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FROLÍK, S. RAJCHL, M. STODOLA, M.
Original Title
Numerical Experiment on Optimal Control for the Dubins Car Model
Type
conference paper
Language
English
Original Abstract
This paper deals with optimal control of the Dubins car model, whose configuration space is three dimensional smooth manifold. There are computed vector fields that generate solvable Lie algebra isomoprhically equivalent to tangent space in each point of the manifold. Then an otpimal control problem for finding the shortest curve between two points on the manifold is formulated. The problem is analytically solved for the nilpotent approximation of the fields and fixed points of the symmetries are found. To these fixed points multiple optimal trajectories can lead. The problem is also solved by using numerical simulations and these are compared with the analyticla solutions.
Keywords
Dubins car model, Lie algebra, Optimal control problem, Pontryagin maximum principle, Nilpotent algebra, Numerical simulations
Authors
FROLÍK, S.; RAJCHL, M.; STODOLA, M.
Released
5. 3. 2021
ISBN
978-3-030-70739-2
Book
Modelling and Simulation for Autonomous Systems
1611-3349
Periodical
Lecture Notes in Computer Science
Number
12619
State
Republic of Italy
Pages from
111
Pages to
122
Pages count
11
BibTex
@inproceedings{BUT183064, author="Stanislav {Frolík} and Matej {Rajchl} and Marek {Stodola}", title="Numerical Experiment on Optimal Control for the Dubins Car Model", booktitle="Modelling and Simulation for Autonomous Systems", year="2021", journal="Lecture Notes in Computer Science", number="12619", pages="111--122", doi="10.1007/978-3-030-70740-8\{_}7", isbn="978-3-030-70739-2", issn="1611-3349" }