Design of an optimal control for an autonomous mobile robot

E.M. Gutiérrez–Arias, J.E. Flores–Mena, M.M. Morin–Castillo, and H. Suárez–Ramírez

Facultad de Ciencias de la Electrónica, Benemérita Universidad Autónoma de Puebla, Av. San Claudio y 18 Sur, Ciudad Universitaria, Colonia Jardines de San Manuel, Puebla, Pue., 72570, México, e–mails: jmgutierrez@ece.buap.mx, eflores@ece.buap.mx, mmorin@ece.buap.mx, hsuarez@hotmail.com.

Recibido el 18 de enero de 2010
Aceptado el 11 de noviembre de 2010

Abstract

In this article, we present an autonomous mobile robot that is provided with two active wheels and passive one, as well as two control algorithms for the stabilization of the programmed paths. The dynamic programming constitute the bases for the determination of both control laws. The first law of optimal control is obtained by solving the Ricatti matricial differential equation. The second is deduced taking into account the work done by Kalman, which makes possible the reduction of a matricial differential equation into an algebraic matricial equation. The simulation of both algorithms is made when the programmed path is a straight line and this makes possible to observe the optimal control law, which represents the principal goal of this paper, and which presents an improved quality for the stabilization that the control law obtained following the work of Kalman.

Keywords: Mobile robot; optimal control; dynamic programming; Ricatti's differential equation.

Resumen

En este trabajo presentamos un robot movil autónomo provisto de dos ruedas activas y una pasiva, así como dos algoritmos de control para la estabilización de las trayectorias programadas; la programación dinámica es el fundamento para determinar ambas leyes de control. La primera ley de control optimo la obtenemos al solucionar una ecuación diferencial matricial del tipo Riccati, la segunda ley se deduce al aprovechar una disertación hecha por Kalman, la cual permite reducir una ecuación diferencial matricial a una ecuación algebraica matricial. La simulación de ambos algoritmos se realiza cuando la trayectoria programada es una línea recta y permite observar que la ley de control óptimo, objetivo primordial de este artículo, presenta una calidad superior en la estabilización que la ley de control obtenida mediante la disertación de Kalman.

Descriptores: Robot móvil; control óptimo; programación dinámica; ecuación diferencial de Riccati.

PACS: 45.40.–f; 45.80.+r; 46.15.Cc; 02.30.Yy.

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Acknowledgments

The authors are grateful for the financial support given by CONACyT of México. JEFM is grateful for the support given by VIEP–BUAP (project 7–ING–2009)

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