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Summary: Geometric motion control for a kinematically redundant robotic
chain: application to a holonomic mobile manipulator
Claudio Alta ni
SISSA/ISAS Int. School for Advanced Studies,
via Beirut 2-4, 34014 Trieste, Italy.
E-mail altafini@sissa.it
January 20, 2003
Abstract
For kinematically redundant robotic manipulators, the extra degrees of freedom available
allows freedom in the generation of the trajectories of the end-e ector. In this paper, for this
scope, we use techniques for motion control of rigid bodies on Riemannian manifolds (and Lie
groups in particular) to design workspace control algorithms for the end-e ector of the robotic
chain and then to pull them back to joint space, all respecting the di erent geometric structures
of the two underlying model spaces. The trajectory planner makes use of geometric splines.
Examples of the di erent kinds of curves that are obtained via the De Casteljau algorithm
in correspondence of di erent metric structures in SE(3) are reported. The feedback module,
instead, consists of a Lyapunov based PD controller de ned from a suitable notion of error
distance on the Lie group. The motivating application of our work is a holonomic mobile
manipulator for which simulation results are described in detail.
Keywords: redundant robotic chains, motion control, holonomic mobile robot.
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