Informatics
Mission Analysis
May 7, 2013

Messenger (reduced version)

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

This trajectory optimisation problem represents a rendezvous mission to Mercury modelled as an MGA-1DSM problem. The selected fly-by sequence is the same used in the first part of the Messenger mission. It is well known that a significant reduction of the required deltaV is possible if a number of resonant fly-bys follow the first Mercury encounter. Those resonant fly-bys are not included in this model creating a much simpler problem.


The code

  1. MATLAB: use the function messenger.m and pass to it the MGAproblem variable contained in messenger.mat
  2. C++: call the function "double messenger(const std::vector& x)" provided in the GTOPtoolbox.

Problem Description

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

State

Variable

Lower Bounds

Upper Bounds

Units

x(1)t010004000MJD2000
x(2)Vinf15km/sec
x(3)u01n/a
x(4)v01n/a
x(5)T1200400days
x(6)T230400days
x(7)T330400days
x(8)T430400days
x(9)eta10.010.99days
x(10)eta30.010.99n/a
x(11)eta30.010.99n/a
x(12)eta40.010.99n/a
x(13)r_p11.16n/a
x(14)r_p21.16n/a
x(15)r_p31.16n/a
x(16)b_incl1-pipin/a
x(17)b_incl2-pipin/a
x(18)b_incl3-pipin/a

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, 20088.703 km/s
x=[2369.89, 1.67208, 0.380256, 0.499911, 400, 168.06, 224.695, 212.292, 0.237501, 0.0223169, 0.161132, 0.468419, 1.80818, 1.64195, 1.1, 1.29702, 2.80363, 1.57266]
DE
B. Addis, A. Cassioli, M. Locatelli, F. SchoenGlobal Optimization Laboratory, University of Florence and University of TurinMay, 20088.631 km/s
x=[1171.64503236 1.40899421278 0.37992647165 0.498004040298 399.999999715 178.372255301 299.223139512 180.510754824 0.234594654679 0.0964769387134 0.829948744508 0.317174785637 1.80629232251 3.04129845698 1.10000000891 1.35077257078 1.09554368115 1.34317576594]
MBH
F. Biscani, M. Rucinski and D.IzzoEuropean Space AgencyFeb., 20098.630 km/s
x=lost
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