I want to calculate the Jacobian of a mobile manipulator (MM). The MM consists of the moving mobile platform and manipulator on top of it. I am familiar with the Analytical and the Geometrical Jacobian. The first one I can find by differentiating the coordinates (w.r.t. an inertial frame) of the End Effector by each joint variable and the second one (from Siciliano):
Also the geometrical and analytical Jacobians are the same on a planar manipulator. Obviously a MM is not planar.
I want to use the Jacobian to model the interaction forces of the manipulator’s end effector. I guess we always need the Geometrical Jacobian for that but I have seen the analytical one also be used but I do not know when you can do that (maybe only on planar manipulators?)
I am modelling an unknown number of manipulator links (n links) and because I solve everything on Matlab I need a systematic approach.