### Abstract

A structure of the optimal trajectory for minimizing fuel consumption in an unstable dynamical environment such as the three-body problem is not well studied. Recently, it has been found that a sparse solution structure appears in the optimal control of a dynamical system. The concept of sparsity explains the property that the minimum fuel trajectory corresponds to the trajectory which minimizes the total thrusting time. In this paper, we propose a numerical method to obtain the minimum fuel sparse optimal trajectory in the unstable dynamical system. As an example, proposed methods are applied to the transfer in the Sun-Earth system.

Original language | English |
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Title of host publication | Spaceflight Mechanics 2019 |

Editors | Francesco Topputo, Andrew J. Sinclair, Matthew P. Wilkins, Renato Zanetti |

Publisher | Univelt Inc. |

Pages | 2599-2618 |

Number of pages | 20 |

ISBN (Print) | 9780877036593 |

Publication status | Published - Jan 1 2019 |

Event | 29th AAS/AIAA Space Flight Mechanics Meeting, 2019 - Maui, United States Duration: Jan 13 2019 → Jan 17 2019 |

### Publication series

Name | Advances in the Astronautical Sciences |
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Volume | 168 |

ISSN (Print) | 0065-3438 |

### Conference

Conference | 29th AAS/AIAA Space Flight Mechanics Meeting, 2019 |
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Country | United States |

City | Maui |

Period | 1/13/19 → 1/17/19 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Aerospace Engineering
- Space and Planetary Science

### Cite this

*Spaceflight Mechanics 2019*(pp. 2599-2618). [AAS 19-359] (Advances in the Astronautical Sciences; Vol. 168). Univelt Inc..

**Sparse optimal trajectory design in three-body problem.** / Kayama, Yuki; Bando, Mai; Hokamoto, Shinji.

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

*Spaceflight Mechanics 2019.*, AAS 19-359, Advances in the Astronautical Sciences, vol. 168, Univelt Inc., pp. 2599-2618, 29th AAS/AIAA Space Flight Mechanics Meeting, 2019, Maui, United States, 1/13/19.

}

TY - GEN

T1 - Sparse optimal trajectory design in three-body problem

AU - Kayama, Yuki

AU - Bando, Mai

AU - Hokamoto, Shinji

PY - 2019/1/1

Y1 - 2019/1/1

N2 - A structure of the optimal trajectory for minimizing fuel consumption in an unstable dynamical environment such as the three-body problem is not well studied. Recently, it has been found that a sparse solution structure appears in the optimal control of a dynamical system. The concept of sparsity explains the property that the minimum fuel trajectory corresponds to the trajectory which minimizes the total thrusting time. In this paper, we propose a numerical method to obtain the minimum fuel sparse optimal trajectory in the unstable dynamical system. As an example, proposed methods are applied to the transfer in the Sun-Earth system.

AB - A structure of the optimal trajectory for minimizing fuel consumption in an unstable dynamical environment such as the three-body problem is not well studied. Recently, it has been found that a sparse solution structure appears in the optimal control of a dynamical system. The concept of sparsity explains the property that the minimum fuel trajectory corresponds to the trajectory which minimizes the total thrusting time. In this paper, we propose a numerical method to obtain the minimum fuel sparse optimal trajectory in the unstable dynamical system. As an example, proposed methods are applied to the transfer in the Sun-Earth system.

UR - http://www.scopus.com/inward/record.url?scp=85072982061&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072982061&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85072982061

SN - 9780877036593

T3 - Advances in the Astronautical Sciences

SP - 2599

EP - 2618

BT - Spaceflight Mechanics 2019

A2 - Topputo, Francesco

A2 - Sinclair, Andrew J.

A2 - Wilkins, Matthew P.

A2 - Zanetti, Renato

PB - Univelt Inc.

ER -