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research-article

Applying a Unit-Consistent Generalized Matrix Inverse For Stable Control of Robotic Systems

[+] Author and Article Information
Bo Zhang

E3419 Lafferre Hall Columbia, MO 65211 bz7v2@mail.missouri.edu

Jeffrey Uhlmann

201 Naka Hall Columbia, MO 65211 uhlmannj@missouri.edu

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanisms and Robotics. Manuscript received July 21, 2018; final manuscript received March 27, 2019; published online xx xx, xxxx. Assoc. Editor: Tuhin Das.

ASME doi:10.1115/1.4043371 History: Received July 21, 2018; Accepted March 27, 2019

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. We analyze and empirically demonstrate how these theoretical guarantees can be directly obtained in a practical robotic arm system.

Copyright © 2019 by ASME
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