Redundant robotic chains on Riemannian submersions

Claudio Altafini

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 described.

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