Add algorithm to compute the standalone Coriolis matrix C(q, ν)

[flferretti]

This PR will add an algorithm to compute the standalone Coriolis matrix basing on the one developed by S. Echeandia et al..

Solves #41

---

📚 Documentation preview 📚: https://jaxsim--75.org.readthedocs.build/75/

[diegoferigo]

Some questions. When I checked your code a while ago, if I recall it was missing the base-related blocks of the matrix. Is this the case?

And I mean, given a model with state $(\bar{\mathbf{q}}, \, \bar{\boldsymbol{\nu}})$, would the following check pass?

$$\text{RNEA}(\mathbf{q}=\bar{\mathbf{q}}, \, \boldsymbol{\nu} = \bar{\boldsymbol{\nu}}, \dot{\boldsymbol{\nu}} = \mathbf{0}, \mathbf{f}^{\text{ext}} = \mathbf{0}) == C(\bar{\mathbf{q}}, \\, \bar{\boldsymbol{\nu}}) \, \bar{\boldsymbol{\nu}}$$

[flferretti]

Thanks Diego, I'll take a look at it! It would probably be a good idea to also add that check in the tests

[diegoferigo]

For the records, for those that are not familiar with the high_level resources, the left-hand side of the previous equation is no more no less than Model.free_floating_bias_forces.

[traversaro]

This also computes as a by-product the time derivative of the mass matrix, right? This may be of interest of @rob-mau .

[traversaro]

Suggested change

	H, H_dot, C = model.coriolis_matrix()
	H, H_dot, C = model.coriolis_matrix()

Could it make sense to add a test here to check that the mass matrix here is the same that the mass matrix computed with CRBA?

[diegoferigo]

Good idea @traversaro.

@flferretti please note that the low-level jaxsim.physics.algos.crba.crba always computes $M_B(\mathbf{s})$ in body-fixed representation since it's the only representation that is independent from the base pose. Then, the rest of the high_level logic converts the body-fixed mass matrix to the active representation.

Make sure to compare the same quantities.

[flferretti]

Thanks @traversaro! I will address your comments one-by-one in future commits

[diegoferigo]

Also, similarly to the other high-level methods, the returned matrices should be converted to the active velocity representation.

[traversaro]

I have some notes on this in https://github.com/ami-iit/idynfor/blob/master/doc/theory_background.md#dynamics , even if the do not covert the
$\dot{M}$ and $C$ case at the moment.

[diegoferigo]

I still haven't run this code, but I was expecting a matrix $C \in \mathbb{R}^{(6+n)\times(6+n)}$. Here it seems be $\mathbb{R}^{6 \times 6}$, am I missing something?

[diegoferigo]

Note that $C$ has to be transformed as 3.60b:

[traversaro]

To be honest, I do not remember if this transformation ensures that the $\dot{M} = C + C^T$ is preserved, but it should be easy to check (we can do this at the whiteboard next week).