Relationship between the pseudoinverse formulation and the compact formulation for obtaining the general solutions of redundant robotic systems

The general solutions of redundant robotic systems have been formulated by the traditional pseudoinverse formulation and the compact formulation. The purpose is to derive the relationship between the pseudoinverse and the compact formulations which are valid both for the force distribution and the kinematic redundancy problems. It is shown that the general solutions of the pseudoinverse formulation can be converted into those of the compact formulation with the free variables chosen as a function of the arbitrary vector of the pseudoinverse formulation. Therefore, every optimization scheme that chooses a specified arbitrary vector to optimize a desired objective can be implemented by compact formulations. The computational requirements for both formulations are evaluated and compared