Analytical Jacobian or Geometrical Jacobian

[mahyaret]

Hello,
Thanks for the great kinodynamics library. I was wondering which functions for computing Jacobian addresses Analytical Jacobian and which one is computing Geometrical Jacobian?
Thanks,
Mahyar

[jmirabel]

What is a Geometrical Jacobian ?

[mahyaret]

Geometrical Jacobian is when the Jacobian is computed according to a geometric technique in which the contributions of each joint velocity to the components of end-effector linear and angular velocity are determined. Analytical Jacobian is when Jacobian is determined via differentiation of the forward kinematics function with respect to the joint variables.
more details can be found here: https://www.etedal.net/2014/12/analytical-jacobian-vs-geometrical.html

[jcarpent]

You can use pin.computeJointJacobians(model, data, q) and pin.getJointJacobian(model, data, joint_id, pin.LOCAL).
This will corresponds to kinematic Jacobian associated to the joint velocity expressed in the LOCAL frame of the joint.

[mahyaret]

I just wanted to be sure which implementation I am using when I call pin.computeJointJacobian(model, data, q). Is it Analytical or Geometrical? since they are not the same thing and related using: J_{Analytical} = T J_{Geometrical}, where T is a transformation matrix. For instance, it is going to be important for mapping wrench vector to joint torques, \tau = J^T F

[jcarpent]

In Pinocchio, the kinematic Jacobians map joint velocities to frame spatial velocity. Then, T can be any transformation between spatial velocity vector.

[mahyaret]

so for instance, if we use pin.computeJointJacobian(model, data, q) for \dot x = J \dot q then \dot x is [\dot x, \dot y, \dot z, \omega x, \omega y, \omega z]^T where \omega is the angular velocity, am I right?

[jcarpent]

Yes

[mahyaret]

Thanks!

[LHTLiu]

import pinocchio as pin

from pinocchio.visualize import MeshcatVisualizer

urdf_path = "../urdf/Franka_urdf/fr3_without_hand.urdf"

model: pin.Model = pin.buildModelFromUrdf(urdf_path)

data = model.createData()

q0 = pin.neutral(model)

end_frame = model.getJointId("fr3_joint8")

pin.computeJointJacobians(model, data, q0)

end_jacobian = pin.getJointJacobian(model, data, end_frame, pin.LOCAL)

why did the following error occur? The IDE I used is pycharm and the system is macbook.

[fabinsch]

see #2181. Please avoid cross-posting the same issue in different places.