design space pruning heuristics and global optimization method for ...
design space pruning heuristics and global optimization method for ...
design space pruning heuristics and global optimization method for ...
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In order to determine the optimum, two-impulse, phase-free delta-V between any<br />
two orbits, the true anomalies at departure <strong>and</strong> arrival are discretized between 0 <strong>and</strong> 360<br />
degrees. Each possible combination of departure true anomaly <strong>and</strong> arrival true anomaly<br />
defines r 1 , r 2 , <strong>and</strong> the transfer angle, from which the minimum ∆V solution can be<br />
obtained. Figure 10b plots contours of minimum delta-V <strong>for</strong> each value of departure <strong>and</strong><br />
arrival true anomaly, also <strong>for</strong> the transfer from “2006 QQ56” to Chicago. Because the<br />
solution <strong>space</strong> is multi-modal, a grid search is used to determine the approximate optimal<br />
solution.<br />
delta-V (AU/TU)<br />
7<br />
6<br />
5<br />
4<br />
3<br />
2<br />
1<br />
0<br />
0 1 2 3 4 5<br />
semi-major axis (AU)<br />
Arrival True Anomaly (rad)<br />
6<br />
5<br />
4<br />
3<br />
2<br />
1<br />
0<br />
0 2 4 6<br />
Departure True Anomaly (rad)<br />
3<br />
2.5<br />
2<br />
1.5<br />
1<br />
0.5<br />
Figure 10: (a) Delta-V as a function of the transfer orbit semi-major axis <strong>for</strong> a two-impulse transfer<br />
(left); (b) contour plot of the minimum two-impulse delta-V transfers over all departure <strong>and</strong> arrival<br />
true anomalies (right).<br />
2.2.3 Pruning Techniques Based on Phasing<br />
The final set of <strong>pruning</strong> metrics considered takes phasing into consideration.<br />
Once again, two-impulse Lambert solutions are calculated, now using the actual asteroid<br />
ephemeris data <strong>for</strong> given departure dates <strong>and</strong> flight times. In this case, because time of<br />
flight is a consideration, the Lambert problem is re<strong>for</strong>mulated in order to solve <strong>for</strong> the<br />
minimum delta-V given r 1 , r 2 , <strong>and</strong> the time of flight. For a given r 1 , r 2 , <strong>and</strong> time of flight,<br />
there are 2N max + 1 solutions to the multi-revolution Lambert problem, where N max is the<br />
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