### Abstract

A system with nonholonomic constraints attracts its attention from the viewpoint of control theory because any conventional control cannot be applied directly to such a system. Since it cannot be stabilized by a static continuous feedback with constant gains, there are several control methods up to now by using a chained form etc. Among them, a switching control method using invariant manifold, which is considered as a generalized form for sliding mode control known as one of conventional switching control methods, and a quasi-continuous exponential stabilizing control method are proposed in a power form system with two inputs and three states or two inputs and n-states. In this study, as a new mehod, a switching control method using an invariant manifold as mentioned above is examined for a "double integrator system," known as an alternative canonical model for nonholonomic systems. In particular, stabilizing controllers are derived for the case of a kinematic model with two inputs and three states and for the case of a dynamic model with two inputs and five states, which is just as an "extended double integrator system." The effectiveness of the proposed controllers is demonstrated through simulations for a mobile robot with two independent driving wheels.

Original language | English |
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Title of host publication | Proceedings of the SICE Annual Conference |

Pages | 3278-3284 |

Number of pages | 7 |

Publication status | Published - 2010 |

Event | SICE Annual Conference 2010, SICE 2010 - Taipei, Taiwan, Province of China Duration: Aug 18 2010 → Aug 21 2010 |

### Other

Other | SICE Annual Conference 2010, SICE 2010 |
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Country | Taiwan, Province of China |

City | Taipei |

Period | 8/18/10 → 8/21/10 |

### Fingerprint

### Keywords

- Double integrator system
- Invariant manifold
- Nonholonomic mobile robots
- Switching control

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Control and Systems Engineering
- Computer Science Applications

### Cite this

*Proceedings of the SICE Annual Conference*(pp. 3278-3284). [5602619]

**A switching control method for stabilizing a nonholonomic mobile robot using invariant manifold method.** / Yamamoto, Takahiro; Watanabe, Keigo.

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

*Proceedings of the SICE Annual Conference.*, 5602619, pp. 3278-3284, SICE Annual Conference 2010, SICE 2010, Taipei, Taiwan, Province of China, 8/18/10.

}

TY - GEN

T1 - A switching control method for stabilizing a nonholonomic mobile robot using invariant manifold method

AU - Yamamoto, Takahiro

AU - Watanabe, Keigo

PY - 2010

Y1 - 2010

N2 - A system with nonholonomic constraints attracts its attention from the viewpoint of control theory because any conventional control cannot be applied directly to such a system. Since it cannot be stabilized by a static continuous feedback with constant gains, there are several control methods up to now by using a chained form etc. Among them, a switching control method using invariant manifold, which is considered as a generalized form for sliding mode control known as one of conventional switching control methods, and a quasi-continuous exponential stabilizing control method are proposed in a power form system with two inputs and three states or two inputs and n-states. In this study, as a new mehod, a switching control method using an invariant manifold as mentioned above is examined for a "double integrator system," known as an alternative canonical model for nonholonomic systems. In particular, stabilizing controllers are derived for the case of a kinematic model with two inputs and three states and for the case of a dynamic model with two inputs and five states, which is just as an "extended double integrator system." The effectiveness of the proposed controllers is demonstrated through simulations for a mobile robot with two independent driving wheels.

AB - A system with nonholonomic constraints attracts its attention from the viewpoint of control theory because any conventional control cannot be applied directly to such a system. Since it cannot be stabilized by a static continuous feedback with constant gains, there are several control methods up to now by using a chained form etc. Among them, a switching control method using invariant manifold, which is considered as a generalized form for sliding mode control known as one of conventional switching control methods, and a quasi-continuous exponential stabilizing control method are proposed in a power form system with two inputs and three states or two inputs and n-states. In this study, as a new mehod, a switching control method using an invariant manifold as mentioned above is examined for a "double integrator system," known as an alternative canonical model for nonholonomic systems. In particular, stabilizing controllers are derived for the case of a kinematic model with two inputs and three states and for the case of a dynamic model with two inputs and five states, which is just as an "extended double integrator system." The effectiveness of the proposed controllers is demonstrated through simulations for a mobile robot with two independent driving wheels.

KW - Double integrator system

KW - Invariant manifold

KW - Nonholonomic mobile robots

KW - Switching control

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M3 - Conference contribution

AN - SCOPUS:78649256021

SN - 9784907764364

SP - 3278

EP - 3284

BT - Proceedings of the SICE Annual Conference

ER -