Numerical Experiment on Optimal Control for the Dubins Car Model

článek ve sborníku ve WoS nebo Scopus

en

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.

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.

Dubins car model, Lie algebra, Optimal control problem, Pontryagin maximum principle, Nilpotent algebra, Numerical simulations

05.03.2021

978-3-030-70739-2

1611-3349

Modelling and Simulation for Autonomous Systems

12619

111–122

11