Messenger (reduced version)
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
- MATLAB: use the function messenger.m and pass to it the MGAproblem variable contained in messenger.mat
- 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) | t0 | 1000 | 4000 | MJD2000 |
| x(2) | Vinf | 1 | 5 | km/sec |
| x(3) | u | 0 | 1 | n/a |
| x(4) | v | 0 | 1 | n/a |
| x(5) | T1 | 200 | 400 | days |
| x(6) | T2 | 30 | 400 | days |
| x(7) | T3 | 30 | 400 | days |
| x(8) | T4 | 30 | 400 | days |
| x(9) | eta1 | 0.01 | 0.99 | days |
| x(10) | eta3 | 0.01 | 0.99 | n/a |
| x(11) | eta3 | 0.01 | 0.99 | n/a |
| x(12) | eta4 | 0.01 | 0.99 | n/a |
| x(13) | r_p1 | 1.1 | 6 | n/a |
| x(14) | r_p2 | 1.1 | 6 | n/a |
| x(15) | r_p3 | 1.1 | 6 | n/a |
| x(16) | b_incl1 | -pi | pi | n/a |
| x(17) | b_incl2 | -pi | pi | n/a |
| x(18) | b_incl3 | -pi | pi | n/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., Izzo | European Space Agency | March, 2008 | 8.703 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. Schoen | Global Optimization Laboratory, University of Florence and University of Turin | May, 2008 | 8.631 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.Izzo | European Space Agency | Feb., 2009 | 8.630 km/s | x=lost | -- |