A good enough approximation of transfer orbits for an AI?

[Pagnatious]

When there's a problem google can't solve it's time to ask the people that know, so here I am again.

I was on hiatus from the game I was working on but now I'm back at it. There should be a thread back in the past regards it with some example stuff.

The idea is a 2d solar system sim with AI ships moving around cargo from planet to planet and so forth. I'm using discrete spheres of influence for simplicity, it makes changing between them crude but it means I can determine ships position in orbits as a function of time without having to iterate.

If it weren't for the gravity of departure and arrival bodies and I assumed instant acceleration I could just solve lambert's problem when a ships wants to transfer to somewhere else and then move it alone that orbit. But planets do have gravity, and ships could end up burning engines in my setting for and unknown amount of time, potentially a full half of the transfer if a ship built for interplanetary decided it wanted to get to the moon really quick.

Doing separate lambert solutions for the departure and arrival phases, as a patched conic, would solve the planet gravity issue, just a matter of getting a destination point for the first patch that is on the main transfer, and similar for arrival.

This doesn't solve the potentially constant thrust issue though. Regards that, I was wondering if movement along a spiral caused by constant thrust could could be determined as a function of time? I've seen some mention of things along those lines http://ccar.colorado.edu/~nerem/zipfiles/altus/ (point 5 onwards) but they seem to assume circular orbits, and I can't really assume that in this case.

If I can get something like that working I can hopefully make a transfer from patching phases.
Eg:
Thrust spiral around earth t0 - t1
Conic leaving earth t1 - t2
Lambert Solution conic transfer t2 - t3
Conic arriving at mars t3 - t4
thrust arrival at mars t4 - t5

Then when I need to know the ships position I can find which phase it would be in and then where along that phase.

Am I being crazy? Perhaps. Might something like this be able to be made work? Or is there some other solution? I don't want to have to iterate positions as I hope to use time compression and it would be nice for a ship to be able to determine its path at the start, even if it's not fully realistic, and then it just be a function of time.

Thanks for reading

 

[wphtech]

As far as I know, there are at least three persons' work that might solve your questions. The first is by Edelbaum, T. N. His simple result is for circular to circular orbit low thrust transfer. The second is by AE Petropoulos. You can read his paper "Shape-based algorithm for automated design of low-thrust, gravity-assist trajectories". It may similar to what you want. The third is by M. Vasile, who has used another shape-based method to solve interplanetary problem.

I have personally tried the method by M. Vasile. I think it is not difficult to implement. But I will say the easiest method is Edelbaum's. Petropoulos's method is attractive and I believe it is used by JPL. But it is hardest to implement among these three. (It is only my intuition. I haven't tried it.)