design space pruning heuristics and global optimization method for ...

In order to determine the optimum, two-impulse, phase-free delta-V between any
two orbits, the true anomalies at departure and arrival are discretized between 0 and 360
degrees. Each possible combination of departure true anomaly and arrival true anomaly
defines r 1 , r 2 , and the transfer angle, from which the minimum ∆V solution can be
obtained. Figure 10b plots contours of minimum delta-V for each value of departure and
arrival true anomaly, also for the transfer from “2006 QQ56” to Chicago. Because the
solution space is multi-modal, a grid search is used to determine the approximate optimal
solution.
delta-V (AU/TU)
7
6
5
4
3
2
1
0
0 1 2 3 4 5
semi-major axis (AU)
Arrival True Anomaly (rad)
6
5
4
3
2
1
0
0 2 4 6
Departure True Anomaly (rad)
3
2.5
2
1.5
1
0.5
Figure 10: (a) Delta-V as a function of the transfer orbit semi-major axis for a two-impulse transfer
(left); (b) contour plot of the minimum two-impulse delta-V transfers over all departure and arrival
true anomalies (right).
2.2.3 Pruning Techniques Based on Phasing
The final set of pruning metrics considered takes phasing into consideration.
Once again, two-impulse Lambert solutions are calculated, now using the actual asteroid
ephemeris data for given departure dates and flight times. In this case, because time of
flight is a consideration, the Lambert problem is reformulated in order to solve for the
minimum delta-V given r 1 , r 2 , and the time of flight. For a given r 1 , r 2 , and time of flight,
there are 2N max + 1 solutions to the multi-revolution Lambert problem, where N max is the
43