A Fibonacci control system with application to hyper-redundant manipulators

TL;DR

This paper introduces a Fibonacci-based control system for hyper-redundant manipulators, analyzing its reachability, controllability, and connections to non-integer base expansions, advancing robotic control theory.

Contribution

It presents a novel Fibonacci control model for snake robots, exploring its mathematical properties and potential applications in robotic manipulators.

Findings

Characterization of the reachable workspace

Analysis of local controllability properties

Connection to non-integer base expansions

Abstract

We study a robot snake model based on a discrete linear control system involving Fibonacci sequence and closely related to the theory of expansions in non-integer bases. The present paper includes an investigation of the reachable workspace, a more general analysis of the control system underlying the model, its reachability and local controllability properties and the relation with expansions in non-integer bases and with iterated function systems.