I have a mobile manipulator that moves on the plane. The base moves in SE(2) and the manipulator is also planar with 4 links. The mobile base will be a differential drive robot and its motion is defined as:
The manipulator is attached to the center of our mobile base. How do I compute the Jacobian of the mobile manipulator?
I know that for the mobile manipulator I have something of the form:
The middle matrix is what I need to compute.
The jacobian is a linear mapping of the forward kinematics function for the degrees of freedom of your system. Therefore, you should think of it as the movement of your end effector with respect to the world. In that case, the movement of the end effector is just the combination of the movement of your body wrt world and movement of ee wrt body. So Jb is equivalent to your first statement and Jm is equivalent to the arm jacobian rotated into the base frame.
With the way you have this setup, that would be a 3x6 matrix by the way. Just use v and omega as you did in the first equation and leave the first 3x2 block as is.
