Numerical Experiment on Optimal Control for the Dubins Car Model

Numerical Experiment on Optimal Control for the Dubins Car Model

Paper in proceedings (conference paper)

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

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

FROLÍK, S.; RAJCHL, M.; STODOLA, M.

05.03.2021

978-3-030-70739-2

Modelling and Simulation for Autonomous Systems

1611-3349

Lecture Notes in Computer Science

12619

Republic of Italy

111

122

11