Robust motion tracking control of piezo-driven flexure-based four-bar mechanism for micro/nano manipulation Hwee Choo Liaw a, * , Bijan Shirinzadeh a , Julian Smith b a Robotics and Mechatronics Research Laboratory, Department of Mechanical Engineering, Monash University, Clayton, VIC 3800, Australia b Department of Surgery, Monash Medical Centre, Faculty of Medicine, Nursing and Health Sciences, Monash University, Clayton, VIC 3800, Australia Received 14 July 2007; accepted 5 September 2007 Abstract This paper presents a robust motion tracking control methodology for a flexure-based four-bar micro/nano manipulator driven by a piezoelectric actuator. This control methodology is proposed for tracking desired motion trajectories in view of the problems of unknown or uncertain system parameters, non-linearities including the hysteresis effect, and external disturbances in the system. In this paper, equations of the angular stiffness, ‘static’ linear stiffness, and structural resonance of a flexure-hinged mechanism are presented. In addi- tion, a lumped parameter dynamic model is established for the formulation of the proposed control methodology. The convergence of the position tracking error to zero is assured by the approach in the presence of the aforementioned conditions. The stability of the closed-loop system is proven theoretically, and a precise tracking performance in following a desired motion trajectory is demonstrated in the experimental study. One of the most important advantages of this control methodology is that the approach requires only a knowl- edge of the estimated lumped parameters in the physical realisation. With the capability of motion tracking, the robust motion control methodology is very attractive in realising high-performance flexure-based control applications in the field of micro/nano manipulation. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Flexure-based mechanism; Piezoelectric actuator; Micro/nano manipulation; Robust motion control; Non-linearities; Parametric uncertainties 1. Introduction Flexure-based mechanisms and piezoelectric actuators have been recognised as the most appropriate platforms and actuation devices, respectively, for accomplishing high-precision motion tasks in the field of micro/nano manipulation [1]. These special mechanisms and actuators offer unlimited motion resolution. They also possess several advantages over the conventional mechanical systems, which are generally based on sliding or revolute lower pairs. These advantages include negligible friction, zero backlash, noiselessness, and easy maintenance. In recent years, there have been advances in piezoelectric actuator driven micro/nano manipulators [2–4]. For optimal mechanical performance, related studies of the micro/nano manipulator have been conducted [5–8]. Increasingly, pie- zoelectric actuator driven manipulation systems are employed in many advanced areas, particularly in the bio- medical engineering and micro-surgery applications [9–12]. At the same time, attention has also been directed towards to the development of piezoelectric actuators [1,13] to enhance their important role in the micro/nano manipula- tion mechanisms and systems. Generally, in the studies of the flexure-based mecha- nisms, the emphasis has been mostly confined to the mechanical design, kinematic modelling, and stiffness anal- ysis [3–8,14–18]. Little effort has been made to implement the motion tracking control for the mechanisms. In addi- tion to the effort focusing on the realisation and under- standing of the flexure-based mechanisms, there are other obstacles to the establishment of an effective control for 0957-4158/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechatronics.2007.09.002 * Corresponding author. Tel.: +61 3 9905 1008; fax: +61 3 9905 1825. E-mail addresses: hwee-choo.liaw@eng.monash.edu.au (H.C. Liaw), bijan.shirinzadeh@eng.monash.edu.au (B. Shirinzadeh), julian.smith@ med.monash.edu.au (J. Smith). Available online at www.sciencedirect.com Mechatronics 18 (2008) 111–120