A Generalized Matrix Inverse with Applications to Robotic Systems

TL;DR

This paper introduces a generalized matrix inverse that ensures consistent control system performance regardless of coordinate transformations or unit systems, enhancing robustness in robotic applications.

Contribution

It demonstrates how a recently developed generalized matrix inverse can be used to guarantee performance invariance in robotic control systems under various transformations.

Findings

Guarantees performance consistency under coordinate changes

Ensures robustness to unit system variations

Applicable to underdetermined and overdetermined systems

Abstract

It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs well in one particular Euclidean coordinate frame then it should be expected to perform identically if that coordinate frame is arbitrarily rotated or scaled. Similarly, the performance of the system should not be affected if its key parameters are all consistently defined in metric units or in imperial units. In this paper we show that a recently introduced generalized matrix inverse permits performance consistency to be rigorously guaranteed in control systems that require solutions to underdetermined and/or overdetermined systems of equations.