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GTOP Database: Global Optimisation Trajectory Problems and Solutions

Problem "Rosetta" (MGA-1DSM)

This is a MGA-1DSM problem relative to a mission to the comet 67P/Churyumov-Gerasimenko. The fly-by sequence is similar to the one planned for the spacecraft Rosetta.

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  • MATLAB: use the function rosetta.m and pass to it the MGADSMproblem variable contained in rosetta.mat
  • C++: call the function double rosetta(const std::vector & x) function provided in the GTOPtoolbox.

    • Short description

    The problem presented in this section is a MGADSM problem relative to a mission to the comet 67P/Churyumov-Gerasimenko. The fly-by sequence selected is similar to the one planned for the spacecraft Rosetta. The objective function considered is the total mission delta V, including the launcher capabilities. The bounds used for the twenty-two dimension decision vector are listed in the following table:

    State Variable LB UB Units
    x(1) t0 1460 1825 MJD2000
    x(2) Vinf 3 5 km/sec
    x(3) u 0 1 n/a
    x(4) v 0 1 n/a
    x(5) T1 300 500 days
    x(6) T2 150 800 days
    x(7) T3 150 800 days
    x(8) T4 300 800 days
    x(9) T5 700 1850 days
    x(10) eta1 0.01 0.9 n/a
    x(11) eta2 0.01 0.9 n/a
    x(12) eta3 0.01 0.9 n/a
    x(13) eta4 0.01 0.9 n/a
    x(14) eta5 0.01 0.9 n/a
    x(15) r_p1 1.05 9 n/a
    x(16) r_p2 1.05 9 n/a
    x(17) r_p3 1.05 9 n/a
    x(18) r_p4 1.05 9 n/a
    x(19) b_incl1 -pi pi rad
    x(20) b_incl2 -pi pi rad
    x(21) b_incl3 -pi pi rad
    x(22) b_incl4 -pi pi rad

    No other constraints are considered for this problem. The objective function is considered to the precision of meters per second.

    Solutions

    A first trajectory has been found (26 March, 2008), (credits: T., Vinko, D., Izzo using DiGMO):

    J(x) = 1.449 km/s,

    x=[1524.25, 3.95107, 0.738307, 0.298318, 365.123, 728.902, 256.049, 730.485, 1850, 0.199885, 0.883382, 0.194587, 0.0645205, 0.493077, 1.05, 1.05, 1.05, 1.36925, -1.74441, 1.85201, -2.61644, -1.53468].

    A better solution has been found (18 April, 2008) using a sequential cooperative approach of DE and PSO:

    J(x) = 1.417km/s,

    x=[1524.26, 3.83938, 0.262978, 0.779762, 365.574, 720.579, 262.222, 728.772, 1848.47, 0.194268, 0.225388, 0.273158, 0.671802, 0.407266, 1.61803, 1.06012, 3.33304, 1.08071, -1.32760, 1.85218, -1.44709, -1.97420].

    A better solution has been found (29 May, 2008) credits: B. Addis, A. Cassioli, M. Locatelli, F. Schoen (Global Optimization Laboratory, University of Florence)

    J(x) = 1.368 km/s,

    x=[1532.24175527, 4.06829338437, 0.720326051073, 0.0348126697442, 365.2434892, 712.701756835, 260.961096679, 729.491441263, 1850, 0.202466066763, 0.486930227754, 0.356331627668, 0.549883084573, 0.431923236806, 1.28119554825, 1.05000000107, 3.1003448392, 1.0841556867 -1.97835856005, 1.81131692678, -1.26622621813, -1.97940868135].

    A better solution has been found (09 Sep, 2008) credits: M. Vasile, E. Minisci (University of Glasgow)

    J(x) = 1.360 km/s,

    x=[1543.30669582458, 4.62591297553792, 0.735711649721644, 0.751372228132414, 365.24128038597, 704.776990594467, 258.110840823509, 730.484771806871, 1849.99995454174, 0.341009328525255, 0.808663668992205, 0.376496220185218, 0.171287567923826, 0.431489206122146, 3.07135208604219, 1.06000000320681, 1.41824842842757, 1.39748724339122, -1.39587494176148 1.77647871470111, -2.52771948343642, -1.58247504575273].

    A better solution has been found (29 Sep, 2008) credits: M. Vasile, E. Minisci (University of Glasgow)

    J(x) = 1.355 km/s,

    x=[1541.2778574301 4.41425813939918 0.738120308957349 0.565680439091451 365.240617831587 708.567754159261 258.093449382336 730.090210655871 1850 0.270070640549605 0.807410043318084 0.0340763968862974 0.665797649174603 0.439110068689427 2.98093380724754 1.06 3.22629172773521 1.06 -1.69972011825889 1.79541928084097 -1.55821584701606 -1.97742285404074].

    A better solution has been found (22 Oct, 2008) credits: B. Addis, A. Cassioli, M. Locatelli, F. Schoen (Global Optimization Laboratory, University of Florence)

    J(x) = 1.344 km/s,

    x=[1543.32709193 4.5134580971 0.728163430778
    0.083363202293 365.241449354 707.419993725 257.129520623 730.483802497
    1849.96966072 0.31440923274 0.803777352667 0.0321377696745
    0.123194720658 0.432626759733 1.4649721658 1.05000000002 3.18319943186
    1.05823552668 -2.15517168796 1.78540451293 -1.63643821124 -1.98027492278].

    The best solution found so far (29 Sep, 2008) credits: M. Vasile, E. Minisci (University of Glasgow)

    J(x) = 1.343 km/s,

    x=[ 1542.80272275624 4.47844417111601 0.731698680164396 0.878289696281778 365.242313115732 707.754644446782 257.323851633799 730.483723605649 1850 0.469187103696963 0.810371727143097 0.0572409393084966 0.123333368519021 0.436535683460624 2.65762617428421 1.05 3.19780616934668 1.05622179187182 -1.2538881176403 1.78760232965523 -1.59467141651773 -1.97732549500432].
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