# Discrete Asymptotic Reachability via Expansions in Non-integer Bases

### Anna Chiara Lai, Paola Loreti

#### Abstract

Aim of this paper is to show the connection between the theory of expansions in non-integer bases and discrete control systems. This idea is supported by an example of application, in the framework of robotics. We show how a model of multi-phalanx self-similar robot hand may be studied by means of results and techniques coming from non-standard numeration systems and related tools, like Iterated Function Systems (IFS) and, more generally, fractal geometry.

#### References

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#### Paper Citation

#### in Harvard Style

Lai A. and Loreti P. (2012). **Discrete Asymptotic Reachability via Expansions in Non-integer Bases** . In *Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,* ISBN 978-989-8565-22-8, pages 360-365. DOI: 10.5220/0004092403600365

#### in Bibtex Style

@conference{icinco12,

author={Anna Chiara Lai and Paola Loreti},

title={Discrete Asymptotic Reachability via Expansions in Non-integer Bases},

booktitle={Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,},

year={2012},

pages={360-365},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004092403600365},

isbn={978-989-8565-22-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,

TI - Discrete Asymptotic Reachability via Expansions in Non-integer Bases

SN - 978-989-8565-22-8

AU - Lai A.

AU - Loreti P.

PY - 2012

SP - 360

EP - 365

DO - 10.5220/0004092403600365