Informatics
Mission Analysis
May 1, 2013

GTOC 1

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

This instance of a Multiple Gravity Assist problem draws inspiration from the first edition of the Global Trajectory Optimisation Competition (GTOC1). It is an MGA problem with a rather long fly-by sequence including mainly Earth and Venus. The final target is the asteroid TW229. The objective of the mission is to maximise the change in sami-major axis of the asteroid orbit following an anaelastic impact of the spacecraft with the asteroid J(x) = m_f U v.


The code

  1. MATLAB: use the function gtoc1.m and pass to it the MGAproblem variable contained in gtoc1.mat
  2. C++: call the function "double gtoc1(const std::vector & x, std::vector& rp)" provided in the GTOPtoolbox.
  3. C++ (PaGMO): use the class pagmo::problem::gtoc_1
  4. Python 2.7 (PyGMO): use PyGMO.problem.gtoc_1().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

StateVariableLBUBUnits
x(1)t0300010000MJD2000
x(2)T1142000days
x(3)T2142000days
x(4)T3142000days
x(5)T4142000days
x(6)T51009000days
x(7)T63669000days
x(8)T73009000days

Constraints on the various fly-by pericenters are also considered to the values:

  • rp1 > 6351.8 km
  • rp2 > 6778.1 km
  • rp3 > 6351.8 km
  • rp4 > 6778.1 km
  • rp5 > 600000 km
  • rp6 > 70000 km

Solutions are rounded to the fourth digit and only improvements on that level is considered. No constraint violation is allowed.


Solutions:

The record holders of this problem are listed below in chronological order:

Author

Affiliation

Date

Obj Fun

Solution

Algo

Tamas Vinko and Dario IzzoEuropean Space Agency23 Jan, 2008-1,580,599
x=[6809.476683160, 169.598512787, 1079.375156244, 56.53776494142, 1044.014046276, 3824.160968179 1042.885114734 3393.057868710]
PaGMO
M. Schlueter, M. GerdtsUniversity of BirminghamJan, 2010-1,581,950
x=[6810.40521106, 168.37469758, 1079.47409963, 56.38731208, 1044.09288643, 3820.84181773, 1044.32726019, 3397.21349495]
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