QUESTION: Typo ?

[EveCharbie]

If I am not mistaken, there is a typo below equation (14), where the q_6 should be q_5.

[moorepants]

Yes, the pitch angle is q5. Thanks for the note.

I haven't rebuilt this document in ages, so I may not fix it and just keep the note here.

[moorepants]

Are you the person working with Jules Ronne?

[EveCharbie]

Yes :)
Thanks a lot for the "open sourceness" of your work, it makes things so much easier!
While I have you, do you have a resource on how to impose the implicit DAE in an OCP context ?

[moorepants]

If you are generating the equations of motion for the bicycle with Kane's method you end up with these equations:

p dynamical differential equations for the p $\mathbf{u}$:

$$ \mathbf{f}_d(\dot{\mathbf{u}}, \mathbf{u}, \mathbf{q}) = \mathbf{F}_r + \mathbf{F}_r^* = 0 $$

N kinematical differential equations for the N $\mathbf{q}$:

$$ \mathbf{f}_k(\dot{\mathbf{q}}, \mathbf{u}, \mathbf{q}) = 0 $$

and M algebraic holonomic constraints:

$$ \mathbf{f}_h(\mathbf{q}) = 0 $$

For the minimal Carvallo-Whipple model: p = 3 and N = 4 and M = 1.

The M algebraic equations should be added as path constraints, the rest as differential equations.

We construct these equations (for a more complex model) here:

https://github.com/mechmotum/muscle-driven-bicycle-paper/blob/main/src/generate_eom.py#L702-L704

That repository solves an open loop controls OCP for the bicycle.

[moorepants]

If you don't fully eliminate the dependent generalized speeds then you would also include the nonholonomic constraints as path constraints.

[EveCharbie]

Thank you very much!