Hard? Optimation is hard isn't it?

[kedaman]

This problem would be much easier if it wasn't about optimation.
A path of a rocket has to be set trough an amount of moving checkpoints while each of them have a different maximum velocity of which the rocket can pass by (otherwise it misses it). The acceleration,initial velocity and position of each checkpoint is known(the acceleration is constant), and the rocket has a initial velocity and poision, known. The list of acceleration changes at certain time has to be calculated. And plus one thing, the length of the rockets acceleration vector can't pass a certain known value. I've done this but without the optimation: it has to be done as fast as possible (travel the path at shortest possible time)

Again, if it remained unclear. I want an algoritm to calculate the full route, which is a list of acceleration vectors and the time they will be active for the rocket. No mass/friction/gravity or other elements are involved.

[kedaman]

I forgot to tell, the orientation is 3 dimensional.

[Guv]

I do not really think I want to touch this with a 304.8cm pole, but I am not sure what the exact problem is.

Is the checkpoint order predetermined? If this is the case, it does not seem to be an optimization problem. There are enough constraints to define a unique trip plan using the maximum allowable rocket acceleration. What ever technique you have used for your current solution should be usable in the following successive approximation scheme. Each checkpoint has a path which can be calculated. From initial conditions for the rocket, assume maximum acceleration and an assumed meeting position with checkpoint one. If you arrive too early, try again with an earlier assumed meeting point. If too late, try again with a later assumed meeting point. Keep this up until you meet the checkpoint. Now you have a new set of initial conditions for the rocket, and the same technique can be used to determine the meeting point with the second checkpoint. And similarly for the third.Is the problem to determine the checkpoint order which minimizes the time for the trip? If this is the case, why not just calculate for all permutations? Are there so many checkpoints that this is not feasible?

[kedaman]

Each checkpoint has a path which can be calculated.

The problem is that you have the rocket end up with a "new velocity" after meeting a checkpoint, affecting the minimal time it would take to the following one (and so on). I don't want to have any "testing algoritms" and my current one calculates the acceleration vector for the fastest way to the first checkpoint and from there to the next but not from the first trough the second and to the third etc..

The checkpoints has to be passed trough the order they are in the list even if they are placed like 13 24. The checkpoint amount is variable but i would accept optimation for the nearest 2 or 3 checkpoints if more would be too hard.

[paulw]

Optimisation across a 3-D Hull is actually a fairly simple problem, however I can't remember the techniques as it was twelve years ago. As Guv says, this does not look, on inspection like an optimisation problem though.

If it is and you can formulate the constraints properly, I can dig out my old texts.

Cheers,

P.

[kedaman]

Paul, thanks for you interest :)
Let's take a sample:
Say you have 3 points, where as the first is the third, which means you have to get from A to B and then back to A
To get fastest way to B from A you set full acceleration until you reach A (we now avoid the speed limit at B) but when you try to get back to A again, it takes a lot more time since the rocket velocity at B is in the opposite direction, which means that it has to decelerate first and then start from a more far distance.
To get from A to B and then back to A the fastest way possible, you set full acceleration, and start decelerate in the middle between A and B (which means it stops at B) and then return to A at the same way. This way it goes much faster.
These are two extreme ways of doing it but usually the third point C is set in another angle to the line AB causing there to be an optimal speed at which you arrive at B, i'm certain of this, but i might be wrong?

Hoping this is going to be simple :)

[kedaman]

oh and when i said the rocket heads back to A the same way, i meant it sets full acceleration all the way.

[paulw]

I think we need to separate this into several different problems because each trip between points can be started relative to the position of the previous checkpoint. We need a formula for the trip from origin to A and then a formula for A to B couched in relative terms of A' the new position of A and so on.

This is a 'grand tour' problem, isn't it. i.e. Visit all the planets in fixed order, what path is best? e.g. It might be best to slowly go to Jupiter from Mars to allow Saturn and Uranus to align for an easier trip later on...

OK. So lets have some formulaes and then we can set to work differentiating them. And yes, this is DEFINITELY an optimization problem.

I'll see if I can find my text book. If not, I am a bit scuppered, but I will let you know tomorrow.

Cheers,

P.

[kedaman]

thanks paul :)
although it's relative in position, it can't be split up into several, if it would (of some reason i have) each of them would be a a problem in it self and i assure there is cases where the rocket doesn't stop at Jupiter but instead just pass by, btw if it was about planets, then you could head around a planet and with that change the direction without having to stop. I have to be prepared for two vessels passing by each other (how did you guess this was about space trips?)

Now what was i trying to say? uh it was about the separate problems, they can't be separated if the rocket doesn't stop at a certain point, since then the rocket could arrive at different speed causing a range of permutations for the next trips..