### Abstract

This paper addresses the problem of generating a position trajectory with pointing direction constraints at given waypoints for underactuated unmanned vehicles. The problem is initially posed on the configuration space mathbb{R}-{3}times mathbb{S}-{2} and thereafter, upon suitable modifications, is re-posed as a problem on the Lie group SE(3). This is done by determining a vector orthogonal to the pointing direction and using it as the vehicle's thrust direction. This translates to converting reduced attitude constraints to full attitude constraints at the waypoints. For the position trajectory, in addition to position constraints, this modification adds acceleration constraints at the waypoints. For real-time implementation with low computational expenses, a linear-quadratic regulator (LQR) approach is adopted to determine the position trajectory with smoothness upto the fourth time derivative of position (snap). For the attitude trajectory, the thrust direction extracted from the position trajectory is used to first propagate the attitude to the subsequent waypoint and then correct it over time to achieve the desired attitude at this waypoint. Finally, numerical simulation results are presented to validate the trajectory generation scheme.

Original language | English (US) |
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Title of host publication | 2019 American Control Conference, ACC 2019 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1930-1935 |

Number of pages | 6 |

ISBN (Electronic) | 9781538679265 |

State | Published - Jul 1 2019 |

Event | 2019 American Control Conference, ACC 2019 - Philadelphia, United States Duration: Jul 10 2019 → Jul 12 2019 |

### Publication series

Name | Proceedings of the American Control Conference |
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Volume | 2019-July |

ISSN (Print) | 0743-1619 |

### Conference

Conference | 2019 American Control Conference, ACC 2019 |
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Country | United States |

City | Philadelphia |

Period | 7/10/19 → 7/12/19 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*2019 American Control Conference, ACC 2019*(pp. 1930-1935). [8815238] (Proceedings of the American Control Conference; Vol. 2019-July). Institute of Electrical and Electronics Engineers Inc..

**Trajectory generation on SE(3) for an underactuated vehicle with pointing direction constraints.** / Dhullipalla, Mani H.; Hamrah, Reza; Warier, Rakesh R.; Sanyal, Amit.

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

*2019 American Control Conference, ACC 2019.*, 8815238, Proceedings of the American Control Conference, vol. 2019-July, Institute of Electrical and Electronics Engineers Inc., pp. 1930-1935, 2019 American Control Conference, ACC 2019, Philadelphia, United States, 7/10/19.

}

TY - GEN

T1 - Trajectory generation on SE(3) for an underactuated vehicle with pointing direction constraints

AU - Dhullipalla, Mani H.

AU - Hamrah, Reza

AU - Warier, Rakesh R.

AU - Sanyal, Amit

PY - 2019/7/1

Y1 - 2019/7/1

N2 - This paper addresses the problem of generating a position trajectory with pointing direction constraints at given waypoints for underactuated unmanned vehicles. The problem is initially posed on the configuration space mathbb{R}-{3}times mathbb{S}-{2} and thereafter, upon suitable modifications, is re-posed as a problem on the Lie group SE(3). This is done by determining a vector orthogonal to the pointing direction and using it as the vehicle's thrust direction. This translates to converting reduced attitude constraints to full attitude constraints at the waypoints. For the position trajectory, in addition to position constraints, this modification adds acceleration constraints at the waypoints. For real-time implementation with low computational expenses, a linear-quadratic regulator (LQR) approach is adopted to determine the position trajectory with smoothness upto the fourth time derivative of position (snap). For the attitude trajectory, the thrust direction extracted from the position trajectory is used to first propagate the attitude to the subsequent waypoint and then correct it over time to achieve the desired attitude at this waypoint. Finally, numerical simulation results are presented to validate the trajectory generation scheme.

AB - This paper addresses the problem of generating a position trajectory with pointing direction constraints at given waypoints for underactuated unmanned vehicles. The problem is initially posed on the configuration space mathbb{R}-{3}times mathbb{S}-{2} and thereafter, upon suitable modifications, is re-posed as a problem on the Lie group SE(3). This is done by determining a vector orthogonal to the pointing direction and using it as the vehicle's thrust direction. This translates to converting reduced attitude constraints to full attitude constraints at the waypoints. For the position trajectory, in addition to position constraints, this modification adds acceleration constraints at the waypoints. For real-time implementation with low computational expenses, a linear-quadratic regulator (LQR) approach is adopted to determine the position trajectory with smoothness upto the fourth time derivative of position (snap). For the attitude trajectory, the thrust direction extracted from the position trajectory is used to first propagate the attitude to the subsequent waypoint and then correct it over time to achieve the desired attitude at this waypoint. Finally, numerical simulation results are presented to validate the trajectory generation scheme.

UR - http://www.scopus.com/inward/record.url?scp=85072299088&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072299088&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85072299088

T3 - Proceedings of the American Control Conference

SP - 1930

EP - 1935

BT - 2019 American Control Conference, ACC 2019

PB - Institute of Electrical and Electronics Engineers Inc.

ER -