### Abstract

An algorithm for discrete-time trajectory generation through a set of waypoints specified in three spatial dimensions is presented. Constructing a desired trajectory that passes through a set of given waypoints is important in several real-life applications such as autonomous guidance of Unmanned Aerial Vehicles (UAV). Commonly, tree search algorithms or polynomial spline-like extrapolations are employed for generating trajectories through a given set of waypoints, but they have not been demonstrated to be optimal or the most computationally efficient. This paper formulates the trajectory generation problem through a given set of waypoints as a discrete-time optimal control problem and provides an optimal trajectory that minimizes a cost that is quadratic in the position vector and its first three derivatives. The 'artificial control input' for the optimal control problem is taken to be the third derivative of the position vector, commonly referred to as the jerk vector. The generated trajectory is shown to pass through the set of specified waypoints and give a smooth position trajectory with continuous jerk. Numerical examples are provided to illustrate the trajectory generation scheme.

Original language | English (US) |
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Title of host publication | 2019 5th Indian Control Conference, ICC 2019 - Proceedings |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 342-346 |

Number of pages | 5 |

ISBN (Electronic) | 9781538662465 |

DOIs | |

State | Published - May 14 2019 |

Event | 5th Indian Control Conference, ICC 2019 - Delhi, India Duration: Jan 9 2019 → Jan 11 2019 |

### Publication series

Name | 2019 5th Indian Control Conference, ICC 2019 - Proceedings |
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### Conference

Conference | 5th Indian Control Conference, ICC 2019 |
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Country | India |

City | Delhi |

Period | 1/9/19 → 1/11/19 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering
- Control and Optimization

### Cite this

*2019 5th Indian Control Conference, ICC 2019 - Proceedings*(pp. 342-346). [8715626] (2019 5th Indian Control Conference, ICC 2019 - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/INDIANCC.2019.8715626

**Discrete-Time Optimal Trajectory Generation Through Multiple Waypoints.** / Warier, Rakesh R.; Sanyal, Amit; Viswanathan, Sasi Prabhakaran.

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

*2019 5th Indian Control Conference, ICC 2019 - Proceedings.*, 8715626, 2019 5th Indian Control Conference, ICC 2019 - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 342-346, 5th Indian Control Conference, ICC 2019, Delhi, India, 1/9/19. https://doi.org/10.1109/INDIANCC.2019.8715626

}

TY - GEN

T1 - Discrete-Time Optimal Trajectory Generation Through Multiple Waypoints

AU - Warier, Rakesh R.

AU - Sanyal, Amit

AU - Viswanathan, Sasi Prabhakaran

PY - 2019/5/14

Y1 - 2019/5/14

N2 - An algorithm for discrete-time trajectory generation through a set of waypoints specified in three spatial dimensions is presented. Constructing a desired trajectory that passes through a set of given waypoints is important in several real-life applications such as autonomous guidance of Unmanned Aerial Vehicles (UAV). Commonly, tree search algorithms or polynomial spline-like extrapolations are employed for generating trajectories through a given set of waypoints, but they have not been demonstrated to be optimal or the most computationally efficient. This paper formulates the trajectory generation problem through a given set of waypoints as a discrete-time optimal control problem and provides an optimal trajectory that minimizes a cost that is quadratic in the position vector and its first three derivatives. The 'artificial control input' for the optimal control problem is taken to be the third derivative of the position vector, commonly referred to as the jerk vector. The generated trajectory is shown to pass through the set of specified waypoints and give a smooth position trajectory with continuous jerk. Numerical examples are provided to illustrate the trajectory generation scheme.

AB - An algorithm for discrete-time trajectory generation through a set of waypoints specified in three spatial dimensions is presented. Constructing a desired trajectory that passes through a set of given waypoints is important in several real-life applications such as autonomous guidance of Unmanned Aerial Vehicles (UAV). Commonly, tree search algorithms or polynomial spline-like extrapolations are employed for generating trajectories through a given set of waypoints, but they have not been demonstrated to be optimal or the most computationally efficient. This paper formulates the trajectory generation problem through a given set of waypoints as a discrete-time optimal control problem and provides an optimal trajectory that minimizes a cost that is quadratic in the position vector and its first three derivatives. The 'artificial control input' for the optimal control problem is taken to be the third derivative of the position vector, commonly referred to as the jerk vector. The generated trajectory is shown to pass through the set of specified waypoints and give a smooth position trajectory with continuous jerk. Numerical examples are provided to illustrate the trajectory generation scheme.

UR - http://www.scopus.com/inward/record.url?scp=85066616653&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066616653&partnerID=8YFLogxK

U2 - 10.1109/INDIANCC.2019.8715626

DO - 10.1109/INDIANCC.2019.8715626

M3 - Conference contribution

AN - SCOPUS:85066616653

T3 - 2019 5th Indian Control Conference, ICC 2019 - Proceedings

SP - 342

EP - 346

BT - 2019 5th Indian Control Conference, ICC 2019 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

ER -