Add tutorials on free times

[YouriRenoud]

No description provided.

[ocots]

To make the doc locally:

julia> pkg="Tutorials"
"Tutorials"

julia> using Pkg; Pkg.activate("docs/"); Pkg.develop(path=pwd()); include("docs/make.jl"); Pkg.rm(pkg)

To visualise:

shell> open docs/build/index.html

[YouriRenoud]

@ocots After our discussion yesterday, I added a theoretical part on the double integrator example, but I’m not sure if I should keep all of it in the tutorial ?

[YouriRenoud]

using OptimalControl
using NLPModelsIpopt
using BenchmarkTools
using DataFrames
using Plots
using Printf

const x₁₀ = -42272.67       # initial position x
const x₂₀ = 0               # initial position y
const x₃₀ = 0               # initial velocity in x
const x₄₀ = -5696.72        # initial velocity in y
const μ = 5.1658620912*1e12 # gravitational parameter
const γ_max = 0.05          # maximal thrust norm
const r_f = 1.0             # target orbit radius (final distance to origin)


function min_orbit_tf()
    @def ocp begin
        tf ∈ R, variable
        t ∈ [0, tf], time
        x ∈ R⁴, state
        u ∈ R², control
        u₁(t)^2 + u₂(t)^2 ≤ γ_max^2
        x(0) == [x₁₀, x₂₀, x₃₀, x₄₀]
        x₁(tf)^2 + x₂(tf)^2 == r_f^2
        0.05 ≤ tf ≤ Inf
        ẋ(t) == [
            x₃(t),
            x₄(t),
            -μ * x₁(t) / ((x₁(t)^2 + x₂(t)^2)^(3/2)) + u₁(t),
            -μ * x₂(t) / ((x₁(t)^2 + x₂(t)^2)^(3/2)) + u₂(t)
        ]
        tf → min
    end

    return ocp
end
nothing # hide

Direct resolution with minimal orbital time :

We now solve the problem using a direct method, with automatic treatment of the free initial time.

ocp = min_orbit_tf()
sol = solve(ocp; grid_size=100)
plot(sol; label="direct", size=(800, 800))

When I define my problem as you can see here, I get an error when calling min_orbit_tf() because x is undefined, and I don't understand why.
Is it related to how I'm using the state and control variable names inside the @def ocp macro? Or could it be a scoping issue within the macro ?

[ocots]

@YouriRenoud @yeetsin12 Réunion à 14h salle TP C20X aujourd'hui.

[ocots]

@YouriRenoud Have a look at my comments.

[jbcaillau]

@YouriRenoud @yeetsin12 just for the record, take a look at https://control-toolbox.org/Kepler.jl/stable (more adapted set of coordinates - aka Gauss coordinates)

[ocots]

I prefer to keep cartesian coordinates here to keep it simple but we can put a link to the Kepler application.

[yeetsin12]

@ocots i fixed the problem of non convergence for indirect orbital problem, and improved the structure of the tutorial a little bit, i think i will start working on another tutorial "intermediate time constraints" unless there is more modifications to be made.

[jbcaillau]

@ocots i fixed the problem of non convergence for indirect orbital problem, and improved the structure of the tutorial a little bit, i think i will start working on another tutorial "intermediate time constraints" unless there is more modifications to be made.

hi @yeetsin12 so it converges?

[yeetsin12]

@jbcaillau yes it converges

[ocots]

@yeetsin12 we can make a point tomorrow at 2pm and I will finalise this PR with you.

If you want to start another, feel free. Go the issue, create a branch, make a first commit and push. Then, new PR and let's go!

You don't need write access since you already have it.

[ocots]

@yeetsin12 Can you come in my office at 2pm?

[yeetsin12]

@ocots i will be there at 2 pm, is the office in F325?

[yeetsin12]

@ocots for today's reunion, will it be at 4pm?

[ocots]

@yeetsin12 Attention, vérifie que tous les packages utiles sont dans le fichier docs/Project.toml, cf. l'erreur https://github.com/control-toolbox/Tutorials.jl/actions/runs/16053926548/job/45303381876?pr=25#step:6:63

[ocots]

@yeetsin12 attention, un peu plus haut dans la PR tu trouveras des commentaires qui viennent de messages directement sur le code. Je ne sais pas si tu les vois.

[yeetsin12]

@ocots non, j'arrive pas à trouver les messages sur le code, c'est dans la partie "files changed"?

[yeetsin12]

@ocots En tout cas, il me reste de modifier le dernier tutoriel de orbital final time, car j'arrive pas à supprimer la partie du code sur "augmented dynamics" ça donne des erreurs en compilation.