[Dev] Kepler add examples

[ocots]

Add examples:

• $L^1$-minimization two-body problem.
• $L^1$-minimization CR3BP.
• Minimum time, CR3BP.

[antoinepichon03]

hello, can I have the permission in this project ?

[antoinepichon03]

Hello,
I solved the two-body orbital transfer problem using an optimal control solver, based on the equations provided in the document you sent (two body problem) . I obtained the following plots, but I’m not entirely sure how to interpret them.

For the initial guess in my code, I used the following conditions:

tf_simple = 10000.0
x_simple(t) = x0 + (xf - x0) * t / tf_simple
u_simple(t) = [0.01, 0.01, 0.01]
nlp_init_simple = (state = x_simple, control = u_simple, variable = tf_simple)

What is your opinion on this plot?

@Nico77310 @ocots

[ocots]

@antoinepichon03 Note that the L1-minimisation two-body problem is also part of the issue control-toolbox/Tutorials.jl#22. @YouriRenoud started to work on this problem. It could be nice to talk with him.

The other problems are not shared.

[jbcaillau]

@antoinepichon03 nice first try. for sure you need a finer grid!

Hello, I solved the two-body orbital transfer problem using an optimal control solver, based on the equations provided in the document you sent (two body problem) . I obtained the following plots, but I’m not entirely sure how to interpret them.

For the initial guess in my code, I used the following conditions:

tf_simple = 10000.0
x_simple(t) = x0 + (xf - x0) * t / tf_simple
u_simple(t) = [0.01, 0.01, 0.01]
nlp_init_simple = (state = x_simple, control = u_simple, variable = tf_simple)
What is your opinion on this plot?

[ocots]

@antoinepichon03 Tu as régularisé le problème via une barrière logarithmique ?

Pour inspiration, voir ma thèse page 44, "Exemple 2 : Problème de transfert orbital". Attention, dans mon exemple le temps final est libre.

[antoinepichon03]

I implemented the regularization, but despite the constraint on the control norm, I sometimes call log with (1-|u|) which is negative... I found a solution for compilation using a "max", but I don't understand why the constraint is not respected. Have you ever encountered this problem before @YouriRenoud?

[YouriRenoud]

I implemented the regularization, but despite the constraint on the control norm, I sometimes call log with (1-|u|) which is negative... I found a solution for compilation using a "max", but I don't understand why the constraint is not respected. Have you ever encountered this problem before @YouriRenoud?

@antoinepichon03 That is the same problem I am facing since few days when I use log(γmax - norm) for the regularization the logarithm always become negative in few iterations even if I have the constrain 0.01 ≤ norm ≤ γmax - 0.01.
What do you mean when you said "using a max" ?