Group Theoretical Synthesis of Binary Manipulators

Abstract

This paper addresses a paradigm based on binary (two-state) actuation which may lead to lower cost and higher reliability for robotic manipulators. Binary manipulators constructed from pneumatic cylinders are both light weight and inexpensive, requiring minimal feedback hardware and trivial computer interfaces. However, for the benefits of binary actuation to be realized, methods developed in the pure mathematics literature over that past thirty years must be used to make the design and inverse kinematics of these manipulators tractable. As is demonstrated, the Fourier transform of functions on the Euclidean motion group is a powerful tool which can be used to this end.