Bernstein Polynomial-Based Method for Solving Optimal Trajectory Generation Problems

Calvin Kielas-Jensen; Venanzio Cichella; Thomas Berry; Isaac Kaminer; Claire Walton; Antonio Pascoal

doi:10.3390/s22051869

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Bernstein Polynomial-Based Method for Solving Optimal Trajectory Generation Problems

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Bernstein Polynomial-Based Method for Solving Optimal Trajectory Generation Problems

Calvin Kielas-Jensen, Venanzio Cichella, Thomas Berry, Isaac Kaminer, Claire Walton and Antonio Pascoal

Sensors (Basel, Switzerland), Vol.22(5), p.1869

02/27/2022

DOI: 10.3390/s22051869

PMCID: PMC8915131

PMID: 35271016

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Abstract

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.

optimal control

Bernstein polynomials

Bézier curves

optimal trajectory generation

Details

Title: Subtitle: Bernstein Polynomial-Based Method for Solving Optimal Trajectory Generation Problems
Creators: Calvin Kielas-Jensen - University of Iowa
Venanzio Cichella - University of Iowa
Thomas Berry - University of Lisbon
Isaac Kaminer - Naval Postgraduate School
Claire Walton - The University of Texas at San Antonio
Antonio Pascoal - University of Lisbon
Resource Type: Journal article
Publication Details: Sensors (Basel, Switzerland), Vol.22(5), p.1869
DOI: 10.3390/s22051869
PMID: 35271016
PMCID: PMC8915131
NLM abbreviation: Sensors (Basel)
ISSN: 1424-8220
eISSN: 1424-8220
Grant note: N000142112091 / Office of Naval Research N000141912106 / Office of Naval Research N0001419WX00155 / Office of Naval Research
Language: English
Date published: 02/27/2022
Academic Unit: Mechanical Engineering
Record Identifier: 9984227002202771

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