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 |
|---|---|
| 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 |
|---|---|
| Volume | 121 |
| ISSN (Print) | 2194-1009 |
| ISSN (Electronic) | 2194-1017 |
Other
| Other | 2nd International Conference on Applied Mathematics and Informatics, ICAMI 2013 |
|---|---|
| Country | United States |
| City | San Andres Island |
| Period | 11/24/13 → 11/29/13 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
Cite this
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 proceeding › Conference contribution
}
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 -