On the iterative steering of a rolling robot actuated by internal rotors

Akihiro Morinaga, Mikhail Mikhailovich Svinin, Motoji Yamamoto

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

This chapter deals with a motion planning problem for a spherical rolling robot actuated by two internal rotors that are placed on orthogonal axes. The mathematical model of the robot, represented by a driftless control system, contains a physical singularity corresponding to the motion of the contact point along the equatorial line in the plane of the two rotors. It is shown that steering through the singularity by finding a globally regular valid basis is not applicable to the system under consideration. The solution of the motion planning problem employs the nilpotent approximation of the originally non-nilpotent robot dynamics, and is based on an iterative steering algorithm. At each iteration, the control inputs are constructed with the use of geometric phases. To solve the state-to-state transfer problem, a globally convergent steering algorithm with adjustable step size is implemented and tested under simulation. It is shown that its steering efficiency is not superior to the algorithm with constant iteration step size.

Original languageEnglish
Title of host publicationAnalysis, Modelling, Optimization, and Numerical Techniques, ICAMI 2013
EditorsGerard Olivar Tost, Olga Vasilieva
PublisherSpringer New York LLC
Pages205-218
Number of pages14
ISBN (Print)9783319125824
DOIs
Publication statusPublished - Jan 1 2015
Event2nd International Conference on Applied Mathematics and Informatics, ICAMI 2013 - San Andres Island, United States
Duration: Nov 24 2013Nov 29 2013

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume121
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

Other2nd International Conference on Applied Mathematics and Informatics, ICAMI 2013
CountryUnited States
CitySan Andres Island
Period11/24/1311/29/13

Fingerprint

Rotor
Motion Planning
Robot
Internal
Singularity
Robot Dynamics
Iteration
Geometric Phase
Control System
Contact
Valid
Mathematical Model
Motion
Line
Approximation
Simulation

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Morinaga, A., Svinin, M. M., & Yamamoto, M. (2015). On the iterative steering of a rolling robot actuated by internal rotors. In G. O. Tost, & O. Vasilieva (Eds.), Analysis, Modelling, Optimization, and Numerical Techniques, ICAMI 2013 (pp. 205-218). (Springer Proceedings in Mathematics and Statistics; Vol. 121). Springer New York LLC. https://doi.org/10.1007/978-3-319-12583-1_14

On the iterative steering of a rolling robot actuated by internal rotors. / Morinaga, Akihiro; Svinin, Mikhail Mikhailovich; Yamamoto, Motoji.

Analysis, Modelling, Optimization, and Numerical Techniques, ICAMI 2013. ed. / Gerard Olivar Tost; Olga Vasilieva. Springer New York LLC, 2015. p. 205-218 (Springer Proceedings in Mathematics and Statistics; Vol. 121).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Morinaga, A, Svinin, MM & Yamamoto, M 2015, On the iterative steering of a rolling robot actuated by internal rotors. in GO Tost & O Vasilieva (eds), Analysis, Modelling, Optimization, and Numerical Techniques, ICAMI 2013. Springer Proceedings in Mathematics and Statistics, vol. 121, Springer New York LLC, pp. 205-218, 2nd International Conference on Applied Mathematics and Informatics, ICAMI 2013, San Andres Island, United States, 11/24/13. https://doi.org/10.1007/978-3-319-12583-1_14
Morinaga A, Svinin MM, Yamamoto M. On the iterative steering of a rolling robot actuated by internal rotors. In Tost GO, Vasilieva O, editors, Analysis, Modelling, Optimization, and Numerical Techniques, ICAMI 2013. Springer New York LLC. 2015. p. 205-218. (Springer Proceedings in Mathematics and Statistics). https://doi.org/10.1007/978-3-319-12583-1_14
Morinaga, Akihiro ; Svinin, Mikhail Mikhailovich ; Yamamoto, Motoji. / On the iterative steering of a rolling robot actuated by internal rotors. Analysis, Modelling, Optimization, and Numerical Techniques, ICAMI 2013. editor / Gerard Olivar Tost ; Olga Vasilieva. Springer New York LLC, 2015. pp. 205-218 (Springer Proceedings in Mathematics and Statistics).
@inproceedings{82bbfde517184e8bafaf4b517bb1b90d,
title = "On the iterative steering of a rolling robot actuated by internal rotors",
abstract = "This chapter deals with a motion planning problem for a spherical rolling robot actuated by two internal rotors that are placed on orthogonal axes. The mathematical model of the robot, represented by a driftless control system, contains a physical singularity corresponding to the motion of the contact point along the equatorial line in the plane of the two rotors. It is shown that steering through the singularity by finding a globally regular valid basis is not applicable to the system under consideration. The solution of the motion planning problem employs the nilpotent approximation of the originally non-nilpotent robot dynamics, and is based on an iterative steering algorithm. At each iteration, the control inputs are constructed with the use of geometric phases. To solve the state-to-state transfer problem, a globally convergent steering algorithm with adjustable step size is implemented and tested under simulation. It is shown that its steering efficiency is not superior to the algorithm with constant iteration step size.",
author = "Akihiro Morinaga and Svinin, {Mikhail Mikhailovich} and Motoji Yamamoto",
year = "2015",
month = "1",
day = "1",
doi = "10.1007/978-3-319-12583-1_14",
language = "English",
isbn = "9783319125824",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer New York LLC",
pages = "205--218",
editor = "Tost, {Gerard Olivar} and Olga Vasilieva",
booktitle = "Analysis, Modelling, Optimization, and Numerical Techniques, ICAMI 2013",

}

TY - GEN

T1 - On the iterative steering of a rolling robot actuated by internal rotors

AU - Morinaga, Akihiro

AU - Svinin, Mikhail Mikhailovich

AU - Yamamoto, Motoji

PY - 2015/1/1

Y1 - 2015/1/1

N2 - This chapter deals with a motion planning problem for a spherical rolling robot actuated by two internal rotors that are placed on orthogonal axes. The mathematical model of the robot, represented by a driftless control system, contains a physical singularity corresponding to the motion of the contact point along the equatorial line in the plane of the two rotors. It is shown that steering through the singularity by finding a globally regular valid basis is not applicable to the system under consideration. The solution of the motion planning problem employs the nilpotent approximation of the originally non-nilpotent robot dynamics, and is based on an iterative steering algorithm. At each iteration, the control inputs are constructed with the use of geometric phases. To solve the state-to-state transfer problem, a globally convergent steering algorithm with adjustable step size is implemented and tested under simulation. It is shown that its steering efficiency is not superior to the algorithm with constant iteration step size.

AB - This chapter deals with a motion planning problem for a spherical rolling robot actuated by two internal rotors that are placed on orthogonal axes. The mathematical model of the robot, represented by a driftless control system, contains a physical singularity corresponding to the motion of the contact point along the equatorial line in the plane of the two rotors. It is shown that steering through the singularity by finding a globally regular valid basis is not applicable to the system under consideration. The solution of the motion planning problem employs the nilpotent approximation of the originally non-nilpotent robot dynamics, and is based on an iterative steering algorithm. At each iteration, the control inputs are constructed with the use of geometric phases. To solve the state-to-state transfer problem, a globally convergent steering algorithm with adjustable step size is implemented and tested under simulation. It is shown that its steering efficiency is not superior to the algorithm with constant iteration step size.

UR - http://www.scopus.com/inward/record.url?scp=84943417230&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84943417230&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-12583-1_14

DO - 10.1007/978-3-319-12583-1_14

M3 - Conference contribution

AN - SCOPUS:84943417230

SN - 9783319125824

T3 - Springer Proceedings in Mathematics and Statistics

SP - 205

EP - 218

BT - Analysis, Modelling, Optimization, and Numerical Techniques, ICAMI 2013

A2 - Tost, Gerard Olivar

A2 - Vasilieva, Olga

PB - Springer New York LLC

ER -