Optimal motion planning for differentially flat systems using bernstein approximation

Venanzio Cichella; Isaac Kaminer; Claire Walton; Naira Hovakimyan

doi:10.1109/LCSYS.2017.2778313

Optimal motion planning for differentially flat systems using bernstein approximation

Venanzio Cichella, Isaac Kaminer, Claire Walton, Naira Hovakimyan

Research output: Contribution to journal › Article › peer-review

Abstract

This letter presents a computational framework to efficiently generate feasible and optimal trajectories for differentially flat autonomous vehicle systems. We formulate the optimal motion planning problem as a continuous-time optimal control problem, and approximate it by a discrete-time formulation using Bernstein polynomials. These polynomials allow for efficient computation of various constraints along the entire trajectory, and are particularly convenient for generating trajectories for safe operation of multiple vehicles in complex environments. The advantages of the proposed method are investigated through theoretical analysis and numerical examples.

Original language	English (US)
Pages (from-to)	181-186
Number of pages	6
Journal	IEEE Control Systems Letters
Volume	2
Issue number	1
DOIs	https://doi.org/10.1109/LCSYS.2017.2778313
State	Published - Jan 2018

Keywords

Autonomous vehicles
Bernstein polynomial
Bézier curves
Discrete approximation
Optimal motion planning

ASJC Scopus subject areas

Control and Systems Engineering
Control and Optimization

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title = "Optimal motion planning for differentially flat systems using bernstein approximation",

abstract = "This letter presents a computational framework to efficiently generate feasible and optimal trajectories for differentially flat autonomous vehicle systems. We formulate the optimal motion planning problem as a continuous-time optimal control problem, and approximate it by a discrete-time formulation using Bernstein polynomials. These polynomials allow for efficient computation of various constraints along the entire trajectory, and are particularly convenient for generating trajectories for safe operation of multiple vehicles in complex environments. The advantages of the proposed method are investigated through theoretical analysis and numerical examples.",

keywords = "Autonomous vehicles, Bernstein polynomial, B{\'e}zier curves, Discrete approximation, Optimal motion planning",

author = "Venanzio Cichella and Isaac Kaminer and Claire Walton and Naira Hovakimyan",

note = "Publisher Copyright: {\textcopyright} 2017 IEEE.",

year = "2018",

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AU - Walton, Claire

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AB - This letter presents a computational framework to efficiently generate feasible and optimal trajectories for differentially flat autonomous vehicle systems. We formulate the optimal motion planning problem as a continuous-time optimal control problem, and approximate it by a discrete-time formulation using Bernstein polynomials. These polynomials allow for efficient computation of various constraints along the entire trajectory, and are particularly convenient for generating trajectories for safe operation of multiple vehicles in complex environments. The advantages of the proposed method are investigated through theoretical analysis and numerical examples.

KW - Autonomous vehicles

KW - Bernstein polynomial

KW - Bézier curves

KW - Discrete approximation

KW - Optimal motion planning

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Optimal motion planning for differentially flat systems using bernstein approximation

Abstract

Keywords

ASJC Scopus subject areas

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