Incorrect Object Orientation in GRAB Environment Reconstruction in MuJoCo

[binbinbai]

Hi,thanks for this great job.
I am reconstructing the GRAB environment in MuJoCo, ensuring that the world coordinate system aligns with that of GRAB. My understanding is that the global_orient parameter represents the axis-angle rotation of the object’s local coordinate system relative to the world coordinate system. Therefore, by aligning the MuJoCo world coordinate system with GRAB, I assumed I could directly use global_orient to set the object's orientation.
However, this approach often results in incorrect orientations. For example, as shown in the attached figure with the "elephant" object, directly applying the provided global_orient does not align the object with its true pose in GRAB.

To investigate, I examined the visualize_grab.py script provided in GRAB. The code responsible for transforming the object vertices from the local coordinate system to the world coordinate system is:
vertices = torch.matmul(v_template, rot_mats) + transl.unsqueeze(dim=1)
This corresponds to the transformation formula:

However, I think the correct transformation should be:

To verify, I negated the axis-angle rotation provided in global_orient and observed that the resulting object orientation matched the true GRAB pose, as shown in the next figure. This suggests that the global_orient should either be inverted (negated axis-angle) or its corresponding rotation matrix should be transposed for the transformation to be accurate.

Is my understanding correct that global_orient provided by GRAB needs to be negated or its rotation matrix transposed to achieve the correct object orientation in MuJoCo?