[Dev] Quadrotor model

[jbcaillau]

@ocots in the dynamics, is it normal that only the third column of R is used?

OptimalControlProblems.jl/ext/OptimalControlModels/quadrotor.jl

Line 82 in 0b18581

at_ = R * [0; 0; at]

Compare with this test in CTParser (coordinate wise version to test :exa, borrowed and slightly adapted from ExaModels.jl):
https://github.com/control-toolbox/CTParser.jl/blob/7b4756110a1e8a9cabfdef7fd918ecc5788a87a0/test/test_onepass_exa.jl#L881

[ocots]

I haven't took a look at the dynamics but it is written:

The problem is formulated as a JuMP model, and can be found [here](https://arxiv.org/pdf/2303.16746)

[ocots]

See https://gitlab.kuleuven.be/robotgenskill/fatrop/fatrop_benchmarks

[ocots]

I have essentially checked the consistency between JuMP and OptimalControl but it would be nice to have a reference for each problem and to check its validity. The reference would be useful for the documentation and to publish something.

[ocots]

@jbcaillau All the tests pass even the objective value for the init. The problem with OptimalControl is not transformed to a Mayer anymore. However, I have an issue with quadrotor:

OptimalControlProblems.jl/test/utils.jl

Lines 261 to 263 in 06d2e73

	if f != :quadrotor
	keep_problem = keep_problem && (typeof(res) == Test.Pass)
	end

See: https://github.com/control-toolbox/OptimalControlProblems.jl/blob/main/test/figures/solution/quadrotor.pdf

I suggest to change the problem with the one you found.

[jbcaillau]

@ocots here it is (check here, it converges with :exa):

    T = 1
    g = 9.8
    r = 0.1

    o = @def begin
        
        t ∈ [0, T], time
        x ∈ R⁹, state
        u ∈ R⁴, control
    
        x(0) == zeros(9)
    
        ∂(x₁)(t) == x₂(t)
        ∂(x₂)(t) == u₁(t) * cos(x₇(t)) * sin(x₈(t)) * cos(x₉(t)) + u₁(t) * sin(x₇(t)) * sin(x₉(t))
        ∂(x₃)(t) == x₄(t)
        ∂(x₄)(t) == u₁(t) * cos(x₇(t)) * sin(x₈(t)) * sin(x₉(t)) - u₁(t) * sin(x₇(t)) * cos(x₉(t))
        ∂(x₅)(t) == x₆(t)
        ∂(x₆)(t) == u₁(t) * cos(x₇(t)) * cos(x₈(t)) - g 
        ∂(x₇)(t) == u₂(t) * cos(x₇(t)) / cos(x₈(t)) + u₃(t) * sin(x₇(t)) / cos(x₈(t))
        ∂(x₈)(t) ==-u₂(t) * sin(x₇(t)) + u₃(t) * cos(x₇(t))
        ∂(x₉)(t) == u₂(t) * cos(x₇(t)) * tan(x₈(t)) + u₃(t) * sin(x₇(t)) * tan(x₈(t)) + u₄(t)
    
        dt1 = sin(2π * t / T)
        df1 = 0 
        dt3 = 2sin(4π * t / T)
        df3 = 0 
        dt5 = 2t / T
        df5 = 2
    
        0.5∫( (x₁(t) - dt1)^2 + (x₃(t) - dt3)^2 + (x₅(t) - dt5)^2 + x₇(t)^2 + x₈(t)^2 + x₉(t)^2 +
           r * (u₁(t)^2 + u₂(t)^2 + u₃(t)^2 + u₄(t)^2) ) → min
    
    end

[ocots]

I found the quadrotor Yassine wrote:

• dynamics
• constraints

But I do not manage to make it work. I remove it from the list for the moment.