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

Haoping WANG1, Christian VASSEUR2, Vladan KONCAR3, Afzal CHAMROO4, Nicolai CHRISTOV5
1,2,5 LAGIS CNRS FRE 3303, Université Lille 1 Sciences et Technologies, Bât. P2,
59655 Villeneuve d’Ascq, France
{haoping.wang, christian.vasseur, nicolai.christov}@univ-lille1.fr
3 GEMTEX, ENSAIT,
9 Rue de l’Ermitage, BP 30329, 59056 Roubaix, France
vladan.koncar@ensait.fr
4 LAII, Université Poitiers,
40 av. du Recteur Pineau, 86022 Poitiers, France
afzal.chamroo@univ-poitiers.fr

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 Systems,  Studies in Informatics and Control, ISSN 1220-1766, vol. 19 (1), pp. 35-44, 2010.

1. Introduction

During the last few years, there has been a considerable amount of interest in the control of vision based underactuated mechanical systems forced by fewer actuators than degrees of freedom, presents a challenging problem. The interest comes from the need of supervision in remote control especially via Internet based network, more flexible contactless wiring and improved signal/noise ratio. Various models of vision based underactuated mechanical control have been reported in attempt to improve the visual servoing’s performance.

Recalling [1] the visual servoing term is defined as using visual feedback to control a robot. For example visual (image based) features such as points, lines and regions can be used to enable the alignment of a manipulator/gripping mechanism with an object. Vision is a part of a control system providing feedback. However, traditionally visual sensing and manipulation are combined in an open-loop configuration, ‘looking’ and ‘moving’, or just for visualizations and animations purposes referring to pendulum control in remote control laboratory [2], [3]. Recently, visual supervision has been gradually combined in the closed control loop particularly for cart-inverted pendulum control such as in [4], [5]. Unfortunately there is no real successful application reported on controlling the cart’s position and pendulum’s angle by visual servoing till now. A fuzzy-logic based controller was reported in [6], but only for controlling a rotary pendulum near the unstable equilibrium zone not exceeding ±5°. For larger deviations, the system turned out to be too slow to compensate. This control was limited in time on a few seconds in keeping the pendulum upright. In [7] a just-in-time human simulated method was developed to stabilize a two-link Direct Drive Arm-pendulum system. The direction of the pendulum movement is restricted on tangential plane for the trajectory of the tip of second link. This human learning and memory based fuzzy control can stabilize the inverted pendulum only for seconds ( 16 s) and with larger angular position oscillations ±26°, just like humans.

Analyzing the difficulties of previous vision based research works related to CIP control; it seemed that the camera signal has not been sufficiently exploited. The problem is that these sensors often deliver sampled and delayed signals due to their digital nature and computation-transfer time (image processing) respectively. Our challenge here is to consider the low cost CCD cameras as contact-less pendulum sensor to stabilize the CIP jumping from a big angular position with a big time delay.

Our efforts have been focused on the development of an accurate observer using the theory of Piecewise Continuous Systems (PCS) [8]. This kind of systems are continuous controlled hybrid systems with independent switching and controlled input [8], [9]. Considering the sampled delayed camera’s measurements (pendulum’s angular position) as autonomous switching and controlled impulse, we estimate the present continuous pendulum’s angular position and angular speed.

With the improved pendulum’s angular position and the estimated angular speed, we can construct our control methods. The research work presented here is an extension and development of the preceding works [8], [9], [10], [11].

The paper is organized as follows: sections 2, 3 and 4 present the description and modelling of the real vision based CIP system, particularly the TSAI calibration method and the way to calculate the delayed and sampled pendulum’s angular position. In section 5 a hybrid control consisting of the Jumping-up control and the two causal stabilization loops under a logic-based switch mechanism is proposed. A Piecewise Continuous Reduced Order Luenberger Observer (PCROLO) is also developed. Simulation and experimental results are given in section 6.

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