A computer-aided analysis of stabilization problems for steady motions of mobile robots as nonholonomic systems

Аuthors

Krasinsky A. Y.^1*, Khalikov A. A.²

1. Moscow State University of Food Production, 11, Volokolamskoe shosse, Moscow, 125080, Russia
2. Moscow State University for Applied Biotechnologies (MGUPB), 33, Talalikhina str., Moscow, 109316, Russia

*e-mail: krasinsk@mail.ru

Abstract

Some possible statements are discussed for stability and stabilization problems related to steady motions of nonholonomic systems. A structure of nonlinear vector equations is analyzed to describe perturbed motions as well as a type of stability achievable after stabilization for various statement of the problem. A software product is described to realize in some symbolic form an algorithm to generate coefficients for stabilizing control and estimation systems. An application of the product is discussed to solve the stabilization problem for steady- state motion of unicycle model. Lagrange variables are used in the problem and stabilizing coefficients are calculated by the Krasovsky method for optimal stabilization problem associated with assigned linear controlled subsystem. As an example a transient process (unicycle tilt angle subject to time) is demonstrated for the unicycle motion under the action of the synthesized control.