Removing mx_reduced by creating "biorbd wrapper"

[EveCharbie]

This change is 

[EveCharbie]

@pariterre @Ipuch This is what I was thinking about for the "biorbd wrapper".
I just did a proof of concept for pendulum.py to know what you guys think before I implement it for all biorbd functions.
This way, we do not have to carry around mx_reduced and I think we do not need .mx anymore neither because everything can be called directly with .cx.
It might get less clean when we add arguments which we cannot assume the shape (e.g. contact forces), but will still work.

[Ipuch]

I would advocate for a supplementary interface (BiorbdModelToCasadiFunc ?) to biorbd. An entire class that does this for every function called by biorbd so we don't have to change the current class BiorbdModel, BiorbdMultiModel, Holonomic etc ...

Also, every function of the models that do not through a MX, absolutely need to be fixed. I'm thinking about rotation matrices that are still objects of biorbd for example.

Good Job !

[pariterre]

Reviewed 5 of 5 files at r1, all commit messages.
Reviewable status: all files reviewed, 3 unresolved discussions (waiting on @EveCharbie)

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bioptim/models/biorbd/biorbd_model.py line 212 at r1 (raw file):

    def reshape_qdot(self, k_stab=1) -> MX:
        q_mx_reduced = MX.sym("q_mx_reduced", self.nb_q, 1)

If we go this route, which I actually like, all MX should be removed from bioptim altogether (not 100% sure it works). It would be the responsability of the BioModel to keep track (if needed) of extra symbolic MX!

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bioptim/models/biorbd/biorbd_model.py line 357 at r1 (raw file):

        q_mx_reduced = MX.sym("q_mx_reduced", self.nb_q, 1)
        qdot_mx_reduced = MX.sym("qdot_mx_reduced", self.nb_qdot, 1)
        tau_mx_reduced = MX.sym("tau_mx_reduced", self.nb_tau, 1)

Same here, it would be the dynamic responsability to declare MX.sym (if for instance they can't use SX, and return something which is dependent on .cx

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bioptim/optimization/optimization_variable.py line 565 at r1 (raw file):

    @property
    def mx(self):
        return self.unscaled.mx

This would therefore rendered useless, which would GREATLY simplify bioptim (as only .cx would be useful)