Recent Trends in Mechatronics

Recent Trends in Mechatronics

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Recent Trends in Mechatronics

edited by

Nadine Le Fort-Piat & Alain Bourjault

London and Sterling, VA

First published in France in 2002 by Hermes Science Publications, Paris First published in Great Britain and the United States in 2003 by Kogan Page Science, an imprint of Kogan Page Limited Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licences issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned addresses: 120 Pentonville Road London N1 9JN UK www.koganpagescience.com

22883 Quicksilver Drive Sterling VA 20166-2012 USA

© Lavoisier, 2002 © Kogan Page Limited, 2003 The right of Nadine Le Fort-Piat and Alain Bourjault to be identified as the editors of this work has been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. ISBN 1 9039 9646 5

British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library.

Library of Congress Cataloging-in-Publication Data Recent trends in mechatronics / edited by Nadine Le Fort-Piat and Alain Bourjault. p. cm. ISBN 1-903996-46-5 1. Mechatronics. I. Fort-Piat, Nadine Le. II. Bourjault, Alain. TJ163.12.R48 2003 621--dc22

2003015994

Typeset by Kogan Page Printed and bound in Great Britain by Biddies Ltd, Guildford and King's Lynn www. biddles. co. uk

Contents Foreword Nadine Le Fort-Piat and Alain Bourjault 1. Trajectory Generation of Standing Movements using a Genetic Approach Lubo Song, Hideaki Shibata and Yoshitsugu Kamiya 2. Manipulation with the LMS Mechanical Hand: A Strategy for Fingertip Manipulation Tasks Jean-Pierre Gazeau, Saïd Zeghloul, Marc Arsicault and Jean-Paul Lallemand

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1

15

3. Omni-directional Obstacle Detection Masahiko Hiraki, Kazuhiro Enami, Kiyoshi Takamasu and Shigeo Ozono

31

4. Mobile Robot Localization using Reflective Marks on a Ceiling Hiroaki Seki, Takashi Yamashita, Yoshitsugu Kamiya, Masatoshi Hikizu and Hideshi Sakashita

45

5. Force Study Applied by a Planar Micromanipulator to Biological Objects Michael Gauthier and Emmanuel Piat 6. Delta3, a New Ultra-high Precision Micro-robot: Design and Control of a Flexure Mechanism Jean-Philippe Bacher, Stefano Bottinelli, Jean-Marc Breguet and Reymond Clavel 7. Prototypes of Thermal Actuated Microlegs: The Insect-like Micro-robot Agnès Bonvilain and Nicolas Chaillet

59

73

87

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8. A New Method for High Resolution Position Measurement at Long Range Christine Prelle, Frederic Lamarque and Pierre-Emmanuel Mazeran

105

Index

119

Foreword Mechatronics is a relatively recent word which was forged by the Japanese Yaskawa in 1971 but used in European scientific literature only since 1984. Today, it corresponds to the existence of a new field of scientific research and industrial development associating several subjects, in this case, mechanics and electronics, as shown by the name, but also optics, energetics, computer science, automatic control, etc. Mechatronics is the fundamental key in the recent progress of mechanical devices towards intelligent products which are becoming more and more present in everyday life. Japan and Asian countries have established significant progress in this area. Recently, France and European countries have made progress and obtained many practical applications. Miniaturization possibilities are available today thanks to the technology previously developed in micro-electronics which enables new implementation in various sectors like sensors, actuators, engine, machines, and robotics. Miniaturization enables the integration of a large number of functions in a smaller or at least in a constant volume and the batch manufacturing process leads at the same time to a cost reduction. Mechatronics products are today present in the industrial environment as well as in our daily life. Mechatronics is the way to lead to intelligent structure machines and micromachines. In all cases, intelligence is included in the products and in their uses. Currently, the mechatronics field is rapidly growing. It is introducing a lot of new technology such as new software technology, network-robotics, and network production systems. These new techniques also give perspectives in sectors such as chemistry and biology with molecules sorting and genomics. This kind of technology introduces us to the world with highly oriented and human-friendly systems. This technology is the key to open the door to the 21st century.

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This special issue of the European Journal of Automated Systems presents recent research results in the mechatronics field. The papers presented here are original papers written from communications selected by the scientific committee of the Third European-Asian Conference of Mecatronics '01. These original papers have been evaluated by the committee and cover different domains of applications in robotics and microrobotics.

Nadine Le Fort-Piat Alain Bourjault UMR-CNRSS Besançon, France

Chapter 1

Trajectory Generation of Standing Movements using a Genetic Approach Lubo Song Electrical and Computer Engineering Department, Cleveland State University, Ohio, USA

Hideaki Shibata and Yoshitsugu Kamiya Department of Mechanical Systems Engineering, Kanazawa University, Ishikawa, Japan

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1. Introduction With the development of medical science, life expectation of human beings have been greatly prolonged. However, a serious social problem is faced: more and more countries become nations of old people. The measures for meeting the needs of the aging society are necessary. For the aging or the disabled, there are lots of inconveniences in their daily lives. For example, the standing movement - one of their normal activities, may be dangerous for them because of the higher possibility of falling down. And the reports on such accidents are common(Nybergand Gustafson, 1995). Therefore, it is important to study the standing movements for the avoidance of such accidents. Although so far much research has been done (Roberts et al., 1996. Vander Linden et al, 1994, Shinkoda et al, 1999), there are still some questions remaining. But with the progress of robotics, more and more industrial robots have been used in our daily lives. The stance robot is one of them. For a stance robot, the most basic and important prerequisite is stability. On the basis of meeting this prerequisite, other operations can be taken into account. In this paper, the trajectory generation of a stance robot in various standing movements is studied. The aim of this study is to obtain a trajectory on which the robot can stand as easily as possible. Regarding trajectory generation research aimed at time-optimal planning (Yen and Liu, 1998; Constantinescu and Croft, 2000; Yamamoto and Mohri, 1989), is popular. N. Olgac and S. Zhou (1988) have tried to generate minimum-energy path only in oscillatory movements. In addition, due to the nonlinear problem and various strict physical constraints (Chiu and Ozaki, 1992; Wu and Young, 1994), optimal planning becomes more difficult. To deal with these difficulties, S.H. Suh and A.B. Bishop use the tube concept to generate collision-avoidance trajectories (Suh and Bishop, 1988), and curves such as Bezier-curves (Tsuchihashi, 1989) and S-curves (Red, 2000) are employed for trajectory generation. Recently, genetic algorithms (Chen and Salzala, 1997; Sun et al., 1996) have been introduced, too. In this article, a genetic approach is applied to generate trajectories of a stance robot in various standing movements. The planning strategy is energy-optimal under the constraints of no turnover and no violations of the joint limits and the torque limits.

2. Problem statement 2.1. Model of a stance robot A stance robot, the object of this study, is simplified as in the model shown in Figure 1. It consists of three joints: joint 1 (ankle), joint2 (knee) and joint3 (hip). According to the model in Figure 1, by using Newton-Euler formulation the kinematic equations of the robot are obtained and listed in the appendix.

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Figure 1. The model of a stance robot

2.2. Problem formulation The standing movement is considered as a process from a given initial posture to an erect posture. The trajectory is expressed as:

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2.2.1. Known conditions If te is supposed to be the motion time of the standing movement, according to the initial and end situations of the robot, the equations below for known conditions can be obtained:

However, te is unknown. 2.2.2. Three constraints Any feasible trajectory must satisfy each of the following constraints. 1. No turnover Due to the fact that when either the heel reaction force (RA) or the tiptoe reaction force (RB) is smaller than zero the robot turns over, the equation for the condition of no turnover can be written as:

where

2. No violation of the joint limits If the joint limits are defined as:

The equation of meeting no violation of the joint limits can be written as:

where

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and HJi (t) is the joint rate and is defined as:

3. No violation of the torque limits If the torque limits are defined as:

The equation of meeting no violation of the torque limits can be written as:

where

and H Ti (t) is the torque rate and is defined as:

2.2.3. Expression of energy Because of the inconvenience involved in direct calculation of the energy, the function below for energy estimation is employed.

According to the equations above, the problem can be stated as: based on equations [2] and [3], determine equation [1] to minimize equation [14] under the condition that equations [4], [7] and [11] are satisfied.

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3. Genetic approach 3.1. Introduction of genetic approach Because of the complexity of the inverse kinematic problem, it is very difficult to get analytical solutions to the problem stated before. So the genetic approach is introduced. First, three nth order polynomials of time t, each of which serves for a joint respectively, are employed to express the trajectory, with their parameters undecided. Then a genetic algorithm is used to optimize the undecided parameters and the time te. In the genetic algorithm, each chromosome indicates an undecided factor and is expressed by several-bit binary numbers. By the way, the higher the order of the polynomial, the better the result is. But it is at the expense of more computation time. In this study, the 7th order polynomial is used.

3.2. Genetic algorithm A simple genetic algorithm for determining the undecided factor consists of several parts listed as follows: 1. Creation of the initial generation. The initial generation has N members, each of which indicates a trajectory. In this procedure, the N members are created with the generation of their chromosomes by getting random numbers. 2. Reproduction. This procedure is applied to select members for the next generation. First, the fitness values of all the members are estimated by a fitness function. Then the members are put in a descending order according to their fitness values. The larger fitness value a member has, the better trajectory it indicates. Finally the members are reproduced to the next generation. The reproduction criterion is: the most a member is in the order, the more it is reproduced. The reproduction procedure starts at the beginning of the order, and does not stop until the next generation has N members. 3. Crossover. The newly reproduced members in the last procedure are paired at random. For each pair of the selected members, a probability of pc is used to determine whether the crossover will be applied to them or not. If positive, a cross site (a bit position) along the chromosomes of the two members is selected at random, and two new chromosomes are created by swapping the cross site. 4. Mutation. This procedure changes the character in an individual binary chromosome on a bit-by-bit basis, with a very small probability pm . For the chromosome of each member, starting from the first bit, pm is applied to determine whether a bit mutates or not. If this is so, this bit flips (changes from 0 to 1 or from 1

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7

5. End conditions. If the number of generations is larger than a preset limit G, the algorithm stops, or otherwise, goes back to 2.

Figure 2. Flowchart for determining priority

3.3. Fitness function Fitness function is very important in the GA algorithm because it controls the optimizing direction of the generation. In many studies, to operate simply and conveniently, the fitness values produced by the fitness function are expressed in the form of actual numbers. In this study, however, it is not appropriate to do so because there are three different constraints and it is difficult to evaluate their importance in actual numbers simultaneously. In fact, fitness values are mainly used to decide which member has the priority to be reproduced into the next generation. In other

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words, for any two members if we can determine which one is prior to the other the problem is resolved. So a rule for determining the priority of two members p and q is defined as: If p meets the three constraints before q, p is prior to q, otherwise q is prior to p. If both p and q meet all the constraints, the one that has the smaller energy estimation is prior. The detailed regulations are shown in Figure 2.

4. Simulation results According to the model and the genetic approach introduced before, various standing movements are studied. The simulation results are shown from Figure 3 to Figure 6. Some configurations for the simulations are listed in the following: The joint limits:

The torque limits:

The crossover probability:

p c =0.7

The mutation probability:

pm = 0.01

The number of generations: G = 500 The number of members:

N = 500

4.1. Normal sit-to-stand movement Figure 3 shows the normal sit-to-stand movement. te is the time of the whole standing movement, and tm is the time of sitting on the chair. The shaded lines before tm indicate the results on the assumption of no chair. To meet the condition of no turnover, the robot only bends its upper body forward while in the chair. After tm , the robot leaves from the chair and begins to stand up.

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9

Figure 3. Normal sit-to-stand movement

4.2. Sit-to-stand movement with knee disability Figure 4 shows the sit-to-stand movement with knee disability. Compared with Figure 3, it indicates that, for a man with knee disability, to stand without no turnover he must put his upper body more forward before leaving from the chair, and as soon as he leaves the chair, his knee almost works with its minus maximum torque for a period to ensure the success of the standing movement. Furthermore, the reaction forces fluctuate more frequently than those in Figure 3. That suggests a higher possibility of turnover.

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Figure 4. Sit-to-stand movement with knee disability

4.3. Sit-to-stand movement with foot being put forward Figure 5 shows the sit-to-stand movement with the initial posture in which the foot is put forward. In this case, the robot bends its upper body more forward too, and leaves the chair as soon as the reaction forces are not smaller than zero. In other words, it takes full advantage of the inertia to stand successfully. In addition, since the robot rises from the chair, the ankle joint has worked with its full load for a period. That means that when the foot is put forward, to finish the sit-to-stand movement successfully, the load acting on the ankle joint increases.

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11

Figure 5. Sit-to-stand movement with foot being put forward

4.4. Normal squat-to-stand movement Figure 6 shows the normal squat-to-stand movement. According to the comparison with the normal sit-to-stand movement, the squat-to-stand movement mainly depends on the ankle and the knee joints, while the sit-to-stand movement depends on the knee and the hip joints.

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Figure 6. Normal squat-to-stand movement

5. Conclusions In this paper, a genetic approach to trajectory generation has been proposed. Based on the approach, various standing movements are studied. The simulation results demonstrate the following conclusions: - the genetic approach is feasible and efficient in trajectory generation; - for a knee-disability, the disabled person can stand up successfully by putting his upper body more forward than a healthy person to reduce his knee's burden. However, he must carefully deal with the potentially greater possibility of turnover; - although it is not easy to satisfy the stable conditions when the foot is put forward in the initial posture, the inertia can be used to assist the standing

Trajectory Generation of Standing Movements

13

movement; - despite the different conditions such as different initial postures, different torque limits, etc., the burden can be distributed to the joints as rationally as possible to ensure the success of the standing movements.

6. References Chen M.W. and Zalzala A.M.S., "A Genetic Approach to Motion Planning of Redundant Mobile Manipulator Systems Considering Safety and Configuration", Journal of Robotic Systems, 14(7), pp. 529-544, 1997. Chiu H. and Ozaki H., A New Solution on Trajectory Planning Problem of A Manipulator with Some Constraints, Bulletin of the Faculty of engineering Kyushu Industry Institute, 29, pp. 21-26, 1992 (in Japanese). Constantinescu D. and Croft E.A., "Smooth and Time-Optimal Trajectory Planning for Industrial Manipulators along Specified Paths", Journal of Robotic Systems, 17(5), pp. 233-249, 2000. Nyberg L., and Gustafson Y., "Patient Falls in Stroke Rehabilitation - A Challenge to Rehabilitation Strategy", Stroke, 26(5), pp. 838-842, 1995. Olgac N. and Zhou S., "Minimum Energy Paths for Optimal Oscillatory Movements of PUMA Arm", Journal of Robotic Systems, 5(4), pp. 389-407, 1988. Red E., "A Dynamic Optimal Trajectory Generator for Cartesian Path Following", Robotica, 18, pp. 451-458, 2000. Roberts P.D. and McCollum G., "Dynamics of the Sit-to-Stand Movement", Biol. Cybern, 74(2), pp. 147-157, 1996. Shinkoda K., Tanaka M., Ikeuchi H., Katoh R. and Yamashita T., "Analysis by Phase Planes of the Sit-to-Stand Movement from A Chair", Transactions of the Japan Society of Mechanical Engineers (Series C), 65(634), pp. 2436-2442, 1999 (in Japanese). Suh S. and Bishop A.B., "Collision-Avoidance Trajectory Planning Using Tube Concept: Analysis and Simulation", Journal of Robotic Systems, 5(6), pp. 497-525, 1988. Sun S., Morris A.S. and Zalzala A.M.S., Trajectory Planning of Multiple Coordinating Robots Using Genetic Algorithms, Robotica, 14, pp. 227-234, 1996 Tsuchihashi T., "Trajectory Generation and Control for Manipulator Using the Bezier Curve", Transactions of the Japan Society of Mechanical Engineers (Series C), 55(509), pp. 124128, 1989 (in Japanese). Vander Linden D.W., Brunt D. and McCulloch M.U., "Variant and Invariant Characteristics of the Sit-to-Stand Task in Healthy Elderly Adults", Aech. Phys. Med. Rehabil, 75(6), pp. 653-660, 1994. Wu T.H. and Young K.Y., Path Planning in the Presence of Obstacles Based on Task Requirements, Journal of Robotic Systems, 11 (8), pp. 703-716, 1994. Yen C.W.V. and Liu T.Z., "Path Constrained Time-Optimal Trajectory Planning for X-Y

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Recent Trends in Mechatronics Robots via An Efficient Dynamic Programming Method", Robotica, 16, pp. 89-96, 1998.

Yamamoto M. and Mohri A., "Planning of Quasi-Minimum Time Trajectories for Robot Manipulators" (Generation of A Bang-Bang Control), Robotica, 7, pp. 43-47, 1989.

Appendix

where

Chapter 2

Manipulation with the LMS Mechanical Hand: A Strategy for Fingertip Manipulation Tasks Jean-Pierre Gazeau, Saïd Zeghloul, Marc Arsicault and Jean-Paul Lallemand Laboratoire de Mécanique des Solides, Université de Poitiers, France

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1. Introduction The capabilities of human beings in the realization of tasks are very large. At present, robots substitute themselves to advantage for man within the framework of industrial tasks and painful or dangerous works. They are able to succeed in hostile circumstances such as nuclear, space or submarine environments. However, these relatively different tasks each require a specific grasping tool, which must be adapted to each task as well as to the objects to be manipulated. This objective of realizing a flexible tool endowed with capabilities similar to the human hand led to the study and to the development of polyarticulated mechanical hands looking more or less anthropomorphic worldwide. Jacobsen's hand (Jacobsen et al., 1986) demonstrated the potentialities of an anthropomorphic design, which opened the way to the other conceptions among which we shall be able to quote as example a hand with four fingers: the hand of the DLR (Deutsches Zentrum fur Luft und Raumfahrt) (Liu et al, 1999) or hands with three fingers of an innovative design: the IRMS laboratory hand (1992) or the Karlsruhe (Fischer and Woern, 1998) hand. The works of the Laboratoire de Mécanique des Solides (LMS) mesh with the framework of these developments. Studies related to the theory of grasping and development of specialized grasping effectors within the laboratory led naturally the LMS to build, in 1996, a polyarticulated mechanical hand with four fingers and sixteen degrees of freedom. The conception of this hand based on an anthropomorphic design was directed to a specific application: the manipulation of objects with the fingertips. In our work, except for the study and the realization of an articulated mechanical hand with four fingers, we developed and used original methods to drive the 16 degrees of freedom of the hand with the aim of fine manipulation of objects. Two types of controls were realized: a position control of fingers and a force control. Once the force and position controls were validated, we developed a manipulation strategy in order to integrate them. Consequently, we integrated into the CAD software named SMAR (system of modelling and animation of robots) developed in the LMS, a new module dedicated to the planning of manipulation tasks with a mechanical hand. This new module enabled us to validate our geometrical approach to carry out a manipulation task. In this paper, we present the strategy developed for the realization of fine manipulation tasks. This strategy is illustrated with results from simulation. We present classical manipulation tasks using SMAR software, which allows modeling and animation of robotized systems, but also coupling between simulation and experimental site. Experimental results are thus developed and the extensions to this work discussed.

Manipulation with the LMS Mechanical Hand

17

2. The LMS hand realisation 2.1. Design The potential of the human hand in dextrous manipulation motivated this study and this respect for the anthropomorphic aspect. The hand realized at the LMS (Gazeau, 200) is a mechanical hand with four fingers (the index, the major and the ring finger and a thumb in opposition) (cf. Figure la). Each finger possesses four degrees of freedom (cf. Figure 1b). Three of the four degrees of freedom authorize the flexion-extension movement of the finger and the fourth allows the realization of the abduction-adduction movement. The implanting of fingers, their dimension and their clearance are similar in those of the human hand. The choice of four fingers rather than three justifies itself in the fact that to reposition the object in the hand during manipulation, a fourth finger is necessary if we want to retain grasp stability. The location of the thumb and its orientation with regard to the palm are very important in the conception of the hand. The reproduction of the various postures of the human hand depends partially on the choice of these two factors.

Figure 1. a) The LMS hand, b) Kinematics

So for the thumb the amplitude of the abduction-adduction movement is much more important (60°), in order to be able to oppose the other fingers. For these, the axis of the abduction-adduction movement is fixed compared to the proximal

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phalanx, which makes it possible to preserve the amplitude of this movement (± 15°), whatever the configuration of the hand. The sixteen joints are animated, each one by a DC actuator located in the forearm. The transmission between the sixteen actuators and the sixteen joints of the hand is ensured by high resistance polyethylene cables. Looking at the instrumentation, incremental encoders placed on the DC motor shafts allow us to control actuators displacement. And we obtain the articular parameters with absolute encoders integrated into joints. We evaluate thereafter, using both set of information, the grasping forces applied by the fingers to a grasped object. This evaluation is based on neural networks (Gazeau et al., 2001).

2.2. Control architecture The control system implemented in the VME environment is monitored by the multitasking real-time operating system OS/9. The actuators' motion is controlled using four axis boards with the motion processor LM628 (Gazeau et al., 1998). Each board is dedicated to one finger (four axes).

3. Control strategy We shall now consider the strategy which will allow, by integration of the individual controls of every finger, evolution towards our objective which is the manipulation of objects with fingertips. Two principal aspects are to be considered when we want to manipulate objects: the planning of a manipulation task on one hand and stability analysis on the other.

3.1. Geometrical and kinematical modelisation The fingers of the LMS hand have 4 degrees of freedom. The thumb is characterized by a different kinematics. We used the modified Denavit-Hartenberg model (Khalil and Kleinfinger, 1986) to establish the geometrical model of the fingers. Figures 2 and 3 present the geometrical model for each of the kinematics.

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Figure 2. Fingers model: index, major and ring finger

The simulation of an unspecified manipulation task requires one to be able to move a point of the fingertip in its workspace. For that we need to invert the geometrical model.

Figure 3. Thumb model

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In order to solve the redundancy of our system, we introduced synchronized variables. Indeed, a human finger has the property in which it is impossible to move the last articulation (q4) without moving the preceding one (q3) and vice versa. This dependence between the articulations is explained by the routing of the tendons in the fingers. After several measurements on different human subjects, it was established finally that (Rijpkema and Girard, 1991): q4 = 2/3. q3 for index, major and ring finger q4 = 7/5. q3 for the thumb The solution of the geometrical model reverse is then q = (q1, q2, q3, 7/5.q3) for the thumb and q = (q1, q2, q3, 2/3.q3) for the other fingers.

3.2. Motion strategy In our analysis relating to the manipulation of objects, the dominating aspect is the geometrical component. Thus the strategy of movement developed is based on geometrical reasoning using information of force and position for the co-ordination of the manipulative actions. The definition of a manipulation task is: Definition We define a manipulation task by the object trajectory Pd(t) ε R6 such that:

where r ε R3 is the gravity center of the grasped object referred to Cartesian space, Φ ε R3 is a vector whose components are the pitch, yaw and roll angles and t the time parameter. In addition we can decompose the trajectory of the object into a succession of small displacements:

Where T 0,f is the homogeneous transformation which makes it possible to transport the object from its initial configuration to its final configuration. The problem is then to determine, for each small transformation T i-l,i, the movements of the fingertips, which ensure this displacement while respecting the kinematical limits of the hand, but also the grasp stability which will be described further. The displacement of the fingertip for each small transformation T i-l,i is dictated by three modes of contact between object and finger: - fixed point mode; - rolling without sliding mode; - sliding mode.

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21

Among these three modes we eliminate the sliding mode as we cannot control the object's sliding with the instrumentation. When the fixed point mode or the rolling without sliding mode are impossible, we can only reposition the finger on the object by using the fourth finger. We thus will build our geometrical reasoning by considering these last modes of displacement. We formulate the following assumptions: - The manipulated objects are indeformable; - We consider manipulation with fingertips; - The fingertip is hemispherical; - The shape of the object, its dimensions and its mass are known. The planning of a manipulation task is based on the geometry of the contact, between the grasped object and the fingers. The manipulated objects are modelled as polygonal objects with several faces. We assume for the contact geometry the contact of half a sphere with a plane (cf. Figure 4). The normal vector n to the object face in contact is known insofar as we know at every moment the desired displacement of the object. The direct geometrical model allows, from knowledge of the measured joint parameters, to establish the coordinates of the fingertip center E. The coordinates of the point of contact P relative to the object frame are directly established by the following relation, dependent on the geometry of the contact:

where R indicates the radius of half the sphere representing the fingertip and n is the external normal vector to the facet in contact.

Figure 4. Modeling of the object-finger contact

The initial grasp of the object in the hand is known. The initial finger contact points on the object are defined in the object frame Rob. Starting from this initial grasp, the objective is then to compute the evolution of the joint parameters for each finger in order to carry out the desired displacement of the object. The general

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strategy used for the planning of a manipulation task can thus be summarized by these stages: 01 Initial grasp choice

02 (Definitionof contact points Pi between object & finger) 03 Decomposition of the trajectory of the object in N 04 small displacements dyi, dW2, dW3, du,,dYG, dZ6 05 FOR i = l TO N 06 (We consider the small displacement N o i of the object)) 07 Update rotation of the object: 08 ~ i Wi = + dWi WZ= ~2 + dW2 W3= W3 + dW3 09 Update translation of the object: I0 & = x c + d x c YG=YG+dYG z c = z G i d z G I 1 Compute small joint displacements dq, 12 IF Solution is OK 13

THEN

14 Update joint parameters q=q+dq 15 ELSE 16 Solution out of range: I7 Repositioning of the fingers on the object 18 Computation of the new point of contact P 19 END

We notice that the angles yl, y2, y3 that are used to parameterize the displacement of the object use the Cardan notation. When the solution is out of range in the algorithm, it is necessary to reposition the object in the hand, in order to be able to continue the manipulation task. So we must use the fourth finger in order to not compromise the grasp stability, and to judiciously reposition the fingers on the object. The displacement of the fingers relatively to the object is described by the fact that it rolls without slipping on the object surface. Therefore we have to compute the small articular variations dqi for each finger (line 11 in the algorithm above) and the new localization of the points of contact after the small object displacement (line 18 in the algorithm above). The reasoning being identical for each finger, we will establish it for a finger and a facet of the object in contact. The fact that the fingers roll without slipping on the surface of the grasped object leads to the following relation: We write for the small displacements model:

With the kinematic model, we can express the velocity of the point E, that is the center of the fingertip, according to the articular finger velocities q,, j = 1...3, as well as the rotation vector of the fingertip relatively to the finger frame Rd as:

Manipulation with the LMS Mechanical Hand

With dP

object

23

as:

Where: dθ = [dθx, dθy, dθz]T

the vector of rotation parameters from the object relative to the finger frame Rd;

dx = [dxG, dyG, dzG]T

the vector of translation parameters from the point G (object center of gravity) relative to the finger frame Rd;

PG = [XPG, yPG ZPG]T

the vector PG relative to the finger frame Rd.

The PGd components of vector PG in Rd frame result easily from the following vectorial relation: PG = PE + EG = R.n + EG

where R is the fingertip radius, n the normal vector to the object face in contact, E the fingertip center computed using the direct geometrical model and G the object's center of gravity. As the object trajectory is known, the problem is then to solve the linear system (3) with 3 equations with 3 unknown factors dqij (j = 1...3). We thus establish the variation of the articular parameters dq of the finger for the small displacement of the desired object. The data necessary for the establishment of this result are the initial articular parameters qj (j = 1...3) and the six components characterizing the small displacement of the object made up of three translations (dXG,dYG,dZG) and three rotations (dψ1,dψ2,dψ3). We can then compute the coordinates from the new point of contact P' in the finger frame (cf. Figure 5) after the small object displacement. The finger joint parameters after the small displacement of the object are computed using the relation:

qj = qj + dqj (j=0..2) We can then directly establish the new coordinates of the fingertip center E which becomes E' when we use the direct geometrical model with these joint parameters. As the new normal n' to the object face in contact is known, it is easy to compute the new contact point Pi' using:

P'iE' = R.n'

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Figure 5. Evolution of the point of contact for a small object displacement

3.3. CAD simulation of a manipulation task In order to validate the control algorithms of the LMS mechanical hand, we developed a graphic application in three dimensions for the simulation of the manipulation tasks. This application (cf. Figure 6) is based on the development of the robotic CAD software from the LMS: SMAR (Zeghloul et al, 1997). The development is carried out by using the following graphic libraries for windows environment: TGS Open Inventor by Template Graphics Software.

Figure 6. A graphical simulation software for the LMS hand

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With the software tool SMAR, it's possible to model and to animate serial robots; thus for the modeling of the hand, we make the assumption that the hand consists of 4 serial robots (the 4 fingers) that cooperate within the framework of a common objective: the realization of a manipulation task with the fingertips. The graphical software interface for the mechanical hand allows the coupling in real time with the experimental site for experiments, relative to virtual reality. In order to validate the manipulation strategy of section 5.3, we integrated this one in the graphical CAD software and we chose classical manipulation tasks like basic rotations and translations from the object around its axis. The object considered is a prism. The first example in Figure 7 presents a translation of the object along the vertical axis.

Figure 7. A 30 mm vertical axis translation of a prism

The second example presents a coupled translation and rotation of a prism along the vertical axis (cf. Figure 8).

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Figure 8. Coupled translation and rotation of a prism along the vertical axis: 20mm and 50°

3.4. Grasp stability When we manipulate an object, each finger used in the manipulation task must apply a force in order to apply to the object the global external force Fe, necessary to ensure its stability. The objective is thus to avoid any slip and any contact break. In order to compute the forces necessary to retain stability during a manipulation task, we chose to implement the method developed by Youg C. Park in (Park and Starr, 1990). These algorithms compute the internal forces that ensure the global stability of the grasped object. A major advantage of this method is the low computing time; so it is well adapted to the real time control. In this approach each contact point between finger and object is a contact point with friction. The method developed supposes that the fingers do not slip on the object.

4. Realization of a manipulation task 4.1. General control strategy The global control scheme for the control of the LMS hand is detailed in Figure 9. After the off line task planning with CAD simulation software, the manipulation task is executed and each finger is controlled individually using the force and/or position control.

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Figure 9. Global control scheme

4.2. Some practical examples In Figure 10, we can observe characteristic configurations of the hand. In these configurations, the thumb oppose the other fingers by changing its configuration of the abduction-adduction movement.

Figure 10. Some characteristic configurations

The simplest example of grasp is that of the two finger grasp, between thumb and index finger. The photographs of Figure 11 show two other typical grasp examples, a power grasp (Figure 11 a) and grasps with fingertips (Figures 11b and 11c). Figure 12 presents some snapshots, extracted from the videos of the first manipulation tests carried out with the hand of the LMS. In these pictures, we see the LMS hand rotating a prism with three fingers.

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Figure 11. Grasp examples: a) Power grasp, b) Fingertip grasp with 3 fingers, c) Fingertip grasp with 2 fingers

To carry out these manipulation tasks, the object is placed in the hand by the operator so that the initial grasp can be made. When the object is grasped, the manipulation starts. The control system cannot currently be sure that the object position in the hand is correct. There is no vision system to control this. So there can be a difference between the real contact points on the object, and those used to compute the joint parameters in the manipulation task planning. So we need to use two video cameras with the hand control system. With this vision system, we shall be able to control in real time the realization of the manipulation task. We will compare the real object position in the hand to the computed objects position and orientation, and make appropriate corrections.

Figure 12. Rotation of a prism using three fingers

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5. Conclusion and future work The geometrical solution used for the planning of manipulation tasks with a mechanical hand led to the validation of the first manipulation tests with the hand of the LMS. We want now to consider more complex manipulation tasks with various objects. So there is another way of research with complex manipulation tasks - it is the problem of object repositioning during a manipulation task. In this way, we started the development of an expert system which will have to provide a solution to the initial grasp of the object. According to the manipulation task, the expert system defines which fingers will be used, what the finger's localization on the object will be and what must be the initial position and the orientation of the object in the hand. In order to continue research on manipulation with the mechanical hand, we plan now to equip the site with a vision system to follow in real time the evolution of the position and orientation of the object in the hand frame. The hand control system must indeed readjust the finger displacements on the object trajectory, to be sure of the precise control of the manipulation task execution. The experimental site upgrade with video cameras is necessary if we want to carry out more complex manipulation tasks. We will be able to then establish a strong coupling between the robotic simulation software and the experimental site for applications related to virtual reality.

6. Bibliography "A New Design for a Dextrous Robotic Hand Mechanism", IEEE Control Systems Magazine, Vol. 12, August 1992, pp. 35-38. Fischer TH., Woern H., "Structure of a robot system: Karlsruhe Dextrous Hand II", Mediterranean Conference on Control and Systems, 1998. Gazeau J.P., Développement de la commande d'une main mécanique à 4 doigts et 16 degrés de mobilité, Ph.D Thesis, Poitiers University, 2000. Gazeau J.P., Zeghloul S., Arsicault M., Lallemand J.P., "The L.M.S. Hand: force and position controls in the aim of the fine manipulation of objects", IEEE ICRA 2001, 21-26 May 2001, Seoul, Korea. Gazeau J.P., Arsicault M., Lallemand J.P., "The L.M.S. Mechanical Hand: Design and Control", RoManSy '98 - Robots Manipulators Systems, 1998, Paris. Jacobsen S.C., Iversen E.K., Knutti D.F., Johnson R.T., Diggers E.K., "Design of the UTAH/MIT dextrous hand", IEEE International Conference on Robotics and Automation, pp. 1520-1532, San Francisco, USA, 1986. Khalil W., Kleinfinger J.F., "A new geometric notation for open and closed loop robots", Proceedings of the 1986 IEEE int. Conf. On Robotics And Automation, pp. 1174-1180, 1986. Liu H., Butterfass J., Knoch S., Meusel P., "A New Control Strategy for DLR's Multisensory Articulated Hand", Control Systems, Vol. 2, 1999, pp. 47-54. Park Y.C., Starr G.P., "Efficient fingertip force computation for object manipulation using dexterous robot hand", Computers & Elect. Engng, Vol. 16, No. 1, 1990, pp. 23-34.

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Rijpkema H., Girard M., Computer animation of knowledge-based human grasping, Computer Graphics, Vol. 25, No. 4, July 1991. Zeghloul S., Blanchard B., Ayrault M., SMAR: A Robot Modeling and Simulation System", Robotica Journal, Vol.15, February 1997, pp. 63-73.

Chapter 3

Omni-directional Obstacle Detection Masahiko Hiraki Institute of Material Structure Science, High Energy Accelerator Research Organization, Ibaraki, Japan

Kazuhiro Enami and Kiyoshi Takamasu Department of Precision Engineering, University of Tokyo, Japan

Shigeo Ozono Department of Precision Machinery Engineering, Tokyo Denki University, Japan

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1. Introduction For the purposes of baggage handling, guarding work or robotic items like mice, there is much published research about mobile robots, especially for indoor use. Mobile robots are mainly put into two categories: nonholonomic mobile robots and holonomic mobile robots. Nonholonomic mobile robots cannot move in all directions. The most famous nonholonomic vehicles are cars that have steering wheels and driving wheels. It is considered that the nonholonomic vehicles can only move ahead or sometimes backward in a very short time. But they are used frequently to carry loads in factories, because of simple structure and low cost. It is necessary for nonholonomic vehicles to detect obstacles, mainly in front. Usually, a CCD camera, an ultrasonic sensor or laser range finder is used (Shin et al, 1996). On the other hand, holonomic mobile robots can move in all directions and sometimes they are called omni-directional robots (Yoshikazu et al, 1996). The omni-directional robots are used indoors, because they can move in all directions and in a narrow space without turning. So it is necessary for omni-directional mobile robots to detect obstacles around them. For omni-directional robots, the obstacle detection systems are various, for example, image processing using CCD cameras, ultrasonic wave sensors systems, and so on (Yasushi, 1995; Jun et al., 2000). However, it is very difficult to recognize obstacles in images from CCD cameras and angle resolution is low when using ultrasonic sensors. A triangulation, using laser slit and CCD camera, is used for obstacle detection because three dimensional shapes of objects can be measured easily (Shin et al, 1996) (Ryoshu et al., 1997). In this research, we develop the novel obstacle detection system using the ring beam system (RBS) that can project laser slit in all directions.

2. Principles of obstacle detection Figure 1 shows principles of detecting obstacles using triangulation. A laser unit projects a laser beam to obstacles and a laser spot or slit on the obstacles can be detected by a CCD camera. We can calculate an angle ψ using an image from the CCD camera and obtain a distance x between the laser unit and obstacle using the following equation:

where h is a height of CCD camera from laser unit shown in Figure 1; it is necessary to calibrate the height h before measurement: generally, we have to calibrate a relative position and relative orientation between laser and CCD camera before measurement.

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Figure 1. Principle of triangulation

Kato and Tsugawa (Shin et al., 1996) researched detection of obstacles by slitray projection. In their research, they used a general projector for slides and the slit ray is projected only ahead of a robot. However, for omni-directional mobile robots, it is necessary to project the laser slit ray in all directions and to detect the laser spots on obstacles around the robots. So, we use the ring beam system developed by Kawaguchi (Yuzou et al., 1997) (Kenichi et al., 1996) and a cone mirror. In order to detect the laser spots on obstacles, we use a CCD camera and a spherical mirror. Figure 2 shows a scheme of the proposed obstacle detecting system. The ring beam projected from RES reflects at the cone mirror and the bright line on the obstacles is detected by the CCD camera via the spherical mirror. The characteristics of the system developed are as follows: there is no moving part in this system and it can detect all obstacles around this system simultaneously.

Figure 2. Scheme of proposed system

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3. Calculating distance using geometric model The experimental system is shown in Figures 3 and 4.

Figure 3. Obstacle detecting system

Figure 4. Specifications of experimental system

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The experimental device consists of a spherical mirror, a CCD camera and a RBS united with a cone mirror, and each component is fixed on an acrylic board. An example of the image is shown in Figure 5. This image is obtained while this experimental system is put on a desk in our laboratory.

Figure 5. Example of picture obtained

Figure 6 shows the geometric model of our experimental system. The centre of spherical mirror whose radius is r is regarded as an origin and coordinates are decided as in the figure. Moreover, it is assumed that the CCD camera and the RBS are distances l and d away from the origin, respectively. Here, we can obtain a relationship between a view angle θ and a distance*to the obstacles, as in the following equations:

The view angle 9 is calculated as follows. The tangent of the view angle ( tan θ ) is proportional to a distance between a centre of image and a bright point, theoretically. However, because a pinhole lens is used instead of a normal lens to reduce cost, the tangent of the view angle is not proportional to the distance. So we need to find the relationship experimentally. Using this relationship found in

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advance, we can calculate the view angle 6 and translate to the distance x by equations [2]-[4].

Figure 6. Geometric model of obstacle detection system

4. Basic experiment In this experiment, we measure inside a box with sides 300mm long as an obstacle. The colour of the box is white and the system developed is fixed on a centre of the bottom of the box. It is difficult to separate bright points on the obstacles from a background. So, in this experiment, we obtain two images: one is an image in the case of applying a laser slit by RBS and another is in case of no laser beam. Next, we calculate differences of these two pictures to detect the bright line on obstacles. In this way, because we cannot take two images simultaneously, the mobile robots need to stop while taking images. This point is a drawback to the obstacle detection system developed to us, so we need to propose another way to detect the bright points. Figure 7 shows the image in the case of applying a laser slit by RBS. The outside of the spherical mirror and the central area that is an acrylic plate with the CCD camera are omitted. In this image, we can see bright points on the white walls and four poles at the corners of experimental system. Next, we calculate the differences between this image and another image that is in case of no laser slit. After that, we translate the image obtained that has gray scale to a black and white image and reduce noise in this image. Figure 8 shows the result of processing the image.

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Figure 7. Image of inside of a box in case of applying a laser slit by RBS

Figure 8. Detecting result of bright line

Finally, we calculate angle θ for each bright point in Figure 8 and calculate the distance x to the obstacles using equations [2]-[4]. Figure 9 shows a measuring result of inside of the box. In this figure, solid lines give the positions of the real obstacles and small circles give the positions of detected obstacles. This result

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shows the possibility of detecting obstacles using our system. However, a maximum measuring error was 15.4mm in this experiment.

Figure 9. Measuring result of inside of box. Solid lines are the positions of the real obstacles and small circles are the result of the experiment

5. Consideration of geometrical errors We think that factors of this error are parametric errors, for example, the length between the CCD camera and the spherical mirror. Therefore, we built a new geometrical model with geometrical errors in Figure 10. As in Figure 6, the centre of spherical mirror whose radius is r is regarded as an origin and coordinates are decided as in the figure.

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Figure 10. New geometrical model with geometrical errors

Moreover, it is assumed that the CCD camera and the RBS are a distance / and d away from the origin, respectively. As geometrical errors, we introduce a position error of CCD camera e, an orientation error of CCD camera ψc and an orientation error of RBS ψr . The position errors and the orientation errors are 3 degrees of freedom. However, it seems that the position errors along z-axis are included in distances l and d . Position errors x and y of the RBS can be ignored, because the slit ray from the RBS extends horizontally and it can be considered that the centre of the RBS is fixed on z-axis. Here, we use the easier 2 DOF model shown in Figure 10, because the result of measuring inside of the box is almost symmetrical with respect to the y-axis in Figure 9. A relationship between a distance x to the obstacles and a view angle θ is calculated by following equations:

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6. Analysis of errors Each geometrical parameter has an influence on the results of measurement. Using equations [5]-[7], differentials between distance x and geometrical parameters are as follows:

Here, each value of differential represents an error in detecting distance for a small variation of the geometrical parameter. If an absolute value of this differential is large, it means that the error of this parameter has a large influence on the measured distance. We can see that the influence of positional error of the CCD camera e is biggest. With respect to orientation errors, the following equations show the differentials.

These differentials cannot be compared with the position errors shown by equation [8] directly, because a unit of equation [8] is different from a unit of equation [9]. However, we can conclude that an influence of orientation error of CCD camera ψc is bigger than an influence of orientation error of RBS ψr .

7. Parameter identification and experiment in real environment We identify the parameter e that is the position error of CCD camera. In fact, it is necessary to consider an error in x-axis ex and in y-axis ey for position errors of the CCD camera. However, the measurement result of the inside of the box in Figure 9 is almost symmetrical with respect to y-axis. Therefore, we identified only the parameter ey. Figure 11 shows a result of the measuring experiment after the identification of the parameter. Here, the parameter ey is 0.14mm. This figure shows a reduction of position errors compared with the result before identification.

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Figure 11. Measuring result of inside of box after parameter identification: Solid lines are the positions of the real obstacles and small circles are the result of the experiment

Using the above modified geometrical model, we carried out an experiment of detecting obstacles in a real environment. We selected a passageway in front of our laboratory for the measuring environment, because the proposed sensing system was loaded on mobile robots for indoor use. The experiment is carried out under fluorescent lights in order to fit the environment of experiment to a real environment. The measuring environment is shown in Figure 12. In this figure, the laser slit from RBS can be seen on a wall and a door. Figure 13 shows a result of an experiment of detecting obstacles. The developed measuring system is put at a position (0,0). In order to check the result of this experiment, we measured at a passageway using a scale, which is one meter long. The four detected points around it are results of detecting the four poles included in the measuring system. The points on the right side of the origin are results of detecting a table that a computer system is put on. The result of this experiment shows the possibility of detecting obstacles under the real environment using our developed system.

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Figure 12. Measured environment: a passageway in front of our laboratory

Figure 13. Result of detecting obstacles: The origin is the centre of experimental system. Solid lines are the positions of the real obstacles and small circles are the result of the experiment

Considering now the resolution of this obstacle detecting system, in this system, the resolution of measuring the distance to the obstacles is decided by a resolution of CCD camera. The resolution of the distance is calculated by following equation.

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where Ax is the resolution of the distance and Ad is the resolution of the view angle. The difference dx / dθ can be calculated using equations [5]-[7]. The resolution of view angle Δθ is obtained from following relationship.

p is a distance between a pixel on detected image and a centre of image and k is a coefficient in order to translate the view angle to the distance p. The resolution of the view angle Ad can be calculated using equation [11] as follows:

Δp is a resolution of CCD camera. Using equations [5]-[7], [10]-[12], we can calculate the resolution Ax for the distance x. The result of this analysis is shown in Figure 14.

Figure 14. Distance to the obstacles and measurement error: small circles are the results of experiment and solid lines are the theoretical resolution

The horizontal axis is the distance to the real obstacle from the centre of our experimental system. And the vertical axis is the difference between a correct distance and measuring distance. In this figure, two solid lines show the theoretical resolution. However, because each pixel on the CCD device is not fixed in a radial pattern, this theoretical resolution is actually different according to an orientation. This figure shows that the measured distances are almost within theoretical resolution.

8. Conclusions In this paper, we proposed a novel obstacle detection system using RBS (ring beam system), a spherical mirror and CCD camera for indoor use mobile robots. Firstly, this paper introduced the principle of the novel obstacle detection system,

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which is same as triangulation. Next, we described the calculating method of distance to obstacles and carried out the basic experiment of detecting obstacles. The result of experiment shows the possibility of detecting obstacles using our system; however, the maximum measuring error was 15.4mm Therefore, we built another geometrical model include geometrical errors and identified parameters based on the result of experiment. After the identification of unknown parameters, we carried out the experiment of detecting obstacles under the real environment. The result of experiment showed that: - the developed system can detect obstacles around this system simultaneously, — the errors of distance measured by this system are almost within theoretical resolution. In the future, we will try to control an omni-directional robot using the environmental data obtained by this system. Acknowledgements The authors would like to thank Kawaguchi-Kougaku-Sangyo Co., Ltd. for loan of the Ring Beam System.

9. References Jun S., Haruo T., Naokazu Y. and Kazumasa Y., "Construction and Presentation of a Virtual Environment Using Panoramic Stereo Images of a Real Scene and Computer Graphics Models", Proceedings 15th International Conference on Pattern Recognition (15ICPR), Vol. 4, 2000, pp. 463-467. Kenichi I., Yuzou K. and Shinichi K., "Generation of Ultra-Fat Optical Ring Beam and Its Application to Laser Levels", Transactions of the Institute of Electronics, Information and Communication Engineers, Vol. J79-C-I, No. 10, 1996, pp. 396-397. Ryoshu F., Hidemitsu A., Kiyoshi T. and Shigeo O., "3D Profile Measurement using a Multigray Scale Compared with Reference Projections", Measurement, Vol. 20, No. 2, 1997, pp.129-134. Shin K. and Sadayuki T., "Obstacle Region Detection Sensor by Extended Slit-Ray Projection: Detection Technique and Architecture for a High-Speed Processing Realization", Proceedings of the 5th Symposium on Robot Sensors, 1996, pp. 109. Yasushi Y., "Real-time Omnidirectional Image Sensors", Journal of the Robotics Society of Japan, Vol. 13, No. 3, 1995, pp. 347-350. Yoshikazu M., Eiji N., Takayuki T. and Kuniharu T., "A study on the Mechanism and Control of Omni-Directional Vehicle", IEEE/RSJ Proceedings of the 1996 IEEE/RSJ International Conference on Intelligent Robots and Systems IROS96, Vol. 1, 1996, pp. 52-59. Yuzou K., Jun M. and Kenichi I., "Principle of Ring Beam System (R.B.S.) and Its Applications", O plus E, No. 210, 1997, pp. 96-99.

Chapter 4

Mobile Robot Localization using Reflective Marks on a Ceiling Hiroaki Seki, Takashi Yamashita, Yoshitsugu Kamiya, Masatoshi Hikizu and Hideshi Sakashita Department of Mechanical Systems Engineering, Kanazawa University, Japan

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1. Introduction The need for robots to move and work near humans is increasing in the office, welfare, and with home service robots for example [TAK 96][COR 98]. The basic technology for such mobile robots to move around is reliable detection of their absolute position and the positioning system should be harmless and not be obstructive to humans. Intelligent visual recognition using natural landmarks is ideal, but is not yet sufficiently reliable. The methods using artificial landmarks are effective to find robot position easily and reliably [BEC 95]. Some kinds of localization systems have been developed, but there are few systems suited for the human-robot coexisting environment. Visible marks with special patterns and colors [VOL 95] disturb human life, or the detection of such marks are liable to be affected by lighting. The system using scanning laser light [NIS 95] is expensive and it is not eye-safe. An active beacon system [SEK 98][KLE 95] is also complicated to install. Therefore, a reliable, safe, and inexpensive positioning system using reflective marks for indoor mobile robots is proposed in this paper. 2. Positioning System Using Reflective Marks Our proposed system is shown in Figures 1 and 2. It is one of the mark-based positioning systems using computer vision. Two marks are placed on a ceiling and a CCD camera (2/3 inch CCD, 256 gray scale, 640 x 480 pixels) is equipped on a mobile robot. The robot's position and orientation are estimated by marks' positions in the camera image. It has different points from typical systems as follows.

Figure 1. Positioning system using reflective marks

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- Marks are of a reflective type and they have a property of reflecting light to its source wherever it comes from. This reflective material is commercially used for safety purposes. The shape of two marks is a circle (outside/inside diameter 200/160 mm) and one has a small circle (diameter 60 mm) for discrimination. -A fisheye lens (focal distance 3.8 mm, covering angle 138 x 101 degrees) is mounted on the camera in order to catch the mark image in wide range. - Infrared LEDs (Light emission diodes) (peak wavelength 890 nm, radiant flux 15 mW, x 8) are attached around the fisheye lens. When LEDs are turned on, their infrared light is reflected toward the camera by only reflective marks and the camera can catch the bright mark image, because the CCD has sensitivity for infrared light. Since many other objects scatter the LED light, the brightness of their image does not change so much. - In order to detect marks easier, the LEDs are turned on and off periodically and the subtraction between the image with light and that without light is utilized. This method can almost eliminate the background image around reflective marks.

Figure 2. Fisheye camera with LEDs and reflective marks This positioning system has following advantages. - It is simple because it has no mechanical scanning. - Infrared light from LEDs is invisible and harmless for humans although a robot (camera) can catch it. - Reflective marks on the ceiling are not obstructive to humans because their color can be matched to the ceiling and they reflect light only to their sources even if the light is visible. They are also inexpensive and easily installed in existing buildings. - Subtraction image is not affected by lighting so much. Since there is almost nothing except the marks' image, it decreases the burden of image processing for mark detection.

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3. Principle of Localization At least two marks are necessary to determine the 2-dimensional position of a robot when it moves on a flat floor. The robot’s position (X, Y, 0)can be calculated from the known locations of marks ( X i ,Y , , Zi) (i =1 ,2) ( Z i is the height from the camera) and their measured coordinates (xi,yi) on the camera image by using geometrical relationship (Figure 3).

Figure 3. Geometrical relationship between CCD image and robot’s position Since the fisheye lens projects mark images on the CCD in proportion to their incidence angles 8i,the marks’ coordinates on the ceiling observed from the robot (Xi, Y,)are obtained by

where f is focal distance. The coordinate transformation of the marks’positions between the base and robot coordinate system is given by the robot’s position.

Four equations are obtained from two marks (i =1 , 2 ) to solve the robot’s position X ,Y,8).At first, solving about the orientation 8,

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Next, the position (X, Y) is given by substituting the orientation Θ into equation [3]. Since that equation is redundant, the average of two solutions is taken.

Figure 4. Influence of measurement error (1 dot) of mark image on position accuracy

The position accuracy is discussed. It depends on the arrangement of marks and the distance from them. Figure 4 shows the error of robot position caused by the measurement pixel error of mark image. Errors of robot position (X +Δ X, Y +Δ Y) at the cross points of 1 m x 1 m are calculated when the corresponding mark position (x i , yi) shifts by 1 dot on the image. Two cases of distance between marks are shown. It can be seen that the position error distributes on concentric circles and it is small near the marks. This is convenient to place marks at the center of a room. When the distance between marks is great, the error becomes small, however, the detectable range by them also becomes small.

4. Detection of Reflective Marks Detection of marks is the key to reliable mark-based positioning. Only reflective marks can be easily recognized by the following image processing utilizing their characteristics, even if the image includes moving men, lamps, furniture and so on. Figure 5 shows this process about the ceiling image of a room for example. 1) A subtraction image is obtained from two images when the infrared LEDs are turned on and off. The background image can be eliminated because its brightness is

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Figure 5. Image processing to detect reflective marks

not changed by the LED light. Since reflective marks reflect the light to the camera and some edges of moving objects change their positions between two images, they are left in the subtraction image. When this subtraction processing is applied on a moving mobile robot, it will be necessary to correct the image shift by the robot's movement in a measurement interval.

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2) Binarization by p-tile method, noise reduction by contraction and expansion, and segmentation are executed on the subtraction image in order. 3) Mark candidates are selected by area (50 ~ 600 pixels) and a simple feature of a circle (the center of a region should be black pixel). Four regions satisfy this condition in Figure 5.

Figure 6. Transformation between real and image coordinates (height from the camera to the ceiling: 2.5 m)

Figure 7. Mark image deformed by fisheye lens

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4) Pattern matching should be made for mark candidates; however, mark images are elliptically deformed by the fisheye lens and this effect is strong near the edge of the image. The deformation can be geometrically calculated as shown in Figures 6 and 7. At first, the position of each mark candidate in the robot coordinate system (X'i Y'i) is obtained from the center of gravity of its region (equation [2]). A circular mark (X', Y') with radius C at (X'i, Y'i) on the ceiling is expressed by

This is transformed into the shape on the image (x, y ) by the characteristics of a fisheye lens (Figure 3).

where Z is the height from the camera to the mark. Since a mark has width, the inside and outside radius should be considered. After comparing the regions of mark candidates with the calculated mark shapes respectively, two regions with large correlation are assigned to reflective marks. Table 1 shows the result of this matching about the image of Figure 5. 5) The distance between two selected marks is checked with the correct value (error 100 mm). 6) Two mark images are discriminated by the existence of a small circular region (10~100 pixels) around them (distance error 20 mm). Robot position is calculated from the centers of gravity of these mark images.

Table 1. Matching result with calculated mark shape

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5. Experiment Experiments were made using a positioning system that was developed. Two reflective marks were placed at a distance of 500 mm on the ceiling and a fisheye camera unit was placed on the floor. The height from the camera to the ceiling was 2.71 m. At first, robustness of the subtraction image under various light conditions was investigated as shown in Table 2. A dotted line mark as well as two circular marks was

Table 2. Images obtained under various light conditions

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placed. The interval of two images with / without LED light is 33 msec (NTSC video signal). It can be seen that subtraction image mainly gets reflective marks regardless of lighting. Even fluorescent lamps near the marks do not affect it. When the ceiling is made bright by daylight, the lens aperture must be decreased not to saturate the brightness of mark image. Because the change of mark's brightness by infrared LEDs becomes relatively small by this adjustment, LEDs must be also brightened up.

Positions (X, Y) at the cross points of 0.5mx0.5m were measured. (sampling every 7 seconds, 10 times)

Figure 8. Position measurement by two marks

Next, the accuracy and effective range of positioning was measured. The minimum sampling time of the system developed is about 2 seconds including image processing, however, experiment was made every 7 seconds. Position was measured at a fixed orientation in a quarter of the area about the marks (Figure 8) and orientation was carried out at two places (Figure 9). It can be seen that the accuracy (maximum error) of the measured position and orientation is about ±50 mm and ±4 degrees respectively and their scatter is small. One of the largest causes for this error is the tilt of the camera. It is also found that the measureable range is within a horizontal radius of about 2.5 m from the marks. Near the boundary of the measurable range, the center of gravity of the mark image, which gives the position, has error owing to the loss of the shape.

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Figure 9. Orientation measurement by two marks

6. LED Configuration The mark image becomes dimmer as the distance from the camera increases. This determines the measurable range. Some ideas are considered to expand the measurable range. One is that the brightness of LED or the threshold of binarization is changed according to the mark's position in the image. The other is that the LEDs around the fisheye lens is arranged so that the mark image with uniform brightness can be obtained in wide range on ceiling. Here, the latter idea is discussed because it doesn't make image processing complicated. If the mark brightness is uniform anywhere in the image, the total intensity can be adjusted by the lens aperture, the number of LEDs, and the current of LEDs. The brightness of a mark in the image / is expressed by the directivity of a LED I L j (ØLj), the attenuation by the distance between a LED and a mark I D ( d ) , and the directivity of a reflective mark I M ( Ø M )•

where ( X ' , Y', Z) is the mark position, r = X'2 + Y'2 is the horizontal distance from the camera, and j is LED number (Figure 11). Therefore, the directivity or orientation of LEDs should be changed in order to adjust the distribution of mark brightness. New LED configuration was made on trial as shown in Figure 10. Two different types of 16 LEDs are alternatively attached around the lens. Their axes are tilted at an angle of 80 and 90 degrees respectively. The reflective material with long line shape was placed on its ceiling and the brightness of each position in the subtraction image was measured. New and original con-

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Figure 10. New LED configuration

Figure 11. Measurement of mark brightness in subtraction image

figurations are compared in Figure 11. It can be seen that the mark brightness in the new configuration became more uniform through the total brightness decreased. In order to find the optimal configuration, it will be necessary to evaluate various LED configurations by the simulation using equation [8].

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7. Conclusion A reliable system to detect the position of an indoor mobile robot by artificial landmarks has been proposed. It is a mark-based localization system using reflective marks on the ceiling and a fisheye camera with infrared LEDs on a robot. The key technique is utilizing the subtraction between the image with LED light and that without LED light in order to eliminate the background. It makes the recognition of reflective marks very easy and robust to lighting. Since this system is safe, inexpensive, and not obstructive to humans, it is useful for service robots to work near humans. The developed system could obtain the 2-dimensional position and orientation about every 2 seconds with an accuracy of ±50 mm and ±4 degrees, respectively, within a horizontal radius of about 2.5 m from the marks. Though this is almost enough for indoor navigation, improvement of accuracy and expansion of measurable range are necessary for more precise and wider positioning. Increase in types of mark shapes and image processing on a moving mobile robot remain to be explored in further work.

8. References [BEC 95] BECKER C., SALAS J., TOKUSEI K., LATOMBE J., "Reliable Navigation Using Landmarks", Proc. IEEE Int. Conf. on Robotics and Automation, 1995, p. 401-406. [COR 98] CORD T., RUPP T., LAZIC D., "A Navigation System for Mobile Service Robots", Proc. 3rd IFAC Symp. on Intelligent Autonomous Vehicles, 1998, p. 781-786. [KLE 95] KLEEMAN L., "A Three Dimensional Localiser for Autonomous Robot Vehicles", Robotica, vol. 13, num. 1, 1995, p. 87-94. [NIS 95] NISHIZAWA T., OHYA A., YUTA S., "An Implementation of On-board Position Estimation for a Mobile Robot - EKF Based Odometry and Laser Reflector Landmarks Detection", Proc. IEEE Int. Conf. on Robotics and Automation, 1995, p. 395-400. [SEK 98] SEKI H., TANAKA Y., TAKANO M., SASAKI K., "Positioning System for Indoor Mobile Robot Using Active Ultrasonic Beacons", Proc. 3rd IFAC Symp. on Intelligent Autonomous Vehicles, 1998, p. 681-686. [TAK 96] TAKANO M., YOSHIMI T., SASAKI K., SEKI H., "Development of Indoor Mobile Robot System Based on RECS Concept", Proc. 4th Int. Conf. on Automation, Robotics and Computer Vision, 1996, p. 868-872. [VOL 95] VOLPE R., LITWIN T., MATTHIES L., "Mobile Robot Localization by Remote Viewing of a Colored Cylinder", Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, 1995, p. 257-263.

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Chapter 5

Force Study Applied by a Planar Micromanipulator to Biological Objects Michael Gauthier and Emmanuel Piat Laboratoire d'Automatique de Besançon, CNRS, Besançon, France

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1. Introduction The main application of this study is the manipulation of cells in laboratories. The field of cell manipulation is vast. Two types of problem can be differentiated in this field: the sorting of cells, and the manipulation (and the treatment) of a target cell. The flow cytometer (FACS) invented by Fulwyler [FUL 68], is in the first category. It allows one to sort cells with speeds of 2.105 cells per second [ENG 00]. The second separation techique is the magnetic separation, which uses antibodies attached to magnetic particles. These antibodies cling to the target cells, so these cells can be moved by magnetic energy [GIA 76]. Various recent applications in this domain are presented in the literature [DOL 00] [LIB 00]. Using the same principle Parton develops a sorter of cells with antibodies attached to sensitive electrostatic particles [PAR 99]. We can also quote the use of ultrasounds to sort out cells according to their density [WHI 96]. All these techniques allow one to sort out a big number of cells but cannot grab a target cell to treat it. Laser trapping is a manipulation device of target cells. This process, introduced by Ashkin [ASH 74], allows the manipulation of a cell with a laser beam. The physical principle of this process is described by Buican [BUI 89]. Applications of direct manipulation of an object by laser trapping are presented by Wilson [WIL 98], and Mori to [MOR 99]. Arai develops a process of indirect manipulation of biological objects by laser trapping [ARA 02]. He pushes a target cell with a small tool manipulated with laser trapping. We can also quote other works on cell manipulation. The works of Le Pioufle [PIO 99] and Fujita [FUJ 01], which permits the hanging of cells on a wafer of silicon to treat them. We also quote single cell manipulation thanks to dielectrophoresis (DEP) [FUH 94]. The device presented in this paper is inspired by planar manipulators using magnetic energy. We cite Inoue [INO 95], and Fearing [FEA 95] who control magnetic robots on a plane, with coils situated under this plane. Coils change the magnetic field at the level of the plane, and control robot movements. Interest in manipulation of a target cell is developed in the literature by Arai [ARA 02] and Morishima [MOR 98]. During the cell manipulation, force applied on the manipulated objet must be controlled [ARA 00]. A too strong force can effectively damage the biological objects. The device presented in this article allows the manipulation of cells in a completely enclosed chamber, so the crosscontamination between the sample and the laboratory environment is avoided. The interest in this kind of manipulation in a closed chamber is developed by Buican [BUI 89]. The device presented here carries out indirect manipulation of cells by pushing. The validity of this kind of manipulation is demonstrated by the indirect manipulation device of Arai [ARA 02].

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2. Presentation of the device The ferromagnetic particle which is going to push cells is set in a closed chamber (see Figure 1). This particle is called "the manipulator". A magnet is moved under the lower glass slide of the chamber, the manipulator follows the movement of the magnet, and thus moves inside the chamber. Cells are very insensitive to magnetic fields [KEM 85], so the ferromagnetic manipulator will be able to be moved without inducing a movement of cells by magnetic energy.

Figure 1. The Wireless Micromanipulation System (WIMS) Two types of ferromagnetic micromanipulators are used - iron manipulator 400 x 300 x 120 μm 3 , - electroplated nickel manipulator (from 400 x 400 x 20 [GAU 02c]

to 1 0 x 1 0 x 5 μm3)

The manipulator used for this study is a piece of iron (400 x 300 x 120 μm3). V denotes the volume of the manipulator: V = 14.5 106 μm3. The magnet is a

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Figure 2. The controller cylindrical magnet of axis yo (see Figure 1) of 5 mm diameter and 1 mm thickness. The magnetic field of the permanent magnet is denoted Bo. This magnetic field around the magnet is described in Figure 3. The remanence magnetic field Br inside the magnet is 0.72 T. The plan of the experimental device is presented in Figure 1. A micro-actuator moves the magnet under the glass slide. The position of the magnet is measured by a laser sensor (1 μm resolution). The position of the manipulator and the target is measured with a CCD camera located above the chamber. The choice of a CCD camera to observe cell manipulation was demonstrated by Morishima [MOR 98] and Arai [ARA 00]. The frames R, and Ro denote respectively the frame of the fixed part of the device, and the frame of the magnet. The point O is defined in Figure 1. Rp denotes the frame of the manipulator, and G its centre of gravity. The controller is defined in Figure 2. Our goal in this paper is to prove that the measurement of the position yo of the permanent magnet allows creation of a software sensor of the force applied by the manipulator on the manipulated object.

3. The manipulator behavior in water We prove in this section that the manipulator is aligned with the magnetic field Bc when it does not push any object.

3.1. The magnetization inside the manipulator We assume that the manipulator has a dimension (in the direction zp) longer than the others (see Figure 3). The length in the direction zp is denoted h. The manipulator is much smaller than the permanent magnet, so we assume that the field B0 is uniform

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around the manipulator. The vector zb, denotes the direction of the locally uniform magnetic field B0, so: B0 = B0 zb (see Figure 3). The angle 9 denotes the angle between the direction of the magnetic field zb, and the direction of the manipulator

Figure 3. The magnetic field around the manipulator The manipulator is made of a soft magnetic material. The vector M denotes the magnetization in the manipulator. We assume that this vector is uniform within the manipulator because of its small size. The length of the manipulator in the direction zp is greater than in the two other directions, so we assume that the magnetization M has the direction zp [GAU 01]. The magnetic field ||B0|| around the manipulator is approximately 0.2 T. This value is greater than the coercive field, so we assume that the value of the magnetization ||M|| is the saturation magnetization Ms:

The typical value for iron is : Ms = 1.5 to 2 T [BER 92]. 3.2. Mechanical actions applied on the manipulator Four mechanical actions are applied on the manipulator when not pushing any object: - the magnetic force applied by the magnet - the magnetic torque applied by the magnet [BER 92] - the force applied by the glass slide - the force applied by the water

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3.3. Force applied by the water We prove that we can neglect the force applied by the water on the manipulator. We do not want to calculate in this part the exact value of Fw, we just want to estimate it. We assume that the dimension h of the manipulator in the direction zp is greater than in the other direction. We assume in this section that the direction zp of the manipulator is close to the direction zo. So we consider that: yp = yo. This hypothesis is only valid in this section to estimate the force Fw. The vector Vy = V y y o denotes the speed between the water and the manipulator. The force Fw in the direction yo is [BRU 70]:

with

The coefficient Cy is defined according to the Reynold's number Re of the device :

with The maximal speed of the permanent magnet in our device is Vmax. The maximal speed of the manipulator is the same. When Vy = Vmax, the force Fw defined in equation (2) is maximal. In that case:

so :

The water speed around the manipulator with Re = 4 is defined in Figure 4. In that case the value of Cy is around 0.87 [BRU 70]. So the force Fw is :

This value is much smaller than the value of magnetic force F (around 2 mN). So we will neglect in this paper the force Fw applied by the water on the manipulator. We have proved that the manipulator behavior in the water and in a dry environment are the same.

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Figure 4. The water around the manipulator 3.4. The orientation behavior The vector zf denotes the direction of F (see Figure 5). αf denotes the angle between zf and zo (also αb, angle between zb and z o ). We prove in this section that the manipulator direction zp is the direction zb of the magnetic field. In other words, we will prove that the angle 9 has a value close to zero.

Figure 5. Axis and angle definition We assume that the magnetic force applied by the magnet on the manipulator —F. z f is applied to the manipulator centre of gravity G. The static equilibrium of the manipulator gives :

9 is small, so equation (8) becomes :

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We notice by simulation that the difference between both angles α f and αb has a maximum of 15°. The magnetic force F calculated then is lower than 2 mN. The magnetic field B0 near the plot G has a maximum of 0.2 T. The typical magnetization for the iron is μ0M8 = 1.5 T [BER 92]. With these values we obtain an angle 9 around 1 °. This value is small, so we will consider that the manipulator is aligned in the magnetic field (0 = 0 and zp = z b ). So equation (1) becomes :

4. Force study The manipulation of a biological object with a manipulator requires the control of the force applied on it [MOR 98] [ARA 00]. A too great force during the manipulation can effectively damage the object. The purpose of this study is to estimate the force applied on an object, and to compare this estimation with experimental results. The magnetic force applied on the manipulator is according to the magnetic field B0 around the manipulator. The field B0 of the magnet is fixed in R0. So the magnetic force is according to the position yoG = yG - y0 of the manipulator in R0. The results of the forces presented below will be according to yOG. 4.1. Magnetic force calculation We consider an element P in the manipulator which has a small volume dV . By definition the elementary magnetic force dFu = dF.u applied to it in the direction u is [BER 92]:

So force Fu in the direction u applied by the magnet on the manipulator is:

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4.2. The dead zone For a value of y°G close to 0, the magnetic force Fy is lower than the friction force (see Figure 11). In this dead zone we cannot move the contact point of the manipulator. If we assume that the adherence coefficient and the friction coefficient / have the same values, Coulomb's law gives [COU 81]:

The dead zone is characterized by a null speed, characterized by:

4.3. Definition of the pushing force We want to determine the force applied by the manipulator on the target object. We consider that the magnet and the manipulator move in the same speed V(G / R) = V(0/R) (see Figure 6). So value y°G is a constant.

Figure 6. The pushing force Fp Three forces are applied on the manipulator (see Figure 6): the magnetic force applied by the magnet, the force applied by the glass slide, and the force Fp applied by the target objet. The static equilibrium of the manipulator gives :

We call Fp, "the pushing force". We calculate below the value of this pushing force.

4.4. Calculation of the pushing force This study is limited to the zone outside of the dead zone. We have a movement in the direction of Fy, so:

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The simulation of the magnetic field gives the magnetic force F according to the position yG - yo- The pushing force Fp is given according to the component of the force F, according to the position yoG. So the simulation gives a model of the relationship between Fp and y°G. Now the value y°G is an input of the controller (see Figure 2), so the controller is able to calculate the force F p (y o G ) thanks to the model developed here.

5. Simulations and experimentations This device is able to push micro-objects and biological objects from 20--μmto 1 mm (see examples in Figures 7 and 8). We have simulated the magnetic field of the magnet, and calculated the magnetic force F. These magnetic field simulations were done with the Flux 3D software, of the CEDRAT company.

Figure 7. Manipulation of a 50 μm diameter PS microball

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Figure 8. Manipulation of an human Oocyte (150 urn diameter)

5.1. The vertical force Fz In this first experiment, the component Fz of the magnetic force in the vertical direction Zo is simulated and measured. We use the equation (11) to calculate by simulation the force Fz. The simulated and measured forces Fz according to ZOG = OG.zo are presented in Figure 9.

Figure 9. Simulation and measurement of the vertical force Fz

These simulations allow one to identify the saturation magnetization present in the manipulator. That value is μ o M s = 1.5 T. An iron typical value is about μ 0 M s ~ 1.5 to 2 T[BER 92]. This value is thus in agreement with typical values for iron. The value of μ o M s = 1.5 T will be used below.

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5.2. The pushing force Fp Experimentations were made to measure the pushing force Fp. The experimental device is presented in Figure 10. We use equations (16) (11) to calculate by simulation the force Fp. The simulated and measured pushing forces are presented in Figure 11.

Figure 10. The measurement device of the pushing force Fp We identify here the friction coefficient / = 0.3. This value for an iron - glass contact is important. The very rough surface of the manipulator seems to increase the friction coefficient between the two surfaces. The maximal pushing force applied by the manipulator in this study is 1.5mN (1400 times its own weight). This force allows movement of objects of various sizes (for 1 mm to

Figure 11. Simulation and measurement of the pushing force Fp

6. Conclusion The device presented here allows the manipulation of biological objects located in an extremely confined environment. A specific control strategy allows achievement of a good position precision (1 μim) [GAU 02b]. The manipulation of a biological object

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has to be developed with a force control and the study developed in this article proves that we can determine the pushing force applied on the manipulated object, thanks to the measurement of the magnet position and manipulator position. The model allows us to create a software force sensor integrated in the position controller.

7. References [ARA 00] ARAI F., OGAWA M., FUKUDA T., "Indirect Manipulation and Bilateral Control of the Microbe by laser Manipulated Microtools", Proc. Of the 2000 IEEE/RSJ Int. Conf. On Intelligent Robots and Systems, 2000. [ARA02] ARAI F., SAKAMI T., MARUYAMA H., ICHIKAWA A., FUKUDA T., "Minimally Invasive Micromanipulation of Microbe by Laser Trapped Micro Tools", Proc. of the IEEE International Conference on Robotics and Automation - ICRA02, Washington D.C. - USA, May 2002. [ASH 74] ASHKIN A., Apparatuses for trapping and accelerating neutral particles, United States Patent, Patent Number US 3 808 550, 30 April 1974. [BER 92] BERTIN M., FAROUX J., RENAULT J., Cours de Physique Electromagnétisme 4 : Milieux diélectriques et milieux aimantés, Ed. Dunod Université, September 1992. [BRU 70] BRUN E. A., MARTINOT-LAGARDE A., MATHIEU J., "Mécanique des fluides", Dunod Chapter VII.8,, 1970, p. 324-357. [BUI 89] BUICAN T. N., NEAGLEY D. L., MORRISON W. C., UPHAM B. D., "New Technologies in Cytometry", Proc. OfSPIE, vol. 1063, 1989, p. 189-197. [COU 81] COULOMB C. A., "Théorie des machines simples en ayant égard au frottement de leurs parties et à la roideur des cordages", Mémoires de mathématique et de physique présentés à I'Academie royale des Sciences,, 1781. [DOL 00] DOLAN G. J., TERSTAPPEN L. W. M. M., Magnetic devices and sample chambers for examination and manipulation of cells, United States Patent, Patent Number US 6 136 182, 24 Oct 2000. [ENG 00] DEN ENGH G. J. V., High speed flow cytometer droplet formation and method, United States Patent, Patent Number US 6 133 044, 17 Oct. 2000. [FEA95J FEARING R., "A planar Milli-Robot System on air Bearing", 7th International Symp. Robotics Research, HerrschingGermany, Oct. 1995. [FUH 94] FUHR G., MULLER T., SCHNELLE T., HAGEDORN R., VOIGT A., FIEDLER S.,

ARNOLD W. M., ZIMMERMANN U., WAGNER B., HEUBERGER A., "Radio-Frequency Microtools for particle and live cell manipulation", Naturwissenschaften Ed. SpringerVerlag Berlin, vol. 81, num. 12, 1994, p. 528-35. [FUJ 01] FUJITA H., "Micromachined Tools for the investigation of Nano World", Proc. of Mecatronics '01 - 5th Franco-Japanese Congress - 3rd European-Asian Congress, Besancon - France, 9-11 Oct 2001, p. 04-10. [FUL 68] FULWYLER M. J., Panicle separator, United States Patent, Patent Number US 3 380 584, 30 April 1968. [GAU 01] GAUTHIER M., PIAT E., "Etude en effort pour la micro-manipulation d objets biologiques avec un pousseur magnétique", 14thjournees desjeunes chercheurs en robotique - JJCR'14, Evry - France, Mai-Juin 2001, p. 62-67.

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[GAU 02a] GAUTHIER M., PIAT E., "Behavior of a magnetic manipulator of biological objects", Proc. of the IEEE International Conference on Robotics and Automation - ICRA02, vol. 2, Washington D.C. - USA, May 2002, p. 3199-3204. [GAU02b] GAUTHIER M., PIAT E., "Control of a particular coarse-fine micropositioning system based on a magnetic actuation", Proc. of the IEEE International Conference on Intelligent Robots and Systems, Lausanne - Switzerland, 30 sept - 4 Oct 2002. [GAU 02c] GAUTHIER M., PIAT E., "Microfabrication and scale effect studies for a magnetic micromanipulation system", Proc. of the IEEE International Conference on Intelligent Robots and Systems, Lausanne - Switzerland, 30 sept - 4 Oct 2002. [GIA 76] GIAEVER I., Magnetic separation of biological particles, United States Patent, Patent Number US 3 970 518, 20 July 1976. [INO95] INOUE T., IWATANI K., SHIMOYAMA I., MIURA H., "Micromanipulation Using Magnetic Field", Proc. IEEE International Conference on Robotics and Automation, Nagoya Japan, May 1995, p. 679 - 684. [KEM 85] KEMSHEAD J. T., UGELSTAD J., "Magnetic separation techniques: their application to medecine", Molecular and cellular Biochemistry, vol. 67, 1985, p. 11-18. [LIB 00] LIBERTl P. A., YUSHON W., Method for Magnetic Immobilization and Manipulation of cells, United States Patent, Patent Number US 6 013 532, 11 janv 2000. [MOR 98] MORISHIMA K., ARAI F., FUKUDA T., MATSUURA H., YOSHIKAWA K., "BioMicromanipulation System for High Troughput Screening of Microbes in MicroChannel", Proc. Of the 1998 IEEE Int. Conf. On Robotics and Automation, Leuven Belgium, May 1998. [MOR 99] MORITO Y., SHIKANO S., NISHIOKA C., HORIO K., Laser Manipulation appartus and cell plate used therefor, United States Patent, Patent Number US 5 952 651, 14 sept 1999. [PAR 99] PARTON A., HUANG Y., WANG X., PETHIG R., MACGREGOR A. R., POLLARDKNIGHT D. V., Methods of Analysis/Separation, United States Patent, Patent Number US 5 993 631, 30 Nov 1999. [P1O99] PlOUFLE B. L., SURBLED P., NAGAI H., CHUN K., MURAKAMI Y., TAMIYA

E., FUJITA H., "Attachment of cells on microsystems: application to the gene transfection", 1Oth International Conference on Solid-State Sensors and Actuators Transducers '99, Sendaï'Japon, June 1999. [WHI96] WHITWORTH G., Particle manipulation in an ultrasonic field, United States Patent, Patent Number US 5 484 537, 16 jan. 1996. [WIL 98] WILSON S. D., CLARKE W. L., Method for trapping manupulating and separating cells and cellular components utilizing a particle trap, United States Patent, Patent Number US 5 752 606, 19 May 1998.

Chapter 6

Delta3, a New Ultra-high Precision Micro-robot: Design and Control of a Flexure Mechanism Jean-Philippe Bacher, Jean-Marc Breguet and Reymond Clavel Institut de Production et Robotique, Ecole Polytechnique Fédérate de Lausanne, Switzerland

Stefano Bottinelli Institut de Production et Robotique, Ecole Polytechnique Fédérale de Lausanne, Switzerland, and Mecartex SA, Losone, Switzerland

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1. Introduction Today, developments in micro-technologies are essentially oriented to photolithographic techniques. The fabrication and assembly of advanced systems such as optical fiber connectors, optical circuits or micro-fluidic devices require high precision, flexibility and reliability. In addition to wafer-based manufacturing techniques, there is still a need for high precision robots, especially for positioning and assembly. There are many ways to improve the precision handling of a required task. In the case of assembly, it is possible to change the process, the environment or the shape of the parts (self alignment). Another possibility is to increase the manipulator's precision. The present paper and related work focus on this possibility, and also on the mechanical structure of the robotic system. An innovative approach permits one to overcome the limitations due to dry friction by the use of flexure mechanisms.

2. Flexure mechanism for high precision robotics The use of flexure joint based mechanisms (flexure joints are also called elastic joints) is a solution to meet the requirements of high precision. In systems with standard elements (ball bearings etc) non-linear control strategies have been proposed to compensate friction (Johnson et al, 1992). Our approach permits the problem of friction to be overcome directly in the mechanism design. Flexure joints are commonly used for one or two degrees of freedom (dof) systems (Smith et al., 1992). There are few examples of use of this technology to design robots with several dof (3 6) (Ryu et al, 1997; Henein et al., 1999). One of the application fields of flexure joint based mechanisms is wafer positioning. In this case, the system consists of a 2-stage positioning scheme (macro-micro). Standard XY tables with DC servomotor and ball screw give the coarse positioning, while piezo-actuated stages are used to reach submicrometric positioning accuracy. Our objective is to reach submicrometer positioning (down to 10 nm) on several millimeters with a 1-stage positioning scheme. This led us to choose direct drive electromagnetic actuators. This choice (type of mechanism and actuator) provides a compact and smart system.

3. Flexure mechanism design 3.1. Basic elastic elements The fundamental components of a flexure mechanism are the "basic elastic elements". There are several types of elastic elements (Figure 1), among them the notch hinge, the cantilever beam and the split tube (Goldfarb et al., 1999). These basic elements have been exhaustively studied in the literature. Several books give

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analytical expressions for the maximal displacement and the stiffness of these basic elements (Smith, 2001; Henein, 2001).

Figure 1. Examples of basic elastic elements

The function of these elements is to allow a deterministic motion (degree of freedom) while constraining all the others. This function leads to the two main characteristics of a basic elastic element; the stroke and the stiffness. The stroke is limited by the maximal stress (which should remain under the endurance limit). The maximal stress vs. stroke characteristic depends on the design of the elastic element, i.e. on the thickness of the element and on the repartition of the strain. As an example of the importance of the repartition of the deformation, it is interesting to compare a notch hinge with a cantilever beam with the same overall dimensions. The stroke of the cantilever beam is larger than that of the flexure hinge if they have the same minimum thickness. In the case of the notch hinge, the whole deformation is localised in a small zone, leading to a stress concentration. The same observations have been made for the corner-filleted flexure hinge (Lobontiu et al., 2001). A general assertion can be made: for the same maximal stroke, the element that has a homogeneous repartition of the strain will be stiffer (often on all the degrees of freedom) than the one that has a localized deformation. The counterpart is the fact that the motion error (see section 3.2) will be bigger for an element that has a homogeneous repartition of the stain. The second main characteristic of a basic elastic element is the stiffness. The stiffness parameters lead to the repartition of the potential energy provided in an element by external forces and torques. The essential information is the following: rigidity of the constrained degrees of freedom and suitability of an elastic element to fulfil dynamic specifications if it is used in a mechanism (the vibration modes values and shapes of a mechanism depend on the stiffness and mass matrix). With the basic elastic elements described previously, it is possible to design "elastic (or flexure) joints".

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3.2. Elastic joints The mechanical design of a robot is based on its kinematics. The goal of kinematics is to provide specified motions with joints and links. The classical mechanical joints (revolute joint, U-joint, slider, cylindrical, ball joint, etc.) can be designed by several ways (with ball, roller, plain, magnetic or air-bearing for example). Elastic joints are widely used in fields such as astronautics (spacecraft, aeronautical structures), measurement devices (for example weight measurement) but yet seldom used in the design of multi-degrees of freedom (multi-DOF) microrobotic systems. Elastic joints are designed with basic elastic elements. They are characterized by a stroke and by a "motion error" (also called "parasitic motion"). This motion error can have two origins: the link geometry and the basic elastic element deformation. The deformation of the elements illustrated in Figure 1 presents a non-perfect rotational motion. The rotation center (often called "compliance center") has a more or less important translation, also depending on the load characteristics (pure torque, etc). The goal when designing elastic joints is to reach motion specifications (stroke and motion error) using imperfect elastic elements and eventually imperfect kinematics (for example, even with perfect revolute joints, the simple parallel four bar linkage has a motion error) (Figure 2a). The compound linear stage is a known example of a "perfect" slider joint designed with imperfect elements (Figure 2b).

Figure 2. Simple a) and compound b) linear elastic stages

The choice of the design of an elastic joint depends on the required kinematics and on the desired motion precision. Several situations can occur. The joint design validation process is summarized below (Figure 3).

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The basic idea of the validation process presented above is that the joint choice depends greatly on the kinematics. Sometimes joint errors can be tolerated and compensated, sometimes not. In the example of the Delta3 robot (see below), imperfect joints have been chosen.

Figure 3. The validation process of an elastic joint design

3.3. From elastic joints to complete mechanical structure Once having chosen a kinematics and an elastic joint design for each joint, the last step is to integrate all the components, leading to the complete mechanical structure. During this step, several design rules should be followed:

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- use monolithic design, integrating several joints into one part, - use redundant design, using the same part several times, - facilitate assembly and disassembly. The respective importance of these rules is difficult to quantify and depends on the manufacturing process that is used. There is often a trade-off between manufacturing and assembly costs. 4. Delta3 mechanical structure 4.1. Kinematics The first step when designing a robot is the choice of the kinematics. The Delta3 robot kinematics (Figure 4) is the same as the linear Delta robot (Clavel, 1991) (Stevens, 1994). The mechanism is parallel with 5 loops and 3 dof (3 translations). A slider (or prismatic) joint and a 3 dimensional parallelogram (spherical four bars linkage) compose each kinematic chain.

Figure 4. Delta robot kinematics with prismatic (P) and spherical (S) joints

The mobility is calculated as follow, using a general mobility criterion:

where: M is the relative mobility of the system of bodies, n the number of bodies (including reference), g the number of joints, fi: degrees of freedom of joint i. In our case: n = 1 1 , g = 15, • fi = 39, so that M = 9. As shown in Figure 4, the two bars of each 3-dimensionnal parallelogram have one internal dof. Subtracting these degrees (6 internal dof) to M gives the mobility of the robot end-platform (i.e. 3).

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4.2. Configuration The second step consists of the spatial configuration choice. The particularity of the Delta3 is that the 3 kinematic chains are perpendicular to each other (Figure 5). Each parallelogram locks a rotation (0x, 6y, 0z) and each prismatic joint controls a translation (X, Y, Z).

Figure 5. Configuration of the Delta3 robot

4.3. Joints Two different joints are used in the Delta3 kinematics: a slider and a ball joint. As slider, the simple elastic stage (see Figure 2) is used. As ball joint, two serial flexure hinges at 90° are used (see Figure 6a). Using the same joint four times, a 3dimensional parallelogram (also called in-space parallel four-bar linkage) is designed (see Figure 6b).

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Figure 6. Ball joint a) and 3-dimensionnal parallelogram b) with flexure hinges

4.4. Inverse kinematics The inverse kinematics is the transformation from task-space trajectory specifications to actuator space trajectory specifications. The model takes into account the geometric motion errors of the simple elastic stages (the output is moving on a circle) and of the parallelograms (the relative displacement is on a sphere). The inverse kinematics of the complete robot (see Figure 7) is obtained by the resolution of three times the equations of the intersection between a sphere and a circle.

4.5. Dynamics The essential characteristics in terms of dynamics are given by the modal analyses. The values and shapes of the vibration modes set the behaviour of the system. In an elastic mechanism, the free degrees of freedom are the first vibration modes of the structure. The values of these first frequencies and the value of the moving mass allow the computation of a second order model of the open loop system. This second order model will be used to calculate feed-forward control terms. Other important values are the frequencies of the vibration modes corresponding to constrained degrees of freedom. A rule of the thumb is to set these values at least twice the desired bandwidth of the system (in the case of the Delta3, the vibration modes of the internal degrees of freedom are far above the bandwidth, so they are not exited). The position of the actuators (and sensors) is another important design point. The actuator that applies a force or a torque on a free degree of freedom should not induce a force or a torque on a constrained degree of freedom. To avoid dynamic coupling, it is important to place the actuators taking into account the mass-

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3

geometry. As much as possible, the actuators of the Delta mechanical structure have been aligned with the gravity center of the moving masses.

4.6. Prototype A prototype has been manufactured and tested. Its characteristics are the following: ±2 mm stroke on the three axes of the robot, 300 Hz bandwidth with amplitude of 10μm (amax = 40 m/s2, vmax = 20 mm/s).

Figure 7. Prototype of the Delta3 high precision robot

The flexure parts of this prototype have been manufactured by electro-discharge machining. Moving magnet actuators and optical linear encoders have been used.

5. Control of high precision flexure mechanisms Once the mechanics of the robot is chosen, the control structure must be specified, depending of the desired performances. The main difference between classical robotics and high precision robotics is the dimension scale. First of all, the weight of the controlled system is much smaller than that of a classical robot, which means that the mechanical system sensitivity to perturbation will be bigger. The

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other point is a question of displacement. A part moving for 1ms at a speed of 1 mm/sec (that means at low speed for a classical robot) has made a displacement of 1 μm, which is a "big" displacement for an ultra-high precision robot. To reach high motion precision (minimum trajectory tracking error) and nanometric positioning accuracy, the control algorithm must be carefully designed. First of all, a second order model of the structure is determined (through measurements or through identification). Then, a classic regulator is tuned (PID or state feedback). A feed-forward term based on the second order model is then added to the PID regulator to reduce the tracking error. If the speed obtained by position derivation is too noisy, a state observer might be used to estimate the speed. Figure 8 summarizes the implemented regulator structure.

Figure 8. Classic regulator structure for high precision robotics

6. Delta example A simple spring-mass system is used as the model of one axis of the robot. In a first step, we assume that there is no coupling between the axes. This assumption is acceptable with regard to the robot configuration. The actuator is not considered in this model. The governing equation can be written as: F(t) - cx(t) - kx(t} = mx(t), or using the Laplace transformation:

This second order transfer function can also be written:

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with

Calculation and identification on the prototype give the following values: k = 850 N/m, m = 0,09 kg, c = 0,5 N/ms -1 , fN = • N/2 • = 15.5 Hz, z = 0,1. Note: the damping ratio z is almost negligible. The above second order system is used to provide a feed-forward term in addition to a PID controller. The results presented below (Figure 9 and 10) are obtained with this control scheme.

Figure 9. Trajectory tracking response on a 100μm step (with limited acceleration) (desired trajectory in black plain line, measured trajectory in gray dotted line)

Figure 10. Series of 2μm steps at 20Hz (obtained with 20 nm sensor resolution and 2 kHz sampling rate)

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7. Conclusion This paper presents a new approach for designing several degrees of freedom (36) ultra-high precision robots. The principle of this approach is to use mechanical structures with flexible links actuated by direct drive electro-magnetic actuators. Very encouraging results have been obtained with the Delta3 prototype that has a three-axes 4 mm range workspace, a maximal resolution of 10 nm and a 200 Hz bandwidth. These performances, in terms of accuracy and dynamics, can be reach only considering both mechanical and control design. The design methodology presented in this paper permits one to reach the targeted performances rapidly. New prototypes of micro-robots are designed to corroborate the developed design procedure and to fulfill new characteristics (4 to 6 degrees of freedom). Acknowledgments The authors are grateful to the AGIE S.A. and Heidenhain A.G. Companies and the TOP NANO 21 Swiss program for supporting this project.

8. References Clavel R., Conception d'un robot parallèle rapide à 4 degrés de liberté, Ph. D. diss., EPFL, Lausanne, 1991. Goldfarb M., Speich J.E., "A Well-behaved Revolute Flexure Joint for Compliant Mechanism Design", Journal of Mechanical Design, Vol. 121, 1999, pp. 424-429. Henein S., Aymon C., Bottinelli S., Clavel R., "Articulated structures with flexible joints dedicated to high precision robotics", Proc. of International Advanced Robotics Programme: Workshop on Micro Robots, Micro Machines and Systems, Moscow, Russia, 1999, pp. 135-140. Henein S., Conception des guidages flexibles, Lausanne, Presses polytechniques et universitaires romandes, 2001. Johnson C.T., Lorenz R.D., "Experimental Identification of Friction and Its Compensation in Precise, Position Controlled Mechanisms", IEEE Transactions on Industry Applications, Vol. 28, Nov./Dec. 1992, pp. 1392-1398. Lobontiu N., Paine J.S.N., Garcia E., Goldfarb M., "Corner-Filleted Flexure Hinges", Journal of Mechanical Design, Vol. 123, 2001, pp. 346-352. Ryu J.W., Gweon D.G., Moon K.S., "Optimal design of a flexure hinge based XY0 wafer stage", Journal of the American Society for Precision Engineering, Vol. 21(1), July 1997, pp. 18-28.

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Smith S.T., Chetwynd D., Foundations of Ultraprecision Mechanism Design, Vol. 2, Series Editor: D. Keith Bowen, University of Warwick, Gordon and Beach Science Publishers, 1992. Smith S.T., Flexures: Elements of Elastic Mechanisms, Gordon and Beach Science Publishers, 2001. Stevens B.S., Clavel R., "The Delta parallel robot, its future in industry", Proc. of the Fifth International Symposium on Robotics and Manufacturing: Research, Education and Application (ISRAM'94), Vol. 5, Hawaii, USA, 1994, pp. 273-278.

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Chapter 7

Prototypes of Thermal Actuated Microlegs: The Insect-like Micro-robot Agnès Bonvilain and Nicolas Chaillet Laboratoire d'Automatique de Besançon, Besançon, France

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1. Introduction It is well known that the design of microrobots gives rise to specific problems related to the microworld, where the surface effects become dominant with regard to the volume effects. Then the miniaturization of robots does not only imply a simple scale factor applied to existing macrotechnologies: it is often necessary to completely re-design the robot for the microworld using new principles, notably concerning the actuation. The design and fabrication of efficient microactuators, mainly using active materials, is then an important research topic for microrobotics because typical actuators used in macrorobotics can lose their efficiency in small dimensions (Tabib-Azar). Moreover, the fabrication of complete structures of microrobots in millimeter-length or in micrometric dimensions often needs the use of clean room microtechnologies. This paper deals with the design, fabrication and experiments of actuated microlegs for an insect-like microrobot. Eventually, the exploitation of such kinds of microrobots can be in the investigation and the inspection of very confined environments, collective exploration tasks, or micropositioning. Because of their large motions and energy density, thermal actuation has been chosen to move their legs. The paper is organized as follows: the first part gives the structure and general principles of motion of our microrobot. The next three parts explain the three generations of designed and fabricated microlegs: the first one uses Ni-Si thermal bimorphs and the others are based on SU8 resist-Si bimorphs. Then perspectives for the microrobot are given.

2. Structure and principle of the legged microrobot Until now, some centimetric miniaturized legged robots have been developed, but very few clean room microfabricated millimetric legged microrobots were designed and actually fabricated. To our knowledge the most interesting prototypes are presented in (Kladitis et al., 1999; Smits, 1992; 1989; Yeh et al., 1996, Yeh and Pister, 2000a; 2000b; 2000c; Ebefors et al., 1999; 2000). They mainly use thermal, piezoelectric and electrostatic actuation. The thermally actuated microrobots need more power than the electrostatic ones, but their density of energy is greater. The time constant is smaller in the electrostatic case, but the displacement is larger in the thermal case. The speed depends on the chosen structure and actuation. From the previous given references it varies from 7μm/s to 7mm/s. The final goal of our study is the fabrication of an integrated structure of an autonomous legged microrobot. Our microrobot is a thermally actuated one with six legs as presented in Figure 1. Each leg has two degrees of freedom.

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In the more distant future, one envisages also to integrate sensors, energy (solar cells or microbatteries), control and telecommunication devices to make the microrobot as autonomous as possible in its environment.

Figure 1. 3D structure of the microrobot

Each microleg is constituted of two thermal bimorphs connected together with a microbeam in order to obtain two degrees of freedom (Figure 2). These microlegs are actuated using the operating cycle shown in Figure 3.

Figure 2. Diagram of the microleg

Figure 3. Expected movements for one microleg seen at its extremity (the dotted line represents the leg in its original position) a) no bimorph supplied; b) the two bimorphs supplied; c) just one bimorph supplied; d) no bimorph supplied

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3. Electrothermal Ni-Si microlegs 3.1. Principle The actuation of the first designed microlegs for our microrobot is based on an electrothermal principle. They use the difference of the thermal expansion coefficients between two materials, silicon and nickel in our case. The electrical energy generates a rise of temperature by Joule effect, which entails a flexion of the actuator (Figure 4).

Figure 4. Deflection of a thermal bimorph

The expression of the free deflection section is (Chu et al., 1993):

The parameters are: F: specific deflection, L: length of the thermal bimorph, AT: rise of temperature, tl, t2: thickness of each material, α1,α2: thermal coefficient of linear expansion, E1, E2: Young modulus of each material. According to these equations, for ΔT, t and L constant, the section is maximum when F is maximum. The optimal thickness ratio is then deduced from [2]:

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Considering the material used in our case, i.e. Si and Ni, in the following, the subscript "1" is replaced by "Si" and the subscript "2" is replaced by "Ni". Equation [3] allows one to optimize the thicknesses ratio in order to obtain the largest deflection. Young's modulus of Si and Ni gives tSi/tNi = 0.75. In our case, the thicknesses are the same, so the ratio is 1. The nickel is deposited by electroplating, the process is described in section 3.2. The reason is the following: a good electroplating must have half of the thickness of the resist (which is 40 μm thick). It is thus still possible to improve deflection by an increase of the thickness of the resist and also the thickness of the electroplating during the fabrication process. Figure 5 shows the drawing of a microleg. This microleg has a length L of 2 mm, a total width w of 350 μm, and a total thickness tSi + tNi of 40 (μm:tsi = 20 μm and tNi = 20 μm. Every thermal bimorph of the microleg has a width wb of 100 μm, and width between the two bimorphs we is 150 μm. The microbeam which connects the two thermal bimorph has a width Wj of 100μm.

Figure 5. Dimensions of the microleg on 2D drawing in three views

3.2. Microfabrication The fabrication of microlegs is made in a clean room. Figure 6 shows a short layout of the process that we first of all developed for our microlegs. The original silicon wafer is 320 μm thick, N doped with a low resistivity (between 0.008 and 0.02 Ω.cm). The process is the following: 1. The fabrication process begins with an 1.2 μm oxidized silicon wafer. Single side photolithography is carried out with 1.4 urn of 5214 resist to remove oxide in buffered hydrofluoric (BHF) for the membranes. Wet etching of silicon is done in potash (KOH) to obtain 20 μm membranes. Single side photolithography with 1.4 μm of 5214 resist is conducted to remove oxide in buffered hydrofluoric (BHF) on the other side to prepare electric contacts and final reactive ion etching (RIE).

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2. Deposit of titanium (100 nm) by radio frequency (RF) cathodic sputtering as adhesion layer, and deposit of copper (500 nm) by magnetron cathodic sputtering as mass plane layer for the electroplating; deposit of Au by lift off with magnetron cathodic sputtering as electrodes and powered contacts are all made. 3. Single side photolithography with 40 μm of SJR5740 resist and electroplating of 20 μrn nickel. 4. Removal of the resist. Wet etching of titanium and copper. Reactive ion etching (RIE) of silicon with SF6 and O2 gas to remove the structures.

Figure 6. Fabrication process of thermal microlegs

After the implementation of the process, thermal microlegs were successfully fabricated (Figure 7).

Figure 7. a) Photo of thermal microlegs bonded on a printed circuit, b) zoom of the connecting microbeam circled on (a)

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The wafer is then glued under a printed circuit, to create the electrical bonding for the experiments.

3.3. Experiments At first, the two beams of a microleg are supplied simultaneously in order to measure its maximal deflection (step b in Figure 3). Figure 8 shows the theoretical and experimental results. As expected using thermal actuators, the motion is quite large (compared to other principles).A second time, only one beam is powered to measure the maximal slope obtained by a microleg (corresponding to the step c in Figure 3). In Figure 9 the experimental results are presented. The measured deflections are in accordance with the theoretical ones. Concerning the dynamics of the microlegs the measured bandwidth (-3dB of attenuation) is of 3.7 Hz (see Figure 10). Based on the experimentations of these first microlegs, it is possible to deduce the expected characteristics for the microrobot: the actuation of the two electrothermal bimorphs of a microleg needs a power of 1.3 W for a deflection of 120 μrn. To walk, the microrobot will use its legs three by three, so it will require at most 3.9 W. On the other hand, we determined the load that the microrobot will be able to carry and the weight of the microrobot (six microlegs and the body). The weight of one microleg is the weight of two microactuators and one connecting microbeam. One microactuator is: 2 mm x 0.1 mm x 0.02 mm of silicon and 2mm x 0.1 mm x 0.02 mm of nickel. The connecting microbeam is 0.1 mm x 0.15 mm x 0.02 mm of silicon. The density of silicon is 2.34xlO-3 g/mm3 and the density of nickel is 8.9x10" 3 g/mm3. Then a microactuator has a weight of 45 μg and the connecting microbeam has a weight of 0.7 μg. The weight of a complete microleg is 90.7 (μg. If we consider that the body has a volume of silicon of 5 mm x 2 mm x 0.38 mm, its weight will be 8.9 mg. Finally, the total weight of the microrobot is 9.1 mg. The load of the microrobot is determined by

with: E =1 56 Gpa: the mean Young's modulus,

m4: the quadratic moment of the actuator, 5 = 120 μm: the deflection of the actuator, L = 2 mm: the length of the actuator.

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Microlegs being on the ground three by three simultaneously, there will be six actuators to support the load. The load (m = 6.P/g, with: g = 9.81 m/s2 ) of the microrobot corresponds to 2.3 grams i.e. 250 times its own weight.

Figure 8. Deflection of the microleg versus the electrical power

Figure 9. Slope of the microleg versus deflection

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Figure 10. Frequency response of the Ni-Si microlegs

The measured slope of the microleg and the length of the foot allows one to evaluate the length of a step: 17 (μm (from a to d in Figure 3). Then with the measured dynamics of a microleg, the speed of our microrobot will be about 64

μm/s. The first steps of the feasibility of this microlegs are presented. Based on these results, we tried to improve the expected characteristics, particularly to reduce the electrical power consumption and to increase the slope of the microlegs.

4. Second generation of microlegs: SU8-Si To improve the characteristics of the microlegs, a new more supple material must be used to replace nickel. Polymers were then studied, notably polyimide which had been also used in the microrobot presented in (Ebefors et al., 1999; 2000). But it is a very expensive material which is not sold in very small quantity. As the polyimide arises like a photosensitive resist, we thought about SU-8 resist, frequently used in LIGA technologies, and which is not easily removable. The mechanical properties of polyimide and SU-8 resist are quite close (Table 1).

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Mechanical Properties

polyimide

SU-8 resist

Young Modulus

2.5 GPa

4 GPa

Thermal Coefficient of Linear Expansion

45.10-6 K-1

52.10 -6 K -1

Then a new generation of microlegs was studied, in which electroplating of nickel was replaced by SU-8 resist. The dimensions are the same as for the previous microlegs. The SU8 resist is then heated by thermal conductivity (resist is not electrically conductive). This photoresist is frequently used, as shown by many works and papers. Some of them describe processes, results and applications of the SU-8 including the use of the resists as a structural material (photoplastic) and multi-level patterning (Dellmann et al, 1997; Lorenz et al., 1998). Others deal with the characterisation of the SU-8 photoresist [14, 15], or about non-conventional use of this photoresist (Thorpe et al., 1998; L'Hostis et al., 2000; Lorenz, 1997). The great difference of thermal expansion coefficient between nickel and SU-8 resist (αNi = 13.3 10-6 K-1 and αSU8 = 52 10-6 K-1) allows a less important raising of temperature for the same deflection of the micro-actuator described in the previous section. It induces a decrease of electrical power consumption. A lower temperature is also an interesting characteristic, not heating too much the ground where the microrobot will walk. Then a new microfabrication process was developed. It was very similar to the previous one. Steps (1) and (2) are the same. Step (3) is the deposit of SU-8 resist, and step (4) is the same as previously described but without removing the resist. The second generation of microlegs were successfully fabricated (see Figure 11). Then the same experiments as for the first microlegs are carried out. In Figure 12, the theoretical and experimental results are presented for the deflection versus the electrical power. The electrical power consumption was divided by a factor of 10, and the temperature was divided by a factor greater than 2. The slope of the microleg (Figure 13) is equivalent to the one obtained for the previous legs, because there were no changes on the connecting microbeam. The measured bandwidth is 2.4 Hz (see figure 14). It is less important than with the Ni-Si microleg, due to the heating of the SU-8 resist by thermal conduction and not by Joule effect. Based on the experimentation of the second generation of microlegs, we deduce the new characteristics of the microrobot: the actuation of the two electrothermal bimorphs of a microleg needs a power of 120 mW for a deflection of 120 μm. To walk, the microrobot will use its legs three by three, so it will necessitate at most 360 mW. Then, with the measured dynamics of a microleg and the length of a step, the speed of our microrobot will be about 42 μm/s.

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In conclusion, it can be noted that the most critical characteristic of the first microlegs, which was the electrical power consumption, was very much improved (divided by a factor of 10) in the second generation of microlegs.

Figure 11. a) Photo of microlegs bonded on a printed circuit; b) Photo of one thermal microlegs SU8 on silicon circled on (a)

Figure 12. Deflection of the microleg versus the electrical power

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Figure 13. Slope of the microleg versus deflection

Figure 14. Frequency response of the SU8-Si microlegs

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5. Third generation of microlegs: antagonist SU8-Si bimorphs In the third generation, we try to still improve the motion of the microlegs, particularly the slope. Based on the previous SU8-Si microlegs, we then developed a third generation of microlegs by using the two thermal micro-actuators in opposition, one of them bends up (actuator 1) and the other one bends down (actuator 2) (see Figure 15). The other difference is the distance between the two thermal microactuators (we = 500μm) which is greater in order to increase the slope of the leg (without changing the deflection of the micro-actuator). These two modifications are carried out to increase the slope of the connecting microbeam and to increase the length of the step as shown in Figure 16. With this new design, the operating cycle of the microleg changes and looks as shown in Figure 17.

Figure 15. 3D diagram of the new microleg

Figure 16. The length of the step a) with a little slope b) with a big slope

Figure 17. Expected movements for one microleg (the dotted line represents the leg in its original position); a) no actuator supplied, b) right actuator supplied, c) two actuators supplied, d) no actuator supplied

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Figure 18. Photo of the microleg

It can be note that the foot of the microleg shown in Figure 18 is not at the center of the connecting microbeam. It is voluntarily done like that to improve the length of the step. This position was chosen after a numeric simulation using ansys, which allows us to know the deformation of the connecting microbeam (Figure 19), and so to place the foot to optimize its slope.

Figure 19. Numeric simulation with Ansys of a microleg with its foot seen at its extremity

These microlegs were experimented with in the same way as the previous ones. Using these legs, we obtain a significant improvement of the slope of the connecting microbeam (about 37 μm), then of the operating cycle and finally of the microrobot speed. The other characteristics are the same as for the microlegs presented in section 4. These experiments allow us to deduct the new step length of 37 microns, and the speed of the microrobot, which will be of the order of 90 (μm/s.

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6. Conclusion and perspectives Based on the fabrication of the microlegs the microrobot consists of machining several microlegs connected to the body on the same silicon wafer. The microrobot was fabricated successfully as shown in Figure 20. Its dimensions are: 5mm x 6mm x 0.5 mm. Some connective problems remain to be solve to supply the microrobot, so then the whole microrobot will be able to be experimented with. Then its characteristics will be measured: the energy consumption, its speed, the transportable load, the slope and the roughness of the surface on which it moves. In the more distant future, the objective is to integrate its control, energy, sensors, to make it as autonomous as possible in its environment.

Figure 20. Microrobot next to a match a) bottom side b) top side

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7. References Chu W. H., Mehregany M., Mullen R. L., "Analysis of tip deflection and force of a bimetallic cantilever microactuator", Journal Micromechanic and Microengeneering, No 3, pp 4-7, 1993. Dellmann L., Roth S., Beuret C., Racine G., Lorenz H., Despont M., Renaud P., Vettiger P. and de Rooij N., "Fabrication process of high aspect ratio elastic structures for piezoelectric motor applications", Proc. Transducers 1997, Chicago, pp 641-644, 1997. Ebefors T., Mattson J., Kalvesten E., and Stemme G., "A Walking Silicon Micro-Robot", 10th Int. Conf. on Solid-State Sensors and Actuators (TRANSDUCERS'99), pp. 12021205, Sendai Japan, June 7-10, 1999. Ebefors T., Mattsson J., Kälvesten E., Stemme G., "A Robust Micro Conveyer realized by Arrayed Polyimide Joint Actuators", IOP Journal of Micromechanics & Microengineering, September 2000. Kladitis P. E., Bright V. M., Harsh K. F., and Lee Y. C., "Prototype Microrobots for Micro Positioning in a Manufacturing Process and Micro Unmanned Vehicles", Proceedings of the 1999 IEEE International Conference on Microelectromechanical Systems (MEMS'99), Orlando, FL, pp. 570-575, January 17-21, 1999. L'Hostis E., Michel P. E., Fiaccabrino G. C., Strike D. J., De Rooij N. F., Koudelka-Hep M., "Microreactor and electrochemical detectors fabricated using Si and EPON SU-8", Sensors and actuators. B, Chemical, Vol. 64, No. 1-3, pp. 156-162, 2000. Lorenz H., Despont M., Fahrni N., Brugger J., Renaud P. and Vettiger P., "High aspect ratio ultrathick, negative-tone near-UV photoresist and its applications for MEMS", Sens. & Act. A, 33-39, A64, 1998. Lorenz H., Laudon M. and Renaud P., "Mechanical characterization of a new high-aspectratio near UV-photoresist", Microelec. Engin., pp.371-374, 41/42, 1998. Lorenz H., Despont M., Fahrni M., LaBianca N., Vettiger P. and Renaud P., "SU-8: a lowcost negative resist for MEMS", J. Micromech. Microeng, pp. 121-1247, 1997. Smits J. G, "Design Considerations of a Piezoelectric-on-Silicon Microrobot", Sensors and Actuators, A35, pp 129-135, 1992. Smits J. G., "Is Micromecanics Becoming a New Subject for Academic Courses or the Design of a Piezoelectric on Silicon Microrobot", Industrie Symposium, IEEE, 1989. Tabib-Azar M., Microactuators Electrical, Magnetic, Thermal, Optical, Mechanical, Chemical and smart structures, Kluwer Academic Publishers, Series Editor: Harry L. Tuller. Thorpe J., Steenson D. and Miles R., "High frequency transmission line using micromachined polymer dielectric", Electron. Lett. 1237-1238, 34, 1998. Yeh R, Kruglick E. J. J., Pister K., "Surface Micromachined Components for Articulated Microrobots",J. MicroelectromecanicalSystems, Vol. 5, No 1, March 1996. Yeh R. and Pister K., "Design of Low-Power Articulated Microrobots", Proc. International Conference on Robotics and Automation, Workshop on Mobile Micro-Robots, San Francisco, April 23-28, pp. 21-28, 2000.

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Yeh R., Pister K., "Low Power Actuators for Autonomous Microrobots", IROS'OO Workshop Presentation, 2000. Yeh R., Pister K., "Integration of Foundry and Custom-fabricated Microrobotic Components", IROS'OO Workshop Presentation, 2000. Zhang J., Tan K. L., Gong H. Q, "Characterization of the polymerization of SU-8 photoresist and its applications in micro-electro-mechanical systems (MEMS)", Polymer testing., Vol. 20, No. 6, pp. 693-701, 2001.

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Chapter 8

A New Method for High Resolution Position Measurement at Long Range Christine Prelle, Frédéric Lamarque and Pierre-Emmanuel Mazeran Université de Technologie de Compiègne, Laboratoire de Mécanique Roberval, Compiègne, France

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1. Introduction Miniaturisation for machines and robots is required in case of reduced environments or to save energy. Our approach considers the positioning function because it is present in many systems. We expect to design a device with a size about 30 cm3, allowing a millimetric range displacement with a nanometric resolution for positioning. The main components of this miniature device are actuators, sensors and a mechanical structure. This paper only concerns the sensor. Commercially available sensors having a nanometric resolution can be separated into two categories: - small size sensors but having a limited range. For example, capacitive position sensors are able to measure displacement with a subnanometer resolution but with a 100μm maximum range, - high range sensors but with prohibitive size. For example, Heidenhain propose an optical linear encoder (LIP 300 series) for measuring steps up to one nanometer. The size of the sensor head is (55mm x 33mm). Laser interferometer position sensors are often used for accurate measurements but classical interferometers are big devices placed far from the mini-system. Several techniques are studied in different laboratories. An inductive sensor (Velten, 1999) has been studied. The size 18mm x 3.2mm is interesting but the resolution is not mentioned (<550μm). A high resolution miniature encoder has been studied (Jourlin, 2000). It is based on the diffractive inteferometric grating rule. With a 30mm size and a 125nm resolution, it is capable of long range measurement. After interpolation, it is possible to obtain a 2nm resolution (Jourlin, 2001). With the same kind of technique, an optical micro encoder using a vertical cavity-emitting laser has been studied. The encoder chip size is approximately 1.5mm x 2.0mm x 0.6mm and the measurement resolution is 0.1μm (Miyajima, 1998). In our laboratory, an optical sensor with nanometric resolution has been developed (Wang, 1999). The first section describes principle and performances of the sensor. The second explains how to transpose the axial resolution of the sensor in lateral resolution and the limitations of that transposition. The next part presents first experimental results. Then, in the last, a technique using the transposition coupled with a grating is presented with first experimental results.

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2. Fiber optic sensor 2.1. Principle The head of the sensor consists of a 5 fiber optics bundle (Figure 1).

Figure 1. Cross-section of the sensor

The emission fiber placed in the centre emits light on a flat mirror. The light reflected by the surface is injected into the reception fibers placed around the emission fiber (Figure 2). The amount of reflected light detected is a function of the distance between the sensor and the surface. The size of that fiber optic sensor head is 2mm in diameter and 10mm long.

Figure 2. Principle of the sensor

2.2. Performances Different kind of sensors have been tested (Wang, 1999), particularly with different signal conditioning modules. The sensor responsivity depends on the reflection coefficient of the moving surface. The higher the reflection coefficient, the better the signal to noise ratio is. A typical sensor response is shown in Figure 3.

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Figure 3. Sensor response

The rising part of the curve corresponds to the best linear responsivity domain. This rising part is about 400 (μm but for a 0.1% linearity the range is restricted to 80 (μm. In that case, the sensor axial resolution is 1.6nm rms. An application of this sensor is for example profilometry (Alayli, 1998) with a 300μm lateral resolution. So, for a nanometric positioning, the maximum range (400μm) is too small. The next paragraph will explain how to change the sensor configuration to improve the range of measurement.

3. Lateral position measurement 3.1. Principle A tilted mirror is used to transpose the axial resolution into lateral resolution (Figure 4). In that configuration, the optic axis of the sensor remains perpendicular to the moving surface but the displacement vector is no more perpendicular to the surface.

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Figure 4. Measurement principle

Let us define Ra as the axial resolution, R1 as the lateral resolution and a as angle between the mirror plane and the displacement direction. The simple relation between the axial resolution and the lateral resolution is shown in [1]:

We see that to obtain a complete transposition of the axial resolution into a lateral resolution, we should have α = 90°. Of course this is an extreme case which is note physically interesting because it corresponds to the previous configuration (section 2). So we have to make a trade-off between the highest resolution and the largest range. For example, if the sensor is used in the configuration described in the paragraph 2 (Ra=1.6nm) and if we expect R1= l0nm, the optimal angle allowing a maximal range is α = 9.2°. Taking into account a 0.1 % linearity criterion, the range of the sensor increase from 80 μm (α = 90°) to 500µm (a = 9.2°). A good trade-off is to choose a = 45°. In that case, R1=2.3 nm and the maximal range is 113µm.

3.2. Experimental results 3.2.1. Experimental increase of range Experiments have been carried out to show the range improvement using a tilted mirror. For a simple alignment procedure, experiments have been carried out with α = 45°.

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A mirror is placed on a linear displacement table (straightness: 0.3µm/120mm) so that the normal vector of the mirror surface remains at a 45° angle with the displacement vector. The fixed fiber optic sensor is placed so that its optical axis is perpendicular to the mirror surface (Figure 5).

Figure 5. Experimental set-up

At the table where is placed the mirror is moved by 10 µm steps. For each position, the sensor voltage is recorded. Measurements have only been carried out on the rising part of the characteristics where the responsivity is maximum. Figure 6 shows a comparison between the sensor response when it is used in the two following configurations: - the normal vector of the mirror surface and the displacement are in the same direction, - the angle between these two vectors is equal to 45°. These two configurations will be respectively called "a = 90°" and "α = 45°" configuration. The best linear characteristics, by means of mean square calculation, have been computed for each response. A 1% linearity criterion has been chosen. With such a criterion, a linearised characteristic can be used on a 200 µm range for the first case and 280µm range for the second one. The responsivities are respectively 25.7mV/µm and IS.0mV/µm. It allows us to verify the theoretical angular position of the mirror (45°). Experimental responsivities lead to a 44.5°±0.5° angle. Uncertainty is explained by the angular errors during the optical alignment procedure.

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Figure 6. Comparison between "α = 90°" configuration (*) and "a = 45°" configuration (.) with a 1% linearity criterion

3.2.2. Experimental resolution A second experiment has been carried out to show the experimental sensor resolution. The mirror is now mounted on a piezo-actuator having a 15µm stroke with a high resolution (0.15nm). The sensor responsivity has been changed to improve the resolution of the measurement. Figures 7 and 8 show 10.0nm steps detected in the two sensor configurations. In the "a = 90°" configuration, the measurement is noisy but 10.0nm steps are easily detected.

Figure 7. 10 nm steps in "a = 90°" configuration

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Figure 8. 10 nm steps in "a = 45°" configuration

In the "a = 45°" configuration, for the same piezo-actuator signal (10 nm steps), measurement is more noisy than in the previous configuration (Figure 7), but still detected. As a matter of fact, in that configuration, a 10.0nm piezo-actuator step is detected as a 7.1 nm displacement of the mirror and the resolution is 2.3nm instead of 1.6 nm in the "a = 90°" configuration. Thus the measurement is closer to the sensor resolution. So, the "a = 45°" configuration allows a 40% wider range with a 2;3nm resolution that is in accordance with our goal to increase the range while keeping a resolution in the 10.0nm order of magnitude. A way to increase widely the range of the sensor for a given nanometric resolution is to use a grating instead of a flat mirror in order to get a periodic measurement on a long stroke. This new configuration will be described in the next part.

4. Long range sensor 4.1. Principle The previous method using a tilted mirror is limited due to the loss of responsivity when the distance between the sensor and the mirror becomes too large. The idea to solve that problem consists in using a grating with a triangular shape (Figure 9).

Figure 9. Triangular grating

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The use of this grating allows one to increase theoretically the range to the length of the grating. If the grating, fixed on the mobile part of the system, is moving to the left from the point A, the distance between the sensor head and the surface will increase. The measurement, when the sensor is in front of the point B, is the same as the one at the point A. So between the points A and B, we recognize the configuration shown in Figure 4. The measurement range is greater than the one obtained by the tilted mirror technique due to the periodicity of the measurement. The grating form and its period have to be chosen taking into account several parameters (Figure 10):

Figure 10. Grating parameters

- α determines the resolution, - h should not exceed the range of the sensor, - (3 should be a right angle in order to have an edge as small as possible, - the numerical aperture and the diameter of the emission fiber core should be as small as possible and at least smaller than 1. Now, the diameter of the emission fiber core is 500µm and the numerical aperture is 0.46. Then this fiber optic sensor is not suitable for experiments with commercial gratings. As a matter of fact, the illumination zone is too large compared with length 1 (Figure 10). So we machined our own grating.

4.2. Experimental results In order to validate the grating principle, experiments have been carried out using an aluminium grating machined by conventional machining (Figure 11). Parameters of the grating are: a = 20°, h = 250µm, 1 = 687µm, β = 90°, grating length: 11.7mm.

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Figure 11. Experimental gratinging

Teeth surface has been observed with a ZYGO NewView 100 interferometric microscope. The surface is homogeneous and the roughness is 0.6µm rms (Figure 12).

Figure 12. Surface roughnessess

Experiments have been carried out using a 0.3µm/ 120mm straightness table to move the grating at the speed of 155µm/s. The position in the displacement direction is measured using an optical linear encoder (Heidenhain LIP 401). At the same time the position measured by the fiber optic sensor is recorded. The upper graph in Figure 13 is the experimental axial position measured by the fiber optic sensor versus the lateral position measured by the linear encoder. On the middle graph is shown the theoretical result. So, we observe the expected periodic signal due to the repetition of the tilted planes (teeth). Of course, the experimental result looks different. This is due to the edge crossing problem. The illuminated zone will never be infinitely small even if the fiber optic sensor conception is optimised. Then when the sensor measures around the edge, the reflected light is coming from two teeth during the transition (Figure 14). That is why the lower graph of Figure 13 represents the selected part of the theoretical result corresponding to the domain where the illuminated zone is on one tooth. If we just consider this selected part it is possible to compare the slopes. The experimental and theoretical slopes are respectively 0.40±0.03 and 0.37±0.03. The

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difference between the two slopes is mainly due to the grating machining which is not precise enough (roughness and geometric parameters) for our application. Nevertheless, this experiment allows one to validate the principle of a periodic measurement on a 11.7mm range.

Figure 13. Axial position versus lateral position

Figure 14. Illuminated surface at an edge crossing

4.3. Discussion There are many ways to improve these first results. For example, an aluminium grating obtained by diamond tool machining will improve the resolution due to the mirror like roughness of the teeth and improve the measurement linearity due to better flatness of the teeth.

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At the edge crossing the measurement is not usable then the resolution is lost. To avoid that problem, two fiber optic sensors will be used (Figure 15).

Figure 15. Improvement of the systemtem

The distance between the two sensors should be different from the grating period in order that the two sensor heads do not cross an edge at the same time. In fact, that distance has to be computed taking into account the grating period and the size of the illuminated zone. The signal processing module counts the edges and synchronises the measurement on the first sensor or on the second one according to the grating position. In this way a measurement is available at any time during the movement and the limitation of the sensor range is the grating length minus the space between the two sensor heads. Optimising the distance between the sensor head and the grating, decreasing the emitting fiber core and the fiber numerical aperture, the results of the Figure 13 can be improved such that the available part of the signal on each tooth is increased. Thus, when the measurement is available at least on half of the tooth, the two-sensor solution is usable.

5. Conclusions A novel use of a fiber optic sensor has been studied. This miniature sensor has a nanometric axial resolution on a small range. We have shown that it is possible to improve the range, only changing the angle between the displacement vector and the optic axis of the sensor, while keeping a resolution below 10nm. Besides, the idea of a periodic measurement to get long range is demonstrated on an 11.7mm long grating. To get high resolution on a millimetric range a two-sensor measurement technique using a high precision machining process for the grating is proposed.

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Acknowledgements Thanks to Jean-Louis Miramand (atelier de prototypage en micromécanique, unité INSERM 483) for the grating machining.

6. Bibliography Alayli Y., Wang D. and Bonis M, "Optical fiber profilometer with submicronic accuracy", SPIE, 3509, pp. 84-87, 1998. Jourlin Y., Parriaux O., Jay J., Noullet J.L., Arguel P., Fourment S., Lozes-Dupuy F., Sarrabayrouse G., "Codeur optique miniature haute resolution", 1er Colloque Francophone "Méthodes et Techniques Optiques pour l'Industrie", Biarritz (France), November 21-24, pp. 208-313, 2000. Jourlin Y., Pigeon F., Parriaux O., Bonis M., Top9u S., Alayli Y., "Double read head for the measurement of differential effects on a grating scale", Proc. of second Euspen international conference, Turin (Italie), pp. 534-537, 27-31, May 2001. Miyajima H., Yamamoto E., Yanagisawa K., "Optical micro encoder with sub-micro resolution using a VCSEL", Sensors and Actuators A, Vol. 71, pp. 213-218, 1998. Velten Th., Stephan D. and Obermeir E., "Micro coil with movable core for application in an inductive displacement sensor", Journal of micromechanics and microengineering, Vol. 9, pp. 119-122, 1999. Wang D., Conception et réalisation d'un minicapteur de déplacement a fibres optiques de resolution nanométrique, Thèse de doctorat, Université de Technologie de Compiègne, 1999.

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Index biological objects, force study applied by planar micromanipulator 59 et seq, 66 simulations and experimentation 68 cell manipulation 60 flow cytometer 60 laser trapping 60 Delta3, ultra-high precision robot, flexure mechanism 73 et seq example 82 mechanical structure 78 distance calculation 34 elastic joints 74, 76 electrothermal Ni-Si microlegs 90 fabrication 91 second generation (SU8-Si) 95 third generation (antagonistic SU8-Si bimorphs) fingertip manipulation tasks 15 et seq fitness function 7 flexure joint based mechanism 74 high precision, control of 81 grasp stability 26 LMS mechanical hand 15 et seq control architecture, strategy 18 motion strategy 20 object-finger contact modeling 21 realisation 17 manipulation task, realization 26 manipulator 61 behavior in water 62 microrobot (Delta3), flexure mechanism 73 et seq insect-like 87 legged 88

obstacle detection, omni-directional 31 et seq geometrical errors 38 principles 32 real environment 41 system 33 normal sit-to-stand movement 8 normal squat-to-stand movement 11 foot forward 10 with knee disability 9 position measurement, high resolution at long range 105 et seq fiber optic sensor 106 lateral position measurement 108 long range sensor 112 robots mobile, holonomic and nonholonomic 32 mobile, localization using reflective marks on ceiling 45 et seq detection 49 LED configuration 55 localization 48 position system 46 omnidirectional 32 stance robot, model 2 et seq genetic approach, algorithm 6 standing movements, trajectory generation 1 et seq thermal actuated microlegs, prototypes 87 et seq wireless micromanipulation system (WIMS) 61