Why Controllability Of Rolling Motions May Fail

Krzysztof Krakowski; Fatima Silva Leite

Why Controllability Of Rolling Motions May Fail

Krzysztof Krakowski, Fatima Silva Leite

School of Science & Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We are interested in knowing whether or not the motion of two smooth surfaces rolling on each other, without slip or twist, can be controlled. We present a few cases of surfaces rolling on a tangent plane where we show that controllability fails and why. The control system associated to a rolling motion defines a distribution in the configuration space. If this rolling distribution is bracket generating, local controllability is guaranteed. After deriving the kinematic equations for rolling Euclidean submanifolds of co-dimension one, we derive a condition for local controllability.

Original language	English
Title of host publication	Proceedings of the 10th Portuguese Conference on Automatic Control (CONTROLO'2012)
Editors	Morgado Dias, Eduardo Marques, Dario Baptista
Place of Publication	Portugal
Publisher	Associação Portuguesa de Controlo Automático (APCA)
Pages	197-203
ISBN (Print)	9789729702532
Publication status	Published - 2012
Event	CONTROLO 2012: 10th Portuguese Conference on Automatic Control - Funchal, Portugal Duration: 16 Jul 2012 → 18 Jul 2012

Conference

Conference	CONTROLO 2012: 10th Portuguese Conference on Automatic Control
City	Funchal, Portugal
Period	16/07/12 → 18/07/12

Keywords

Calculus of Variations, Systems Theory and Control Theory

Access to Document

https://hdl.handle.net/1959.11/13585

Handle.net

Persistent link

Cite this

@inproceedings{55c917c0bfb3411fbee51a6d4ce28f77,

title = "Why Controllability Of Rolling Motions May Fail",

abstract = "We are interested in knowing whether or not the motion of two smooth surfaces rolling on each other, without slip or twist, can be controlled. We present a few cases of surfaces rolling on a tangent plane where we show that controllability fails and why. The control system associated to a rolling motion defines a distribution in the configuration space. If this rolling distribution is bracket generating, local controllability is guaranteed. After deriving the kinematic equations for rolling Euclidean submanifolds of co-dimension one, we derive a condition for local controllability.",

keywords = "Calculus of Variations, Systems Theory and Control Theory",

author = "Krzysztof Krakowski and \{Silva Leite\}, Fatima",

year = "2012",

language = "English",

isbn = "9789729702532",

pages = "197--203",

editor = "Morgado Dias and Eduardo Marques and Dario Baptista",

booktitle = "Proceedings of the 10th Portuguese Conference on Automatic Control (CONTROLO'2012)",

publisher = "Associa{\c c}{\~a}o Portuguesa de Controlo Autom{\'a}tico (APCA)",

note = "CONTROLO 2012: 10th Portuguese Conference on Automatic Control ; Conference date: 16-07-2012 Through 18-07-2012",

}

Krakowski, K & Silva Leite, F 2012, Why Controllability Of Rolling Motions May Fail. in M Dias, E Marques & D Baptista (eds), Proceedings of the 10th Portuguese Conference on Automatic Control (CONTROLO'2012). Associação Portuguesa de Controlo Automático (APCA), Portugal, pp. 197-203, CONTROLO 2012: 10th Portuguese Conference on Automatic Control, Funchal, Portugal, 16/07/12. <https://hdl.handle.net/1959.11/13585>

Why Controllability Of Rolling Motions May Fail. / Krakowski, Krzysztof; Silva Leite, Fatima.
Proceedings of the 10th Portuguese Conference on Automatic Control (CONTROLO'2012). ed. / Morgado Dias; Eduardo Marques; Dario Baptista. Portugal: Associação Portuguesa de Controlo Automático (APCA), 2012. p. 197-203.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Why Controllability Of Rolling Motions May Fail

AU - Krakowski, Krzysztof

AU - Silva Leite, Fatima

PY - 2012

Y1 - 2012

N2 - We are interested in knowing whether or not the motion of two smooth surfaces rolling on each other, without slip or twist, can be controlled. We present a few cases of surfaces rolling on a tangent plane where we show that controllability fails and why. The control system associated to a rolling motion defines a distribution in the configuration space. If this rolling distribution is bracket generating, local controllability is guaranteed. After deriving the kinematic equations for rolling Euclidean submanifolds of co-dimension one, we derive a condition for local controllability.

AB - We are interested in knowing whether or not the motion of two smooth surfaces rolling on each other, without slip or twist, can be controlled. We present a few cases of surfaces rolling on a tangent plane where we show that controllability fails and why. The control system associated to a rolling motion defines a distribution in the configuration space. If this rolling distribution is bracket generating, local controllability is guaranteed. After deriving the kinematic equations for rolling Euclidean submanifolds of co-dimension one, we derive a condition for local controllability.

KW - Calculus of Variations, Systems Theory and Control Theory

UR - http://www.apca.pt/index.php/site/publicacoes/6

M3 - Conference contribution

SN - 9789729702532

SP - 197

EP - 203

BT - Proceedings of the 10th Portuguese Conference on Automatic Control (CONTROLO'2012)

A2 - Dias, Morgado

A2 - Marques, Eduardo

A2 - Baptista, Dario

PB - Associação Portuguesa de Controlo Automático (APCA)

CY - Portugal

T2 - CONTROLO 2012: 10th Portuguese Conference on Automatic Control

Y2 - 16 July 2012 through 18 July 2012

ER -

Why Controllability Of Rolling Motions May Fail

Abstract

Conference

Keywords

Access to Document

Handle.net

Fingerprint

Cite this