Solving Inverse Kinematics on SE(3) (rotation part specifically)

[ThisIsBohao]

Hi, I have a quick conceptual question on how curobo implements a differentiable representation of the end effector kinematics in order to solve inverse kinematics problems on SE(3) using optimization.
I noticed that curobo computes the 4x4 homogenous transformation matrix. It also provides functions that converts rotation matrices to quaternions. I wonder how curobo implements the gradient of the kinematics constraints so that the orientation eventually converges to target values. Is the gradient not computed explicitly but computed by automatic differentiation in torch library?

[balakumar-s]

It is calculated explicitly here:

curobo/src/curobo/curobolib/cpp/kinematics_fused_kernel.cu

Line 1037 in 911da8c

if (j_type == Z_ROT)

We also refer to the calculation in Table 7 in our report (page 50): https://curobo.org/reports/curobo_report.pdf