Which point in space is the Jacobian matrix computed at?

[Wayne-Z]

Hello,
I tried to calculate the Jacobian matrix of the end effector of the kinova-gen3 robot in the world frame to calculate v_ee by v_ee=Je*q_d, I used getFrameJacobian(model,data,end_effector_joint_id, WORLD.Je) and getJointJacobian(model,data,7,WORLD,Je) to get the Jacobian matrix, their results are the same, but different from the correct Jocabian matrix of the end effector, as shown in the figure.

Correct Jacobian matrix of EE wrt World frame: v_EE=J*q_d
   0.311402   -0.129344     0.16731   0.0141984   0.0663689  -0.0996134 2.08167e-17
   0.238223   -0.203283     0.26236   -0.241407   0.0482815    0.134534 -3.1225e-17
          0    0.134845   -0.173676    -0.28996   -0.141173  -0.0008199           0
          0    0.843695   -0.261631   -0.632851     0.73305    0.406432    0.693336
          0   -0.536822   -0.411191   -0.609998   -0.670318    0.295668    0.516433
         -1           0   -0.873196    0.476867    0.115374   -0.864519    0.502576

Jacobian matrix of EndEffector_joint by pinocchio
 -1.1492e-06     0.152892     0.111602     0.483362     0.454702    -0.524243     -0.11523
  -4.322e-19     0.240293   -0.0831721    -0.460524     0.461164      0.14222     0.484543
           0  7.95716e-07   0.00572665    0.0523776    -0.209705    -0.197815    -0.338931
 -2.7629e-18     0.843695    -0.261631    -0.632851     0.733051     0.406426     0.693336
 7.34641e-06    -0.536822    -0.411184    -0.609999    -0.670318     0.295675      0.51643
          -1 -2.70512e-07    -0.873199     0.476866     0.115368    -0.864519     0.502579

Then I calculate the jacobian matrix of another link use getFrameJacobian, and I found that the Jacobian matrix of this link is same to the end_effector_joint with the last few columns of the matrix become 0. But they are different point in space and the matrix should be different.

Jacobian matrix of HalfArm1_Link
 -1.1492e-06     0.152892            0            0            0            0            0
  -4.322e-19     0.240293            0            0            0            0            0
           0  7.95716e-07            0            0            0            0            0
 -2.7629e-18     0.843695            0            0            0            0            0
 7.34641e-06    -0.536822            0            0            0            0            0
          -1 -2.70512e-07            0            0            0            0            0

So, I would like to ask which point in space the Jacobi matrix obtained from Pinocchio corresponds to？Please correct me if I have used it incorrectly.

[Wayne-Z]

I think I found the issue. The jacobian matrix in world frame get from pinocchio is relative to World Coordinate Origin rather than target point. It means that, it is $ z_i \times ^i p_o^o $ rather than $ z_i \times ^i p_n^o $ in the first three rows of J.

[jcarpent]

Yes, you're right. You should work with LOCAL or LOCAL_WORLD_ALIGNED type of frame.

[Wayne-Z]

Dear jcarpent,
Thanks for your advice. I change the frame to LOCAL frame of EndEffector_Link, it is the jacobian of EndEffector_Link w.r.t LOCAL frame!
I have one more question, if I want get the jacobian of a Fixed_joint, which function should I use: getJointJacobian() or getframeJacobian()? Pinocchio seems to provide no joint_ID for fixed_joint, only joint_ID for movable joints.
Thanks a lot for any help on this.

[jcarpent]

Sorry for the late reply. You should indeed use getFrameJacobian() for fixed joints represented as frames.
You can also use this function for movable joints (as all the joints have an associated frame in the vector of frames).

[xiaosuyang]

For a biped robot ,where is the WORLD frame? Is it moving with baselink(torso)?,