how to change e_wk in QP form???

[niteofhunter]

I read your journal publication "Representation-Free Model Predictive Control for Dynamic Motions in Quadrupeds" very well and I have a question about this paper.

in your publication, we should make QP form with the cost function

but the problem arose in the cost of angular velocity

I think R_k is the unknown matrix that we should get from MPC.

So, I can't understand how to change e_Wk (30) to the QP form

I also saw your code here to find out how to do that.

However, this code shows only situations in which, Wdk = [0,0,0] (not gaiting) and RtkRdkWdk = [0,dth0,0] (I don't know why it's derived)

Could you show me how to change e_Wk to QP form???

Thank you ^^

P.S. As Your publication give many backgrounds, it is very good for novices like me ^^

[YanranDing]

Hi Jae-Bong,

That's a good question. Please take a look at the file "fcn_get_QP_form_eta.m"

Line 63,69 are the setup for the cost on the angular velocity.
In (30), you are right Rk is unknown and thus part of the decision variables.
But e_wk is in affine form of the variables, and its 2-norm can be incorporated in QP form.
Wdk is the desired angular velocity, which does not necessarily need to be [0,0,0]

Here, Xt is the initial condition.

Hope it helps!

Best,
Yanran

[niteofhunter]

Thank you. ^^