This article is cited in 16 papers

Deterministic Systems

Construction of invariant ellipsoids in the stabilization problem for a wheeled robot following a curvilinear path

A. V. Pesterev, L. B. Rapoport

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

Abstract: The synthesis control problem for the plane motion of a wheeled robot is studied. The goal of the control is to bring the robot to an assigned curvilinear trajectory and to stabilize its motion along it in the presence of phase and control constraints. For a synthesized control law, invariant ellipsoids – quadratic approximations of the attraction domains of the target trajectory – are constructed, which allow one to check in the course of the robot motion whether the control law can stabilize motion along the current trajectory segment. To take into account constraints on the control, methods of absolute stability theory are applied. The construction of the invariant ellipsoids reduces to solving a system of linear matrix inequalities.

PACS: 45.80.+r

Presented by the member of Editorial Board: B. T. Polyak

Received: 11.05.2008

 English version: Automation and Remote Control, 2009, 70:2, 219–232

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