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It is well-understood that the robustness of mechanical and robotic controlsystems depends critically on minimizing sensitivity to arbitraryapplication-specific details whenever possible. For example, if a system isdefined and performs well in one particular Euclidean coordinate frame then itshould be expected to perform identically if that coordinate frame isarbitrarily rotated or scaled. Similarly, the performance of the system shouldnot be affected if its key parameters are all consistently defined in metricunits or in imperial units. In this paper we show that a recently introducedgeneralized matrix inverse permits performance consistency to be rigorouslyguaranteed in control systems that require solutions to underdetermined and/oroverdetermined systems of equations.

A Generalized Matrix Inverse with Applications to Robotic Systems