QR decomposition function for Mujoco

[jeongsukchul]

Intro

Hi!

I am a graduate student at SNU, I use MuJoCo for my research on contact dynamics.

I'm interested on modifying mujoco contact solver, and see the effects with mujoco visualization.

currently i'm working on PGS solver, and want to do some modification when the delassus matrix is rank deficient.
I know the mujoco contact solver uses regularization R matrix to make delassus matrix invertible, but i'm focusing on the solution set of CCP or NCP problem with hard contact.

i'm solving SOCP problem with QP cost(quadratic on delassus matrix G and linear on residual terms g) and friction cone constraint.

i want to see the other solution for this problem, so i'm working on the solution set of Gx=g (x is contact force),
because it is no (G+R)x=g with G+R invertible, it can be converted to x = x0 + Fz where F is null matrix of G.

When i do web surfing, the efficient and easy algorithm for finding null matrix F is doing QR decomposition on G.
But because the delassus matrix G is not Eigen variable, it is custom mujoco variable with mjtNum* , so i don't know how can i do efficient QR decomposition algorithm for G with mujoco variables.

Also mujoco mujoco matrix solver like
mju_choleFactor can gives cholesky decomposition but i don't know how to use this to make null matrix.

Questions

1. how can i make custom QR decomposition in mujoco with c++?
2. Is there any plan for making some linear algebra helper functions like SVD, conditional numbers etc.

Thanks.

My setup

Mujoco, C++, ubuntu

My question

Questions

1. how can i make custom QR decomposition in mujoco with c++?
2. Is there any plan for making some linear algebra helper functions like SVD, conditional numbers etc.

Thanks.

Minimal model and/or code that explain my question

If you encountered the issue in a complex model, please simplify it as much as possible (while still reproducing the issue).

Model:

minimal XML

<mujoco>
  <worldbody>
    <light pos="0 0 1"/>
    <geom type="sphere" size="1" rgba="1 0 0 1"/>
  </worldbody>
</mujoco>

Code:

import mujoco
import mediapy as media
model = mujoco.MjModel.from_xml_string(xml)
data = mujoco.MjData(model)

with mujoco.Renderer(model) as renderer:
  mujoco.mj_forward(model, data)
  renderer.update_scene(data)

  media.show_image(renderer.render())

Confirmations

• I searched the latest documentation thoroughly before posting.
• I searched previous Issues and Discussions, I am certain this has not been raised before.