Momentum regressor

[lvjonok]

Hello Pinocchio Team!

I have previously contributed kinetic and potential energy regressors, which are useful for system identification and adaptation. Now, it is time to extend this with momentum regressors.

Derivation Overview

Below is a quick derivation to support my code:

1. The mass inertia matrix in regressor form can be expressed as:

$$ M(q)\dot{v} = Y(q, 0, \dot{v})\pi - Y(q, 0, 0)\pi $$

2. The momentum of the system in regressor form can be written as:

$$ p = M(q) v = \frac{\partial L}{\partial v} = Y(q, 0, v)\pi - Y(q, 0, 0)\pi = Y_p(q, v) \pi $$

Next, we consider the derivative of the momentum:

$$ \dot{p} = \frac{d}{dt} \left( \frac{\partial L}{\partial v} \right) = \frac{\partial L}{\partial q} + Q $$

For system identification, we can construct the following equation:

$$ (Y_p(q_2, v_1) - Y_p(q_1, v_1)) \pi = \int_{t_1}^{t_2} \left( \frac{\partial L}{\partial q}\frac{\partial q}{\partial \theta} \pi + Q \right) dt $$

Changes Introduced in the PR

In my PR, I have augmented the data structure with two members: data.momentumRegressor and data.dpartial_lagrangian_q. These fields will be populated after the call to computeMomentumRegressor.

I am looking forward to your review and am open to any questions or comments!

Additionally, I am excited to gain experience writing C++ code. If there are any changes needed, I would prefer to make them myself rather than having you do it, as it would be a great learning opportunity for me. 😊

[hrp2-14]

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If this wasn't intentionnal, you can change the base branch of this PR to devel
(No need to close it for that). Best, a bot.

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