Optimal Multi-Vehicle Motion Planning using Bernstein Approximants
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Authors
Cichella, Venanzio
Kaminer, Isaac
Walton, Claire
Hovakimyan, Naira
Pascoal, Antonio M.
Subjects
Bernstein polynomial
Bézier curve
multiple vehicles
optimal motion planning
Bézier curve
multiple vehicles
optimal motion planning
Advisors
Date of Issue
2020
Date
2020
Publisher
IEEE
Language
en_US
Abstract
This paper presents a computational framework to efficiently generate feasible and safe trajectories for multiple autonomous vehicle operations. We formulate the optimal motion planning problem as a continuous-time optimal control problem, and approximate its solutions in a discretized setting using Bernstein polynomials. The latter possess convenient properties that allow to efficiently compute and enforce constraints along the vehicles' trajectories, such as maximum speed and angular rates, minimum distance between trajectories and between the vehicles and known obstacles, etc. Thus, the proposed method is particularly suitable for generating trajectories in real-time for safe operations in complex environments and multiple vehicle missions. We show, using a rigorous mathematical framework, that the solution to the discretized optimal motion planning problem converges to that of the continuous-time one. The advantages of the proposed method are investigated through numerical examples.
Type
Preprint
Description
The article of record as published may be found at https://doi.org/10.1109/TAC.2020.2999329
Series/Report No
Department
Mechanical and Aerospace Engineering (MAE)
Organization
Naval Postgraduate School
Identifiers
NPS Report Number
Sponsors
The work was supported by the National Science Foundation: OCE-1333738. Aircraft measurements were supported by Office of Naval Research grants N00014-10-1-0811 and N00014-16-1-2567.
Funder
The work was supported by the National Science Foundation: OCE-1333738. Aircraft measurements were supported by Office of Naval Research grants N00014-10-1-0811 and N00014-16-1-2567.
Format
15 p.
Citation
Cichella, Venanzio, et al. "Optimal Multi-Vehicle Motion Planning using Bernstein Approximants." IEEE Transactions on Automatic Control (2020).
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.