Relaxed dubins problems through three points

Zheng Chen; Tal Shima

doi:https://doi.org/10.1109/MED.2019.8798584

Relaxed dubins problems through three points

Zheng Chen, Tal Shima

Aerospace Engineering

Technion - Israel Institute of Technology

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

Abstract

In this paper, we study the Relaxed 3-Point Dubins Problem (R3PDP), which consists of steering a Dubins vehicle through three consecutive waypoints with prescribed heading orientation angle at the initial waypoint. From a geometric point of view, we show that the shortest path must lie in a sufficient family of 12 candidates, and a formula in terms of the parameters of the R3PDP is established for all the 12 candidates. Analyzing the formula indicates that the shortest path of the R3PDP is determined by the zeros of some nonlinear equations. We propose some efficient algorithms to find the zeros of those nonlinear equations so that any R3PDP can be efficiently solved. Finally, some numerical examples are simulated, illustrating the developments of the paper.

Original language	English
Title of host publication	27th Mediterranean Conference on Control and Automation, MED 2019 - Proceedings
Pages	501-506
Number of pages	6
ISBN (Electronic)	9781728128030
DOIs	https://doi.org/10.1109/MED.2019.8798584
State	Published - Jul 2019
Event	27th Mediterranean Conference on Control and Automation, MED 2019 - Akko, Israel Duration: 1 Jul 2019 → 4 Jul 2019

Publication series

Name	27th Mediterranean Conference on Control and Automation, MED 2019 - Proceedings

Conference

Conference	27th Mediterranean Conference on Control and Automation, MED 2019
Country/Territory	Israel
City	Akko
Period	1/07/19 → 4/07/19

All Science Journal Classification (ASJC) codes

Computer Science Applications
Control and Optimization
Modelling and Simulation

Access to Document

https://doi.org/10.1109/MED.2019.8798584

Cite this

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title = "Relaxed dubins problems through three points",

abstract = "In this paper, we study the Relaxed 3-Point Dubins Problem (R3PDP), which consists of steering a Dubins vehicle through three consecutive waypoints with prescribed heading orientation angle at the initial waypoint. From a geometric point of view, we show that the shortest path must lie in a sufficient family of 12 candidates, and a formula in terms of the parameters of the R3PDP is established for all the 12 candidates. Analyzing the formula indicates that the shortest path of the R3PDP is determined by the zeros of some nonlinear equations. We propose some efficient algorithms to find the zeros of those nonlinear equations so that any R3PDP can be efficiently solved. Finally, some numerical examples are simulated, illustrating the developments of the paper.",

author = "Zheng Chen and Tal Shima",

note = "Publisher Copyright: {\textcopyright} 2019 IEEE.; 27th Mediterranean Conference on Control and Automation, MED 2019 ; Conference date: 01-07-2019 Through 04-07-2019",

year = "2019",

month = jul,

doi = "https://doi.org/10.1109/MED.2019.8798584",

language = "الإنجليزيّة",

series = "27th Mediterranean Conference on Control and Automation, MED 2019 - Proceedings",

pages = "501--506",

booktitle = "27th Mediterranean Conference on Control and Automation, MED 2019 - Proceedings",

}

Chen, Z & Shima, T 2019, Relaxed dubins problems through three points. in 27th Mediterranean Conference on Control and Automation, MED 2019 - Proceedings., 8798584, 27th Mediterranean Conference on Control and Automation, MED 2019 - Proceedings, pp. 501-506, 27th Mediterranean Conference on Control and Automation, MED 2019, Akko, Israel, 1/07/19. https://doi.org/10.1109/MED.2019.8798584

TY - GEN

T1 - Relaxed dubins problems through three points

AU - Chen, Zheng

AU - Shima, Tal

PY - 2019/7

Y1 - 2019/7

N2 - In this paper, we study the Relaxed 3-Point Dubins Problem (R3PDP), which consists of steering a Dubins vehicle through three consecutive waypoints with prescribed heading orientation angle at the initial waypoint. From a geometric point of view, we show that the shortest path must lie in a sufficient family of 12 candidates, and a formula in terms of the parameters of the R3PDP is established for all the 12 candidates. Analyzing the formula indicates that the shortest path of the R3PDP is determined by the zeros of some nonlinear equations. We propose some efficient algorithms to find the zeros of those nonlinear equations so that any R3PDP can be efficiently solved. Finally, some numerical examples are simulated, illustrating the developments of the paper.

AB - In this paper, we study the Relaxed 3-Point Dubins Problem (R3PDP), which consists of steering a Dubins vehicle through three consecutive waypoints with prescribed heading orientation angle at the initial waypoint. From a geometric point of view, we show that the shortest path must lie in a sufficient family of 12 candidates, and a formula in terms of the parameters of the R3PDP is established for all the 12 candidates. Analyzing the formula indicates that the shortest path of the R3PDP is determined by the zeros of some nonlinear equations. We propose some efficient algorithms to find the zeros of those nonlinear equations so that any R3PDP can be efficiently solved. Finally, some numerical examples are simulated, illustrating the developments of the paper.

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M3 - منشور من مؤتمر

T3 - 27th Mediterranean Conference on Control and Automation, MED 2019 - Proceedings

SP - 501

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BT - 27th Mediterranean Conference on Control and Automation, MED 2019 - Proceedings

T2 - 27th Mediterranean Conference on Control and Automation, MED 2019

Y2 - 1 July 2019 through 4 July 2019

ER -

Relaxed dubins problems through three points

Abstract

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All Science Journal Classification (ASJC) codes

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