### 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 language | English |
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Title of host publication | Analysis, Modelling, Optimization, and Numerical Techniques, ICAMI 2013 |

Editors | Gerard Olivar Tost, Olga Vasilieva |

Publisher | Springer New York LLC |

Pages | 205-218 |

Number of pages | 14 |

ISBN (Print) | 9783319125824 |

DOIs | |

Publication status | Published - Jan 1 2015 |

Event | 2nd International Conference on Applied Mathematics and Informatics, ICAMI 2013 - San Andres Island, United States Duration: Nov 24 2013 → Nov 29 2013 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 121 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Other

Other | 2nd International Conference on Applied Mathematics and Informatics, ICAMI 2013 |
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Country | United States |

City | San Andres Island |

Period | 11/24/13 → 11/29/13 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*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.

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

*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

}

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 -