ESA Home
GSP Home
About the ACT
Research
Ariadna
Publications
Keep in touch!
More
Informatics
GTOP Database: Global Optimisation Trajectory Problems and Solutions

Problem "Cassini2" (MGA-1DSM)

This code evaluates the DV required to reach Saturn using an Earth Venus Venus Earth Jupiter Saturn fly-by sequence with deep space manouvres.

Download

  • MATLAB: use the function cassini2.m and pass to it the MGADSMproblem variable contained in cassini2.mat
  • C++: call the function double cassini2(const std::vector & x) function provided in the GTOPtoolbox.

    • Short description

    Consider a different model for the Cassini trajectory: deep space maneuvers are allowed between each one of the planets. This leads to a higher dimensional problem with a much higher complexity. We also consider, in the objective function evaluation, a rendezvous problem rather than an orbital insertion as in the MGA model of the Cassini mission. This is the main cause for the higher objective function values reached. For the twelve dimension state vector we use the bounds given in the following table:

    State Variable LB UB Units
    x(1) t0 -1000 0 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 100 400 days
    x(6) T2 100 500 days
    x(7) T3 30 300 days
    x(8) T4 400 1600 days
    x(9) T5 800 2200 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 6 n/a
    x(16) r_p2 1.05 6 n/a
    x(17) r_p3 1.15 6.5 n/a
    x(18) r_p4 1.7 291 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 preliminary trajectory has been found (26 March, 2008), (credits: T., Vinko, D., Izzo using DiGMO):

    J(x) = 8.924 km/sec,

    x=[-815.144, 3, 0.623166, 0.444834, 197.334, 425.171, 56.8856, 578.523, 2067.98, 0.01, 0.470415, 0.01, 0.0892135, 0.9, 1.05044, 1.38089, 1.18824, 76.5066, -1.57225, -2.01799, -1.52153, -1.5169]

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

    J(x) = 8.530 km/sec,

    x=[-775.073192377, 3.34939840763, 0.519859871615, 0.377648835192, 164.514496917, 420.857826262, 54.7953357438, 587.550012334, 2172.83783929, 0.666969680984, 0.437098773474, 0.0143681690338, 0.0151496118993, 0.0852702838402, 1.54714942102, 1.18980793974, 1.25955058062, 71.3030467945, -1.62797088705, -1.98297404025, -1.53976626419, -1.51425029677]

    A better solution has been found (07th July, 2008) credits: M. Vasile, E. Minisci (University of Glasgow) using Differential Evolution

    J(x) = 8.419 km/sec,

    x=[ -778.047305631216, 3.18312649956441, 0.517194165210629, 0.399454532008061, 164.47695637194, 423.970795573978, 54.7479052540502 589.990666953636, 2199.60570034135, 0.762963004566719, 0.550121138102629, 0.0126601160795708, 0.17223077205906, 0.270111519882677, 1.42837324938403, 1.1774879453091, 1.26425574056075, 70.1906989621161, -1.59765413874108, -1.98140734837078, -1.53978935969435, -1.51329954805784]

    A better solution has been found (26th July, 2008) credits: M. Vasile, E. Minisci (University of Glasgow) M. Locatelli (University of Turin), using Monotonic Basin Hopping

    J(x) = 8.409 km/sec,

    x=[-779.060197373242, 3.32046443745595, 0.531333503613675, 0.376218447342955, 168.685775870437, 422.672656805198, 53.3360098337041, 589.777827855018, 2200, 0.718720247401635, 0.532962541494841, 0.159170896444411, 0.470495109020601, 0.0986526263521857, 1.46946051297954, 1.05138706406598, 1.30594027188689, 69.8194077461197, -1.60160853231321, -1.9600386515463, -1.55445003054861, -1.51343200828766]

    A better solution has been found (19th September, 2008) credits: B. Addis, A. Cassioli, M. Locatelli, F. Schoen (Global Optimization Laboratory, University of Florence and University of Turin)

    J(x) = 8.405 km/sec,

    x=[-778.765203484, 3.23018448427, 0.523118701494, 0.392764786131, 165.698711849, 424.757237926, 53.7855982056, 589.617865592, 2197.32875485, 0.733366262496, 0.545182500335, 0.02342601953, 0.07119604834, 0.0508270625102, 1.31540232722, 1.09024682281, 1.29246247343, 70.037231829, -1.58673415524, -1.96631114594, -1.54982899287, -1.51341338598]

    A better solution has been found (04th December, 2008) credits: M. Vasile, E. Minisci (University of Glasgow) M. Locatelli (University of Turin)

    J(x) = 8.385 km/sec,

    x=[-779.046753814506, 3.25911446832345, 0.525976214695235, 0.38086496458657, 167.378952534645, 424.028254165204, 53.2897409769205, 589.766954923325, 2200, 0.769483451363201, 0.513289529822621, 0.0274175362264024, 0.263985256705873, 0.599984695281461, 1.34877968657176, 1.05, 1.30730278372017, 69.8090142993495, -1.5937371121191, -1.95952512232447, -1.55498859283059, -1.5134625299674]

    The best solution known to this problem (22th May 2009) (credits: M. Schlueter, J. Fiala, M. Gerdts, University of Birmingham) found by MIDACO within the project "Non-linear mixed-integer-based Optimisation Technique for Space Applications" co-funded by ESA Networking Partnership Initiative, Astrium Limited (Stevenage, UK) and the School of Mathematics, University of Birmingham, UK.

    J(x) = 8.383 kg km/sec,

    x=[-779.629801566988, 3.265804135361, 0.528440291493, 0.382390419772, 167.937610148996, 424.032204472497, 53.304869390732, 589.767895836123, 2199.961911685212, 0.772877728290, 0.531757418755, 0.010789195916, 0.167388829033, 0.010425709182, 1.358596310427, 1.050001151443, 1.306852313623, 69.813404643644, -1.593310577644, -1.959572311812, -1.554796022348, -1.513432303179].
    Currently visiting the ACTweb
    tracker