End-link dynamics of redundant robotic limbs: The Reaction Null Space approach

It is shown that the Reaction Null Space formulation — a method developed for motion analysis and reactionless motion generation of free-floating and flexible-base robots — can be used to fully decouple the end-link dynamics of a kinematically redundant fixed-base robot. Decoupling is achieved thereby via the pseudoinverse of a coupling-inertia submatrix, in quite a different way from the dynamic decoupling achieved via the inertia-weighted generalized inverse of the manipulator Jacobian and known from the Operational Space formulation. The properties of the new formulation are clarified with the help of a comparative study on a representative motion/force control scenario. The simulation results show that the two formulations deliver identical results as far as end-link dynamics are concerned. The new method has an advantage with regard to joint space dynamics, though, which becomes apparent especially in the neighborhood of kinematic singularities, where the inertiaweighted generalized inverse of the manipulator Jacobian is ill-behaved.