The Operational Space Formulation

The qperational space dynamic formulation describes the dynamic behavior of a robot manipulato in terms of its end effecUM . The dynamic equations of motion for a single chain, written in end effector (or operational space) coordinates are [19]  

X = 6x1 vector of end effector coordinates, k, k = 6x1 spatial vectors of end effector rates and accelerations, fi(x, x) = 6x1 vectOT of centripetal and Coriolis forces, and p(x) = 6x1 vectOT of gravity forces. 

Mathematically, A is associated with the kinetic energy matrix of this formulation [19]. In a more basic physical sense, A is an inertial quantity which combines the dynamic properties of the entire actuated chain and projects them to the tip or end effector. That is, if a spatial force, F, is exerted at the tip of a 

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Khatib also discusses the operational space formulation for redundant manipulators. In this case, the definition for the operational space inertia matrix... 

O. Khatib. A Unified Approach for Motion and Force Control of Robot Manipulators The Operational Space Formulation. IEEE Journal of Robotics and Automation, RA-3(l) 43-53,1987. 

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