Informatics
Mission Analysis
May 7, 2013

Cassini 2

A visualization of the best solution found
A visualization of the best solution found

Here we consider a different model for the Cassini trajectory with respect to the "Cassini1" case: deep space maneuvers are allowed between each one of the planets. This leads to a higher dimensional problem and to a higher complexity. We also consider, in the objective function evaluation, the final DV as a rendezvous rather than as an orbital insertion as in the "Cassini1" case.


The code

  1. MATLAB: use the function cassini2.m and pass to it the MGAproblem variable contained in cassini2.mat
  2. C++: call the function "double cassini2(const std::vector & x)" provided in the GTOPtoolbox.
  3. C++ (PaGMO): use the class pagmo::problem::cassini_2
  4. Python 2.7 (PyGMO): use PyGMO.problem.cassini_2().obj_fun(x)

Problem Description

The box bounds on each of the decision vector variable are given below.

State

Variable

Lower Bounds

Upper Bounds

Units

x(1)t0-10000MJD2000
x(2)Vinf35km/sec
x(3)u01n/a
x(4)v01n/a
x(5)T1100400days
x(6)T2100500days
x(7)T330300days
x(8)T44001600days
x(9)T58002200days
x(10)eta10.010.9n/a
x(11)eta20.010.9n/a
x(12)eta30.010.9n/a
x(13)eta40.010.9n/a
x(14)eta50.010.9n/a
x(15)r_p11.056n/a
x(16)r_p21.056n/a
x(17)r_p31.156.5n/a
x(18)r_p41.7291n/a
x(19)b_incl1-pipirad
x(20)b_incl2-pipirad
x(21)b_incl3-pipirad
x(22)b_incl4-pipirad

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


Solutions:

The best solutions submitted to this problem are listed below in chronological order

Author

Affiliation

Date

Obj Fun

Solutions

Algo

T., Vinko, D., IzzoEuropean Space AgencyMarch, 20088.924 km/s
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]
DE
B. Addis, A. Cassioli, M. Locatelli, F. SchoenGlobal Optimization Laboratory, University of Florence and University of TurinMay, 20088.530 km/s
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]
MBH
M. Vasile, E. MinisciUniversity of GlasgowJuly, 20088.419 km/s
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]
DE
M. Vasile, E. Minisci, M. LocatelliUniversity of Glasgow, University of TurinJuly, 20088.409 km/s
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]
MBH
B. Addis, A. Cassioli, M. Locatelli, F. SchoenGlobal Optimization Laboratory, University of Florence and University of TurinSept., 20088.405 km/s
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]
MBH
M. Vasile, E. Minisci, M. LocatelliUniversity of Glasgow, University of TurinJuly, 20088.385 km/s
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]
--
M. Schlueter, J. Fiala, M. GerdtsUniversity of Glasgow, University of BirminghamMay, 20098.383 km/s
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]
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.
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