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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...

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Autores principales: Kielas-Jensen, Calvin, Cichella, Venanzio, Berry, Thomas, Kaminer, Isaac, Walton, Claire, Pascoal, Antonio
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
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.
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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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