Geometric motion control for a kinematically redundant robotic chain: application to a holonomic mobile manipulator

For kinematically redundant robotic manipulators, the extra degrees of freedom available allows freedom in the generation 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 detail.