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Bernstein Polynomial-Based Method for Solving Optimal Trajectory Generation Problems
This paper presents a method for the generation of trajectories for autonomous system operations. The proposed method is based on the use of Bernstein polynomial approximations to transcribe infinite dimensional optimization problems into nonlinear programming problems. These, in turn, can be solved...
Autores principales: | , , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8915131/ https://www.ncbi.nlm.nih.gov/pubmed/35271016 http://dx.doi.org/10.3390/s22051869 |
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author | Kielas-Jensen, Calvin Cichella, Venanzio Berry, Thomas Kaminer, Isaac Walton, Claire Pascoal, Antonio |
author_facet | Kielas-Jensen, Calvin Cichella, Venanzio Berry, Thomas Kaminer, Isaac Walton, Claire Pascoal, Antonio |
author_sort | Kielas-Jensen, Calvin |
collection | PubMed |
description | This paper presents a method for the generation of trajectories for autonomous system operations. The proposed method is based on the use of Bernstein polynomial approximations to transcribe infinite dimensional optimization problems into nonlinear programming problems. These, in turn, can be solved using off-the-shelf optimization solvers. The main motivation for this approach is that Bernstein polynomials possess favorable geometric properties and yield computationally efficient algorithms that enable a trajectory planner to efficiently evaluate and enforce constraints along the vehicles’ trajectories, including maximum speed and angular rates as well as minimum distance between trajectories and between the vehicles and obstacles. By virtue of these properties and algorithms, feasibility and safety constraints typically imposed on autonomous vehicle operations can be enforced and guaranteed independently of the order of the polynomials. To support the use of the proposed method we introduce BeBOT (Bernstein/Bézier Optimal Trajectories), an open-source toolbox that implements the operations and algorithms for Bernstein polynomials. We show that BeBOT can be used to efficiently generate feasible and collision-free trajectories for single and multiple vehicles, and can be deployed for real-time safety critical applications in complex environments. |
format | Online Article Text |
id | pubmed-8915131 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-89151312022-03-12 Bernstein Polynomial-Based Method for Solving Optimal Trajectory Generation Problems Kielas-Jensen, Calvin Cichella, Venanzio Berry, Thomas Kaminer, Isaac Walton, Claire Pascoal, Antonio Sensors (Basel) Article This paper presents a method for the generation of trajectories for autonomous system operations. The proposed method is based on the use of Bernstein polynomial approximations to transcribe infinite dimensional optimization problems into nonlinear programming problems. These, in turn, can be solved using off-the-shelf optimization solvers. The main motivation for this approach is that Bernstein polynomials possess favorable geometric properties and yield computationally efficient algorithms that enable a trajectory planner to efficiently evaluate and enforce constraints along the vehicles’ trajectories, including maximum speed and angular rates as well as minimum distance between trajectories and between the vehicles and obstacles. By virtue of these properties and algorithms, feasibility and safety constraints typically imposed on autonomous vehicle operations can be enforced and guaranteed independently of the order of the polynomials. To support the use of the proposed method we introduce BeBOT (Bernstein/Bézier Optimal Trajectories), an open-source toolbox that implements the operations and algorithms for Bernstein polynomials. We show that BeBOT can be used to efficiently generate feasible and collision-free trajectories for single and multiple vehicles, and can be deployed for real-time safety critical applications in complex environments. MDPI 2022-02-27 /pmc/articles/PMC8915131/ /pubmed/35271016 http://dx.doi.org/10.3390/s22051869 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Kielas-Jensen, Calvin Cichella, Venanzio Berry, Thomas Kaminer, Isaac Walton, Claire Pascoal, Antonio Bernstein Polynomial-Based Method for Solving Optimal Trajectory Generation Problems |
title | Bernstein Polynomial-Based Method for Solving Optimal Trajectory Generation Problems |
title_full | Bernstein Polynomial-Based Method for Solving Optimal Trajectory Generation Problems |
title_fullStr | Bernstein Polynomial-Based Method for Solving Optimal Trajectory Generation Problems |
title_full_unstemmed | Bernstein Polynomial-Based Method for Solving Optimal Trajectory Generation Problems |
title_short | Bernstein Polynomial-Based Method for Solving Optimal Trajectory Generation Problems |
title_sort | bernstein polynomial-based method for solving optimal trajectory generation problems |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8915131/ https://www.ncbi.nlm.nih.gov/pubmed/35271016 http://dx.doi.org/10.3390/s22051869 |
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