Relationship between joint torques and end-effector wrench about modernrobotics HOT 2 CLOSED

Hi Henrique,

Those two functions will output J_b and J_s known as manipulator Jacobian. They can not be used for the mapping in Figure 5.4. The Jacobian used in Figure 5.4 is part of analytic Jacobian. The author got it by deriving from forward kinematics instead of converting between Jacobians, which is shown in the preface of Chapter 5. But you can get that using conversion as well.

Hope my explanation makes sense to you. It is a pretty good question though.

Many thanks,
Huan Weng

from modernrobotics.

In order to compute the Geometric Jacobian, J_Geom, from a Body Manipulator Jacobian, J_b, I have been using the following transformation:

Following is the respective Python code:

T_sb = mr.FKinSpace(self.M, self.Slist, thetalist)
R_sb, _ = mr.TransToRp(T_sb)

vel_transform = np.eye(6)
vel_transform[:3, :3] = R_sb
vel_transform[3:, 3:] = R_sb

J_b_theta = mr.JacobianBody(self.Blist, thetalist)

J = np.dot(vel_transform, J_b_theta)

This is basically computing the Manipulator Jacobian given in end-effector frame and then rotating it by the rotation of the end-effector itself in space-frame coordinates.

from modernrobotics.