169 and 170: sequences were optimized in low-thr
- Page 171 and 172: application is for the conceptual d
- Page 173 and 174: types of the TSP, they have not bee
- Page 175 and 176: methodology would be applied in the
- Page 177 and 178: APPENDIX A SET OF GTOC2 ASTEROIDS T
- Page 179 and 180: 3054373 "2000 UK11" 0.88325596 0.24
- Page 181 and 182: 3152317 "2003 GQ22" 0.87232869 0.18
- Page 183 and 184: 3283227 "2005 MR5" 0.85281863 0.295
- Page 185 and 186: 2000089 Julia 2.5500653 0.18377079
- Page 187 and 188: 2000496 Gryphia 2.1987751 0.079568
- Page 189 and 190: 2001216 Askania 2.2322234 0.1793551
- Page 191 and 192: 2000134 Sophrosyne 2.5632069 0.1166
- Page 193 and 194: 2000712 Boliviana 2.5738464 0.18812
- Page 195 and 196: 2005209 "1989 CW1" 5.1533221 0.0495
- Page 197 and 198: 36 2006 RJ1 0.9508113 0.30070707 1.
- Page 199: REFERENCES [1] Rayman, M.D., Willia
- Page 203 and 204: [38] Petropoulos, A., Kowalkowski,
- Page 205 and 206: [57] Wuerl, A., Crain, T., Braden,
- Page 207 and 208: [78] Cosmic Vision: Space Science f
- Page 209: time, she enjoys traveling as well