Geometric motion control for a kinematically redundant robotic chain: application to a holonomic mobile manipulator
Claudio Altafini
Journal of Robotic Systems, 20(5):211-227, 2003.
For kinematically redundant robotic manipulators, the extra degrees of freedom available allows freedom in the generatio
n of the trajectories of the end-effector.
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-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 trajectory planner makes use of geometric splines.
Examples of the different kinds of curves that are obtained via
the De Casteljau algorithm in correspondence of different metric
structures in SE(3) are reported.
The feedback module, instead, consists of a Lyapunov based PD controller
defined 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 d
etail.
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