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Design and Implementation of Robust Hybrid Control of Vision Based Underactuated Mechanical Nonminimum Phase Systems

Haoping WANG
LAGIS CNRS 8146, Université des Sciences et Technologies de Lille, UFR IEEA, Bâtiment P2
59655 Villeneuve d’Ascq Cedex, France

Christian VASSEUR
LAGIS CNRS 8146, Université des Sciences et Technologies de Lille, UFR IEEA, Bâtiment P2
59655 Villeneuve d’Ascq Cedex, France

Vladan KONCAR
GEMTEX, ENSAIT
9 Rue de l’Ermitage, BP 30329, 59056 Roubaix, France

Afzal CHAMROO
LAII, Université Poitiers
40 Avenue du Recteur Pineau, 86022 Poitiers, France

Nicolai CHRISTOV
LAGIS CNRS 8146, Université des Sciences et Technologies de Lille, UFR IEEA, Bâtiment P2
59655 Villeneuve d’Ascq Cedex, France

Abstract: This paper presents a vision based Cart-Inverted Pendulum (CIP) system under a hybrid feedback configuration: the continuous cart’s position measured by encoder and the delayed & sampled inverted pendulum’s upper coordinates, obtained from a visual sensor. The challenge here is to stabilize the CIP from a big inclined initial angle by using a low cost CCD camera. Under this scheme, we propose a hybrid control which consists in a Jumping-up (Bang-Bang) control and a two causal stabilization loops control: the first one (inner loop) realizes a linearization and the stabilization control of the pendulum based on an innovative Piecewise Continuous Reduced Order Luenberger Observer coupled with a linearization module, the second one (the outer loop) realizes a Lyapunov based control for the unstable internal system with lower dynamics than that of the pendulum. This hybrid control method is capable of balancing the CIP system within small cart’s displacement. Performances issues of the proposed method are illustrated by the experimental figures and videos.

Keywords: Visual servoing, underacturated mechanical systems, nonminimum phase systems, Lyapunov functions, piecewise continuous systems.

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CITE THIS PAPER AS:
Haoping WANG, Christian VASSEUR, Vladan KONCAR, Afzal CHAMROO, Nicolai CHRISTOV, Design and Implementation of Robust Hybrid Control of Vision Based Underactuated Mechanical Nonminimum Phase SystemsStudies in Informatics and Control, ISSN 1220-1766, vol. 19 (1), pp. 35-44, 2010.