How is the Cartesian orientation of body inertia "ximat" calculated

[Chuanfang-Neptune]

Intro

Hi!

I am a graduate student using MuJoCo for my research on simulating quadruped robots.

My setup

I'm using MuJoCo version 3.1.5.

My question

When I tried to visualize the inertia box of a robot part which is non-symmetric in MuJoCo GUI I noticed a tilted inertia box.

I figured out that the tilted box could be corrected if I deleted the non-diagonal elements of the inertia matrix. But I'm still very confused because the non-diagonal elements of the inertia matrix is less than 1% of the diagonal ones.
I tried to look into the code to check how the inertia box was visualized in MuJoCo, which seemed to be in 3 steps:

1. Store the cartesian orientation of body inertia in ximat.
2. Use mjv_initGeom to set the orientation matrix of the inertia box same as ximat
3. Visualize the inertia as rotated inertia box.

It seemed that the size of the inertia box size is depended on the diagonal elements and the orientation is dependent on the "cartesian orientation of body inertia matrix". But I could not find how this matrix ("cartesian orientation of body inertia matrix") was computed in the code. Could anyone please give a pointer?

Thanks!

Minimal model and/or code that explain my question

No response

Confirmations

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

[v-r-a]

Hi,

Though I do not have an exact answer to your problem, the following might help:

If you were looking at the visualize section, and found mjtNum Ixx = m->body_inertia[3*i+0], note that body_inertia in mjModel contains the moment of inertia terms only because they are expressed in a frame aligned with the body's principle axes (body_iquat in mjModel defines the orientation of this 'inertia frame' wrt the body's local frame), see this.
I am not sure, but the Eigen decomposition to find principle axes probably happens somewhere inside user_model.cc

During simulation, the orientation of bodies is computed (as the forward kinematics propagates) in mj_kinematics. So, we get the dynamic quantities like xmat and ximat in mjData.

Then, the dimensions of the equimomental inertia box/ellipsoid are computed as you have seen already...