[label:question] Question about Jacobians `Phi_tr` in UpdaterWheel::preintegration_3D

[qpc001]

in this line:

Phi_tr.block(3, 0, 3, 3) = -R_3D.transpose() * skew_x(R_3D.transpose() * (new_p - p_3D));

I think new_p is equal to (p_3D + R_3D.transpose()*v*dt), then the line comes to:

Phi_tr.block(3, 0, 3, 3) = -R_3D.transpose() * skew_x(R_3D.transpose() * (R_3D.transpose()*v*dt));

But it seems that the final result should be:

Phi_tr.block(3, 0, 3, 3) = -R_3D.transpose() * skew_x(v*dt));

So I think the origin line should be the following code:

Phi_tr.block(3, 0, 3, 3) = -R_3D.transpose() * skew_x(R_3D * (new_p - p_3D));

Just remove the .transpose()

[WoosikLee2510]

It is very hard to understand your question, could you refer the lines of the code you read and drive it from there? Also, your second eq doesn't seem right - R_3D.transpose() * (R_3D.transpose()*v*dt) the reference frame should match. I.e., cannot multiply the same rotation matrix R_3D.transpose() * R_3D.transpose().

[qpc001]

It is very hard to understand your question, could you refer the lines of the code you read and drive it from there? Also, your second eq doesn't seem right - R_3D.transpose() * (R_3D.transpose()*v*dt) the reference frame should match. I.e., cannot multiply the same rotation matrix R_3D.transpose() * R_3D.transpose().

很难理解你的问题，你能参考你读到的代码行并从那里驱动它吗？ 此外，你的第二个eq似乎不正确- R_3D.transpose() * (R_3D.transpose()*v*dt)参考框架应该匹配。也就是说，不能乘以相同的旋转矩阵R_3D.transpose() * R_3D.transpose()。

But the original code in https://github.com/rpng/MINS/blob/bd115706ec2e617b584f0d1aa7c6e2f775817939/mins/src/update/wheel/UpdaterWheel.cpp#L764 is equal to Phi_tr.block(3, 0, 3, 3) = -R_3D.transpose() * skew_x(R_3D.transpose() * (R_3D.transpose()*v*dt));, if new_p= p_3D + R_3D.transpose()*v*dt