Add the possibility to change the weight in TSID/IK

[GiulioRomualdi]

This closes #474

[traversaro]

@GiulioRomualdi did you wanted to ask for a review instead of assigning?

[GiulioRomualdi]

@GiulioRomualdi did you wanted to ask for a review instead of assigning?

Ops 😃

[S-Dafarra]

The code looks good to me. What I find misleading is that weight is singular, but it is expecting a vector instead of a number. In general, I did not understand what is the effect of this weight? In a quadratic cost function we could have two weights
$$
w1 c(x)^T diag(w2) c(x) + w1' c(x)'^T diag(w2') c(x)'.
$$
Which weight are we changing?

[GiulioRomualdi]

Hi @S-Dafarra

The weight I'm referring to is the one associated with the norm. In TSID (same for the IK) each component of the cost function is a l2 weighted norm of the form

where W, in our case is a diagonal matrix. In setTaskWeight the diagonal of the diagonal matrix is passed to the solver

[S-Dafarra]

Ok I see. Basically, it is the w2 in #475 (review). Can we also set the w1? If not, then there is no ambiguity

[GiulioRomualdi]

Ok I see. Basically, it is the w2 in #475 (review). Can we also set the w1? If not, then there is no ambiguity

w1 is always 1 in tsid/ik