Abstract
This paper is focused on analysis of the control solution using the transverse function approach. The controller considered here is designed for a nonholonomic vehicle with on-axle passive trailers. The main problem investigated is the optimal parametrization of the transverse functions in order to ensure low sensitivity to the measurement noise and high tracking accuracy. Theoretical analysis referring to transverse function scaling using dilation is illustrated by results of extensive numerical simulations. Taking into account these results the controller properties are considered. Finally, possibility of the controller implementation is discussed.
Highlights
Motion control of nonholonomic systems has become of great importance for many applications in robotics
The controller we focus on is based on the transverse function approach
We focus on selection of transverse function separately
Summary
Motion control of nonholonomic systems has become of great importance for many applications in robotics. It was shown that time-varying signals which introduce permanent excitation to the closed-loop system give possibility to establish asymptotic stability [23, 26] Another closed-loop control approach takes advantage of feedback singularity at the desired point [2, 10, 27]. One of the latest method of stabilization have been formulated by Morin and Samson [11] It takes advantage of transverse functions and refers to fundamental properties of an affine control system and its own control Lie algebra. The time-evolution of the transverse functions are governed by an augmented dynamics that is dependent on the tracking error This approach has been effectively used to control invariant systems (defined on Lie group) for which global stabilization result can be guaranteed.
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