Redundant robotic chains on Riemannian submersions
IEEE Transactions on Robotics and Automation, 20(2):335-340, 2004.
For redundant robotic chains composed of simple one-degree
of freedom joints or links, a geometric interpretation of the forward
kinematic map in terms of Riemannian submersions is proposed.
Several properties of redundant robots then admit clear geometric
characterizations, the most remarkable being that the Moore-Penrose
pseudoinverse normally used in Robotics coincides with the horizontal
lift of the Riemannian submersion.
Furthermore, this enables us to use all the techniques for motion
control of rigid bodies on Riemannian manifolds (and Lie groups in
particular) to design workspace control algorithms for the
end-effector of the robotic chain and then to pull them back to joint
space, all respecting the different geometric structures of the two
underlying model spaces.
The application to the control of a holonomic mobile manipulator is