Informatics
GTOP Database: Global Optimisation Trajectory Problems and Solutions
 Problem "Messenger-Full" (MGA-1DSM) This trajectory optimisation problem represents a rendezvous mission to Mercury modelled as an MGA-1DSM problem. It includes the final resonant fly-bys, and seeks to minimse the on-board propellant consumption.
 Download MATLAB: use the function messengerfull.m and pass to it the MGAproblem variable contained in messengerfull.mat C++: call the function double messengerfull(const std::vector & x) provided in the GTOPtoolbox. Python (recommended): import PyGMO and call PyGMO.problem.messeger_full.objfun(x)

Short description

This trajectory optimisation problem represents a rendezvous mission to Mercury modelled as an MGA-1DSM problem. The selected fly-by sequence and other parameters are compatible with the currently flying Messenger mission. With respect to the problem "Messenger" the fly-by sequence is more complex and allows for resonant fly-bys at Mercury to lower the arrival DV.

As far as chemical propelled interplanetary trajectories go, this particular one is particularly complex and difficult to design. The amount of specialistic knowledge that needs to be used to obtain a successfull design is significant and, before the remarkable results from G. Stracquadanio, A. La Ferla and  G. Nicosia (see below) were found, it was hardly believable that a computer, given the fly-by sequence and an ample launch window, could design a good trajectory in complete autonomy.

For the twenty-six dimensional global optimisation problem we consider the bounds listed in the following table:

 State Variable LB UB Units x(1) t0 1900 2300 MJD2000 x(2) Vinf 2.5 4.05 km/sec x(3) u 0 1 n/a x(4) v 0 1 n/a x(5) T1 100 500 days x(6) T2 100 500 days x(7) T3 100 500 days x(8) T4 100 500 days x(9) T5 100 500 days x(10) T6 100 600 days x(11) eta1 0.01 0.99 days x(12) eta2 0.01 0.99 n/a x(13) eta3 0.01 0.99 n/a x(14) eta4 0.01 0.99 n/a x(15) eta5 0.01 0.99 n/a x(16) eta6 0.01 0.99 n/a x(17) r_p1 1.1 6 n/a x(18) r_p2 1.1 6 n/a x(19) r_p3 1.05 6 n/a x(20) r_p4 1.05 6 n/a x(21) r_p5 1.05 6 n/a x(22) b_incl1 -pi pi n/a x(23) b_incl2 -pi pi n/a x(24) b_incl3 -pi pi n/a x(25) b_incl4 -pi pi n/a x(26) b_incl5 -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 Received Objective Function (km/s) Solution Vector Credits: Date: 6.943 N/A M. Schlueter, J. Fiala, M. Gerdts, University of Birmingham (found by MIDACO solver) 19/06/2009 6.404 N/A G. Stracquadanio, A. La Ferla, G. Nicosia, University of Catania (Found by SAGES Self-Adaptive- Gaussian Evolutionary Strategy) 17/11/2009 6.047 N/A M. Schlueter, University of Birmingham, M. Gerdts, University of Wuerzburg, M. Munetomo and K. Akama, Hokkaido University, S. Erb and G. Ortega, ESTEC/TEC-ECM (found by MIDACO solver) 30/11/2009 4.254 N/A F. Biscani and D. Izzo, ESTEC Advanced Concepts Team. Found using PaGMO 01/12/2009 2.970 N/A G. Stracquadanio, Dept of Biomedical Engineering, Johns Hopkins University, A. La Ferla, G. Nicosia, University of Catania (Found by SAGES Self-Adaptive- Gaussian Evolutionary Strategy) 28/02/2011 2.113 N/A G. Stracquadanio, Dept of Biomedical Engineering, Johns Hopkins University, A. La Ferla, G. Nicosia, University of Catania (Found by SAGES Self-Adaptive- Gaussian Evolutionary Strategy) 10/04/2012
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