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.

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The article is devoted to a motion control problem for a differentially driven mobile robot in the task of trajectory tracking in the presence of skid-slip effects. The kinematic control concept presented in the paper is the Vector Field Orientation (VFO) feedback approach with a nonlinear feed-forward skid-slip influence compensation scheme. The VFO control law guarantees asymptotic convergence of the position tracking error to zero in spite of the disturbing influence of skid-slip phenomena. The paper includes a control law design description, stability and convergence analysis of a closed-loop system, and practical verification of the proposed control concept. The experimental results illustrate control quality obtained on a laboratory setup equipped with vision feedback, where the Kalman filter algorithm was used in order to practically estimate skid-slip components.

Abstract. The paper presents the application of a smooth kinematic algorithm to control multi-body vehicle which consists of the unicyclelike tractor with three trailers. The controller takes advantage of the transverse functions and properties of the IV-order two input chained system. The derivation of the algorithm is presented in details. In order to improve the performance of the controller in the real application a selected tuning techniques are discussed. The properties of the closed-loop control system are examined based on results of numerical simulations concerning the point stabilization and trajectory tracking tasks.

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