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Eindhoven University of Technology

MASTER

Smart memory alloy actuated slave system for medical robotics, with haptic feedback

Franken, M.

Award date:2003

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Smart memory alloy actuated slave system for medical robotics, with haptic feedback.

M. F'ranken DCT Report nr. 2003.50

11th June 2003

Master's thesis

Coaching:

dr. ir. I.M.M. Lammerts prof. dr. ir. M. Steinbuch

Eindhoven University of Technology

Department of Mechanical Engineering

Section of Control Systems Technology

Summary

Technical applications in the medical field are rapidly developing. One of the developments has been taken place in minimal invasive surgery. Medical robotic master-slave systems have been designed to provide the possibility to perform minimal invasive surgery easier than with conventional minimal invasive tools. However, the main drawbacks of these systems: they are, h g e , expensive and hme ne haptic feedback (in other words, the surgeon does not feel what is touched).

In this report1 a 1 DOF master slave system for medical robotics with haptic feedback is designed. The new slave system is actuated, by two antagonistic wires (1 DOF: the opening and closing of a grasper) made from a Smart Memory Alloy (SMA). SMA actuators have a high force-volume ratio, which makes it possible to produce smaller and lighter instruments. Prototypes of active tools that are actuated by SMA in its bending direction have already been developed earlier.

The working principle of SMA is based on the shape memory effect that needs heating to make the strained SMA go back to its initial shape. Unfortunately, this effect results in large response times and may lead to heating of tissue. In this final project, the slow response of the SMA is encountered by a second, antagonistic SMA wire. Furthermore, initial experiments have been performed with forced cooling to increase the bandwidth of the system. By simulating the heat transport mechanisms in the living tissue, the heating process and the effect on the human body have been investigated.

For haptic feedback, the delivered force at the slave side is reconstructed and fed back to the master manipulator. This grasping force can be measured with a force sensor, but unfortunately the force sensor is far too big to be integrated in a MIS tool that needs to be inserted in the human body. Therefore, in this research project the force delivered by the slave system is predicted on the basis of a (non-linear) model of the SMA wires and of the rest of the dynamical system. Experiments have been performed in which the predicted force is compared with the measured force.

On the basis of this research, it can be concluded that SMA actuators can possibly be used for surgical interventions inside the human body. Furthermore, the first step has been made in realizing a small and "smart" master-slave 1 DOF robotic system for medical applications, which enables the surgeon to feel the reaction forces of the touched environment.

l ~ h i s research project is part of the research performed in the bio-robotics group of the department of mechanical engineering in collaboration with the department of biomedical engineering (http://www.bmt.tue.nl/biorobotics)

Samenvat t ing

De ontwikkeling van technologische toepassingen op medisch gebied gaan in een snel tempo. Een van de toepassingen is de ontwikkeling van medische robot systemen voor minimale in- dringende chirurgie. Meester slaaf robot systemen worden ontworpen om de taak van de chirurg beter uitvoerbaar te maken dan met conventionele hulpmiddelen. Echter, het groot- ste nadeel van deze systemen is het feit dat ze greet,, duur er, gem f,erugkappeling van gevod hebben. Met andere woorden, de chirurg is niet in staat om te voe!en wat er aangeraakt wordt.

In dit verslag2 wordt een meester slaaf system, met 1 graad van vrijheid namelijk het openen en dichten van een grijper, met terugkoppeling van gevoel ontwikkeld. Het nieuwe slaaf systeem wordt aangedreven door twee antagonistisch geplaatste draden, gemaakt van geheugenmetaal (in dit geval nitinol). Nitinol heeft een hoge kracht-gewicht verhouding en dit maakt het mogelijk om kleinere en lichtere instrumenten te maken. In eerder onderzoek zijn er a1 pro- totypen van active buigende hulpmiddelen ontworpen.

Het principe van het gebruik van geheugenmetaal, is gebaseerd op het 'shape memory effect' waarbij verwarmen leidt tot het terugkeren in de oorspronkelijk vorm van het materiaal. Omdat dit effect gebaseerd is op het verwarmen van het materiaal, leidt dit inherent tot trage systemen en tot opwarmen van weefsel, wanneer dit in het menselijk lichaam gebruikt wordt. De lage snelheid van het systeem wordt gedeeltelijk gecompenseerd door de aanwezigheid van de antagonistische actuator. Verder zijn er initiele experimenten uitgevoerd waarbij gekeken is of dat de snelheid van het systeem verhoogd kon worden door active koeling. Het warmte transport van het menselijk lichaam is gesimuleerd om zo meer inzicht te verkrijgen in het effect van het verwarmen van een draad in het lichaam.

Om het gevoel te reconstrueren is het nodig om de kracht die wordt uitgeoefend op de omgeving te weten. De kracht kan gemeten worden door krachtsensoren, helaas zijn deze te groot om te worden gei'ntegreerd in een systeem dat het lichaam in moet. Er is daarom gekozen om de kracht te schatten met behulp van een (niet-lineair) materiaal model. Experimenten, waarbij de geschatte kracht wordt vergelijken met de gemeten kracht, geven goede resultaten.

Op basis van dit werk, kan worden geconcludeerd dat geheugenmetaal gebruikt kan worden als mogelijke actuator voor chirurgische instrumenten in het menselijk lichaam. Daarnaast, is de eerste stap gemaakt met het koppelen van een klein, 1 graad van vrijheid, meester slaaf robot systeem for medische toepassingen. Dit zal de chirurg de mogelijkheid geven om de kracht te voelen die is geleverd als reactie kracht door de omgeving.

2 ~ i t onderzoeksproject is een onderdeel van het onderzoek uitgevoerd binnen de bio-robotica groep verbonden aan de faculteit werktuigbouwkunde in samenwerking met de faculteit biomedische technologie (http://www.bmt.tue.nl/biorobotics)

Contents

Summary i

Samenvatt ing ii

Contents iii

1 Introduction 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Minimal invasive surgery (MIS) 1

. . . . . . . . . . . . . . . . . . . . . . . 1.2 Current master-slave systems in MIS 2 . . . . . . . . . . . . . . . . . . . . . 1.3 Problem definition and a project survey 3

I Design and control of a 2-SMA actuated slave system 5

2 Shape Memory Alloy in medical applications 7 . . . . . . . . . . . . . . . . . . . . . . . 2.1 The thermal shape memory behavior 7

. . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Passive Shape Memory Alloy 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Active Shape Memory Alloy 9

. . . . . . . . . . . . . 2.4 Discussion: SMA as actuator in medical applications ? 11

3 Active SMA in a human body ? 13 . . . . . . . . . . . . . . . . . . . . . . . 3.1 Global warming of the human body 13 . . . . . . . . . . . . . . . . . . . . . . . 3.2 Local heat transfer within the tissue 13

. . . . . . . . . . . . . . . . 3.3 Temperature simulation outside the human body 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Forced cooling 17

. . . . . . . . . . 3.5 Discussion: SMA for medical applications in a human body 18

4 Design of a 2-SMA actuated slave system 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Demands and requirements 19

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Final slave system 20

5 A model of the 2-SMA actuated slave system 23 . . . . . . . . . . . . . . . . . . . . . 5.1 Constitutive material model for a SMA 23

. . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Model of the dynamic system 26 . . . . . . . . . . . . . . . . . . . 5.3 A solving method for the non-lineair system 26

. . . . . . . . . . . . . . . . 5.4 Constitutive material model for force simulation 28

6 Controller tuning in frequency and time domain 31 . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Linearized system transfer function 31

. . . . . . . . . . . . . . . . . 6.2 Time responses in experiments and simulations 33

CONTENTS

I1 A Master Slave system with haptic feedback 37

7 Haptic feedback in medical robotics 39 7.1 Haptic Sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

8 Coupling the master and slave manipulators 4 1 8.1 The master manipulator system . . . . . . . . . . . . . . . . . . . . . . . . . . 41 8.2 Control strategies for bilateral actuation . . . . . . . . . . . . . . . . . . . . . 42 8.3 Time responses of the coupled master slave system . . . . . . . . . . . . . . . 43

9 Conclusions and recommendations 45

Literature 47

A First order DV for heat development in wire 49

B Simulation results for 1 SMA wire 51

C Control scheme implementation in Simulink 57

D Smart memory alloy selling companies 65

Chapter 1

Introduction

Current surgery is more and more performed with high-tech accessoires, even some kinds of surgery, like Minimal Invasive Surgery (MIS), could not be performed without technical accessoires. This development leads to advantages for patients, but not all of these developments are positive for the surgeon. This first chapter gives an introduction in minimal invasive surgery, the advantages and the withdrawals. Furthermore it discusses the current problems with .the high-tech medical robotic systems for MIS. In the last section a new technical solution is proposed together with a survey of this report.

1.1 Minimal invasive surgery (MIS)

Minimal Invasive Surgery, also called 'keyhole surgery' is more and more often performed in the operation room (OR). Special instruments are inserted (Invasive) through 3 B 6 small incisions, which vary in size from 5 [mm] to 12 [mm] (Minimal). Through one of the incisions, a small telescope is inserted into the cannula. In this way a 2D visual image is created and visualized on a monitor outside the body. Often, one of the other incisions is used to introduce a gas or liquid to create more space in the human body. Additional ports are typically required to place special instruments to operate with, such as a grasper (figure 1.1). Already many kinds of surgery are being performed, utilizing this technique with good results in gynecology, general, pediatric, chest, orthopedic, urology and vascular surgery.

Because the incisions are relatively small, the benefits for the patient are enormous: the body trauma is reduced, there is a shorter anesthesia time, there is often less blood loss and less post-operative pain and discomfort. Furthermore the patient can be relatively quickly active again, hence leading to less costs and a shorter hospital stay and a decrease in waiting lists.

Figure 1.1 : A laparoscopic forceps

However, the advantages for the patient have some counter effects for the surgeon. By performing 'keyhole' surgery, the surgeon can no longer use skills that were easily applied with open surgery. Performing MIS results in a reduced quality of the visual information: in stead

1.2. CURRENT MASTER-SLAVE SYSTEMS IN MIS

of looking direct at the operated area the surgeon has to look to a 2D video screen. The freedom of movement in the body of the patient is decreased, and the surgeon can no longer touch and feel the tissue, bone or organ with his hands. To overcome these problems, medical robotic systems have been developed: they will be discussed in the following section.

1.2 Current master-slave systems in MIS

For today's operation rooms, two medical robotic master-slave systems are commercially available, the $a vinciT" system (figure 1.2) and the Zeus@ surgical system (figure 1.3). Both systems consist of an ergonomic master console, where an upscaled reconstructed 3D image of the operated area of the human body is projected. At the master console of --

the Z K s @ t h e surgeon Fan iGi%rol the slave robot with two joysticks and uses voice control to position the camera. In the davinciTM, on the other hand, the surgeon uses two scissors- like-joysticks for the remote controlling of the slave. Figure 1.2: The da vinciTM system [15]

When the surgeon touches a button with his/her feet the slave system stops and the joysticks can be used to position the camera. The slave part of both systems consists of several robotic arms: 1 arm for positioning the camera, the other robotic arms are carrying surgical tools (like graspers, scissors and needles). These robotic arms have 7 degrees of freedom: 3 translations, 3 rotations and 1 open/close movement.

Part of the problems that were present during conventional minimal invasive surgery, are solved using these robotic systems. The surgeons position is more ergonomic, his/her movements are down scaled and the image is enlarged and is 3D reconstructed from a 2D image. Nevertheless, using a medical robotic system introduces new problems: in stead of using small, cheap MIS tools a huge and expensive system fills the OR. Further- more, the medical robotic systems have a total lack of haptic feedback hence, the surgeon

Figure 1.3: The Zeus@ surgical system misses the total sense of physical touch.

1.3. PROBLEM DEFINITION AND A PROJECT SURVEY

1.3 Problem definition and a project survey

Current medical robotic master-slave systems have the following disadvantages: 1: They are large, expensive and heavy.

2: Only visual information is send back to the master system and no information about viscosity and stiffness of the touched tissue, bone or organ reaches the surgeon.

During this final project, a smal 1 DOF slave manipulator has been developed and integrated in a master-slave system. T i e master and slave manipuiators wiii be coupled in such way that force feedback is present in the total system. Part I of this report handles the design, actuation and control of a small 1 DOF slave system that represents the opening and closing tip of a gripper (figure 1.1). In Past I1 the new developed slave manipulator will be integrated with a 1 DOF master manipulator to a master-slave system with force feedback.

Since especially the slave system has to be small, Smart Memory Alloy (SMA) has been chosen to actuate the slave system, in stead of for instance electro motors. Smart memory alloy has a high force-to-weight ratio: for example, a SMA wire of 0.1x0.6 [mm2] can provide forces up to 30 [N]. Therefore, the actuator can be placed almost anywhere, which makes it very suitable for small medical applications. In chapter 2, an overview of smart memory alloy in current medical applications is given, as well as related research projects. Actuation of SMA is based on the thermal shape memory effect: strains up to 7 % can be recovered after a phase transformation, that is initiated by heating the material. The actual working principle of a smart memory alloy is discussed in the first section of chapter 2. Since cooling of the material to room temperature will not leed to a deformation, SMA is only capable of actuation in one direction. Hence, for a grasper an antagonistic force is needed: a second smart memory alloy wire is used to actively move in the other direction. The slave system of the gripper is designed in chapter 4. SMA wires that are actively used, can reach temperatures up to 100 O C . If one wants to use this inside the human body, it can result in severe and irreversible damage. Therefore a feasibility study of the effect of using SMA's inside the human body is presented in chapter 3. Also, the effects of insulation and active cooling will be discussed in this chapter. The phase transformation of the material leads to a highly non-lineair behavior, in chapter 5 a model for this behavior and the total dynamic system is derived. With this model it is possible to predict and simulate the force delivered by the actuators, i.e. large and expensive force sensors no longer needed. The derived model results, in chapter 6, in tuning of the controller. In this chapter results of experiments and simulations are presented and discussed.

Part I1 discusses the realization and control of the coupled master-slave system with haptic feedback. In chapter 8, the slave system that is designed in Part I is coupled to the master system that was already available [13]. After a brief discussion of haptic feedback, the control strategy and results are discussed.

Finally, in chapter 9 the conclusions and recommendations for further research are stated.

1.3. PROBLEM DEFINITION AND A PROJECT SURVEY

Part I

Design and control of a 2-SMA actuated slave system

Chapter 2

Shape Memory Alloy in medical applications

Superelasticity and the thermal shape memory behavior are two properties of Shape Memory Alloys (SMA) that make them very useful for a variety of applications. After an introduction in the material behavior in section 2.1, a selection of medical and industrial products with SMA will be discussed.

2.1 The thermal shape memory behavior

Plastic deformed shape memory alloys can return to their original shape by heating, this effect is called 'thermal shape memory behavior'. This effect is based on the principle of a phase transformation in the alloy and strains up to 8% can be recovered. The alloy that is mostly used as shape memory alloy consists of nikkel and titanium (Nitinol), with some additional alloys to specify the desired material properties; other commercial important alloys that are used are CuZnAl and CuAlNi. In this report, nitinol is used as actuator alloy.

(a) Phase transformation during deformation and heating (b) Shape memory and superelasticity

Figure 2.1: Working principle of Shape Memory Alloys

Figure 2.l(a), shows a schematic representation of the shape memory effect and the corresponding phase transformation. When the original SMA (that has an austenite crystal structure) is deformed at room temperature (M, < O,,,), the the martensite growth in the

2.2. PASSIVE SHAPE MEMORY ALLOY

material is induced until the material has a complete martensite structure. By increasing the temperature of the alloy above the point As (Austenite start temperature), the extra energy leads to austenite formation which means that the alloy is changing phase and returning to its original shape, at point Af (Austenite Finish temperature). Cooling back to room temperature Ms < @,,,,, leaves the material in its stable austenite phase, the cycle can be repeated and makes SMA a possible actuator. In figure 2.l(b) the corresponding process is illustrated with help of typical stress-strain curves at different temperatures. Since the material is not capable of an active delivery of negative forces, the hysteresis curve at lowest temperature is dashed when being negative. When applying a load the stress strain behavior will follow the lowest curve, this result in a plastic deformation, (assuming that the load was big enough). Removing the load results in a plastic deformation that is placed in figure 2.l(b) at the lowest curve crossing the x-ax. If the material is heated, the curve representing the stress-strain behavior of the material is moving upwards. The point where this curve is> crossing the x-ax is moving to the left and the deformation decreases. When the material is heated so much that the complete hysteresis curve has moved above the x-as, the original shape is recovered.

If one wants to use the thermal shape memory effect, it is necessary that Ms < 8,,,, < A j because in that case the hysteresis curve is partly crossing the x-ax. If the Af 5 8,,,, the curve is completely placed above the x-ax and no actuation by heating is possible. Straining and relaxing the wire will result in a complete walk through of the hysteresis curve, this effect is called 'superelasticity'. This effect is shown in the upper hysteresis curve in figure 2.l(b), where Af < 8,,,, and the phase is completely austenitic.

A SMA actuator is only capable of active actuation in one direction, which is called the 'one way shape memory effect' (OWSME). Unlike the normal shape memory effect and the superelasticity, the two way shape memory effect (TWSME) is not a SMA property but an ability which can be obtained by a mechanical and thermal treatment ("training") of the SMA. The difference with the normal shape memory behavior is that, due to the treatment, the material has a stable shape in the martensite phase as well as in the austenite phase. There is no external force needed to induce a shape change, whereas changing from one phase into the other will also result in a shape change [lo]. In this report, a nitinol wire with the OWSME and an antagonistic nitinol (OWSME) wire as external force are used as actuators.

2.2 Passive Shape Memory Alloy

The superelasticity makes the material extremely useful for applications in Minimal Invasive Surgery (MIS). Surgeons can pass complex instruments through a cannula, and have the instruments elastically return to the deployed configuration once through. Elasticity is used in flexible tools, right angle needles, suture passers, retractors, graspers, baskets (figure 2.2(a)), retrieval bags and flexibel scissors (figure 2.2(b)). An other advantage of smart memory alloy is the fact that it can apply a constant stress over a wide range of shapes, which makes the material useful for orthodontic and bone corrections (figure 2.2(c)).

2.3. ACTIVE SHAPE MEMORY ALLOY

(a) 3 baskets tools (b) Scissor (c) Bone An- chors

Figure 2.2: Different tools using SMA

An other well known example is the aortic stent graft (figure 2.3(a)), that is used to prevent an aneurysm (dilatation of the aorta) from rupture. The stent consists of several circular winded SMA wires that are compressed in a small (diameter less then 1 cm) delivery system. Through a small incision, the stent is delivered in the aorta. Once placed at the right position in the aorta, the stent expends, due to the elasticity property of the SMA, to its original size. Where it will fit exactly in the diameter of the aorta and prevents the aorta from rupture.

The second example next to the stent is the Simon Nitinol Filter (figure 2.3(b)). This Filter deploys under the thermal heat of produced by the body, to its original shape, i.e. the shape of the Filter before the deformation. This thermal shape memory behavior is used in paragraph 2.3 for the active actuation of robotic systems. Smart memory alloys are not only used in

(a) stent grafts (b) Simon Nitinol Filter

Figure 2.3: Tools that are inserted in the human body

medical applications, but are more and more used in smart consumer applications. Although SMA material is most common in wire form, it can be produced in a variety of forms (wire, tubes, plates, ribbon). A extensive overview of products that uses shape memory alloy, is given in table 2.2 151.

2.3 Active Shape Memory Alloy

Superelesticity as well as thermal shape memory behavior are material depended properties. The production process specifies which property is enabled Af < 8,,,, or Af > 0,,,, , i.e. the production proces specifies whether the superelesticity or the shape memory behavior can be used. The shape memory effect gives the possibility to use SMA as an actuator, since applying heat to the SMA results in a movement. There are several possibilities to apply heat,

2.3. ACTIVE SHAPE MEMORY ALLOY

Property Thermal Shape Memory Flexibility and Kink Resistance

Elastic Springback

Constancy of Stress

Table 2.1: Nitinol in different applications

I Eyeglass Frames I Stents

for instance by leading a cold or hot water flow along the wire. A more practical solution is to apply current, through the resistance of the wire this will result in a heat development.

Consumer Applications Actuators Fishing Lures Eyeglass Frames Cell Phone Antennas Cell Phone Antennas

Brassiere Wire

Elastic Deployment

Thermal Deployment

Biomechanical Compatibility Dynamic Interference Biocompatibility MRI Compatibility

Medical applications that are using SMA wires as actuators, are not yet introduced in the operation room neither are they commercially available. However, the wide spectrum of research with respect to SMA as actuator for industrial application and especially for medical applications, proves the potential of SMA as future actuator. SMA actuators have a high force-to-weight ratio and can therefore replace large and heavy pull systems with cables and motors and covering up less space. A catheter [6] actuated by SMA wires, as shown in figure

Medical Applications Hart Valve Tools Guidewires Endontic Files MIS tools Homer Mammaloke@ Needles Archwire

MIS Instruments Stents hingeless Instruments Baskets Stents Simon Blood Filter@ Bone Anchors Staples, Spacers Stents, Filters Implants Open MRI Instruments Needles

Figure 2.4: Multilink active catheter

2.4. DISCUSSION: SMA AS ACTUATOR IN MEDICAL APPLICATIONS ?

2.4 (2.4(a): initial position, 2.4(b): actuated position), can bend over an angle of 45". In [8], also a bending forceps for minimal invasive surgery is constructed and actuated by four SMA wires that are electrically heated. The bending is controlled by a ON-OFF control method in which the current on the 4 wires is either on or off. And in [7], a micro gripper joint actuator and a bending endoscope are developed and are temperature and position controlled. In [12], J.M. Peeters developed a SMA actuated gripper of a laparoscopic forceps. The gripper was actuated by one SMA wire that was deformed by an antagonistic force, in this case a passive spring. The gripper was controlled by a combination of a linear and non-linear controller.

Smart memory alloy wires are often called 'artificial muscles', which is logic concerning the fact that muscles contract reacting on electric pulses and need an antagonistic muscle to make a two way active motion. In [9], this 'artificial muscles' are used for the actuation of a prostheses for an arm. These initial experiments showed relatively large motions and the possibility for artificial limbs. In revalidation SMA actuators can be used as a lengthening device [lo], where a special device constructed out of SMA rings 'walking' along the bone, while applying a force on the bone in order to stimulate the growing proces.

2.4 Discussion: SMA as actuator in medical applications ?

Even though SMA is widely accepted in numerous passive applications, the use of SMA as actuator in medical and industrial products, has not yet come to its break through. However, the performed research shows the possibilities and advantages of SMA as actuators. Three problems still hamper a common use of SMA as actuator. The first of the three problems is the high power consumption, which leads to heat development. This can be undesired, especially when the actuators are used inside the body. The second problem is the heat dependency, causing the actuation rate to be relatively slow: a new actuation cycle can only be executed after cooling of the actuator. To check the possibilities of using active SMA in a human body and forced cooling to improve the actuation speed, some simulations and experiments are performed in chapter 3. Another possibility to improve the actuation speed is to work with an active antagonistic force, which is recommended in the work of Peeters [12], by using for example two antagonistic SMA actuators. The third problem is the highly non-linear behavior that leads to a difficult control. All of the three problems will extensively be discussed during this report.

2.4. DISCUSSION: SMA AS ACTUATOR IN MEDICAL APPLICATIONS ?

Chapter 3

Active SMA in a human body ?

SMA wires will be used as actuators for a MIS tool and, if possible, they will be used inside the human body. During the heating period of the SMA wire, the temperature of the wire can exceed 100 "C. In literature, it is assumed that it is possible to use SMA inside the human body; however no background of this assumption is found. Hence, it is still uncertain what the influence of the heating of the SMA will be on the human body. And therefore it has to be investigated what the global and local temperature effects in the human body will be when heating a SMA wire.

3.1 Global warming of the human body

The power that is put into the SMA wire can be described as:

re1 L Pgenerated = I ~ R with R = - A (3.1)

where Pgenerated is the generated Power by the wire, I is the electric current, R the total electric resistance of the wire, rel the specific electric resistance and L and A the length and the cross-sectional area of the wire respectively.

With, Re1 = 72e-8 [Rm] [4], L = 0.2 [m] and A = 0.1x0.6 [mm2], gives R = 2.4 [O], where experimental measurements gave 5.1 [R]. Using equation 3.1, with I = 0.5 [A], leads to a generated power of Pgenerated = 0.6 [W]. In comparison, the heat production of the total human body is about 87 Watt, therefore the global influence of the heating of the SMA on the temperature in the human body can be neglected, since it is only 0.7% of the total heat production. Nevertheless, the local influence of the heating process will be much more and needs more attention. To investigate the local effects, the heat transport through tissue is simulated in a numerical model.

3.2 Local heat transfer within the tissue

A model of the heat transport mechanism occurring in the living tissue has been formulated by H.H. Pennes in the so-called "bioheat equation" [I]. This differential equation describes the heat dissipation in a homogenous, infinite tissue volume.

3.2. LOCAL HEAT TRANSFER WITHIN THE TISSUE

Viscera

Body Elements

Abdomen (Cylinder)

Table 3.1: Modei parameter of the human body

v = 20°c

359' segment 1

segment 2

L cm

55.20

Figure 3.1 : Schematic representation of the passive system

Equation 3.2, consists of four terms that are discussed from left to right. The first term is the radial heat flow from warmer to colder tissue regions heat-conduction term, where Ic is the tissue conductivity [%I, 0 is tissue temperature [OC], r is radius [m], w is a geometry factor [-I; w = 1 for polar coordinates and w = 2 for spherical coordinates. The second term is a metabolism q, [%I, the extern heat production for instance when shivering. The third is the

blood perfusion heat-convection term, where p, is density of blood [$I, wbl is blood perfusion rate [$I, cbl is heat capacitance of blood [&I, and Obl. is arterial blood temperature [OC]. This combined effect is balanced by the storage of heat within the tissue mass, right-hand side of equation 3.2, where p is tissue density [3], c is tissue heat capacitance [&I and t is time [s] ) . [2]

Material

Viscera Bone Muscle Fat Skin

The bio-heat differential equation is implemented in MATLAB@ by F.E.M. Janssen [3]. The modelled part of the body is the abdomen, the lower part of the human torso. The abdomen is modelled as a cylinder (w = I) , with outer radius 12.60 [cm] and is divided in several layers that are representing the different tissues. From the center of the cylinder to the outside, the model consists of the following layers IVisceralBonelMusclelFatlSkinI. Every layer has its own tissue parameters, the material constants k, p,c, the basal heat- generation term qm and the basal blood perfusion rate wbl (table 3.1). To implement the SMA wire in the program, some adjustments had to be made. The first adjustment is adding a layer to the model that represent the SMA (r = 0.01 [cm]) . The order of layers will change to lvisceral bonelinsulationlsma - wirelinsulationlmuscleI f atlskinl , as shown in figure 3.1. The dimensions of the wire are small and the metabolism is high in respect to the surrounding tissues. When the wire is placed in the center of the simulation model, numerical problems are derived. To prevent numerical problems the wire is placed in the middel of the different tissues. The second adjustment is that the model is divided in two segments, one big segment

N

1 3 3 6 6

3.2. LOCAL HEAT TRANSFER WITHIN THE TISSUE

that is almost the complete abdomen so 359 " of the cylinder and a very small segment of 1 " of the cylinder. The segment of 359 ", has a metabolism that is equal to zero, no heat is developed in that part of the abdomen. The segment of 1 " is representing the heated SMA-wire and has a metabolism (q,) that correspond with a temperature of the wire that is realistic, between 35 and 100 "C. This is simply achieved by scaling the metabolism. Fur- thermore, only radial heat transport is present in the model, (g # 0, = 0, = 0). This may be assumed since the radial surface will be larger then the tangential surface. According to figure 3.2, a metabolism that result in a total heat production of 0.0174 [W] correspond to a temperature of the wire of 77 "C.

(a) Temperature response in time and posi- (b) Temperature deviation in steady state tion, heat production = 0.0174 W condition, heat production0.0174 W

Figure 3.2: Heat development, heat production = 0.0174 W

Because the temperature of the surrounding tissues that touche the wire, is equal to the wire temperature, insulation is advisable. However, insulating the wires will lead to reduced heat loss, i.e. with a heat production of 0.0174 [w , the wire temperature will be much higher with insulation then without. For instance to maintain the same temperature of the wire with insulation (r = 3 [mm]) , the input power only has to be 0.00906 [W] instead of the 0.0174 [W].

At a temperature of 55 ["C], human cells and tissue start to coagulate and the cells are destroyed, the temperature of 55 ["C] will therefore be set as the highest boundary. With a known insulation material and the above stated limitation, the maximum wire temperature can be calculated.

3.3. TEMPERATURE SIMULATION OUTSIDE THE HUMAN BODY

75 -

-70

$ 5 SO 0 m

2 40

E 30

20 0 2

0 2 o poslt~on [m]

(a) Temperature response in time and posi- (b) Temperature deviation in steady state tion, heat production = 0.00906 W condition, heat production 0.00906 W

Figure 3.3: Heat development with insulation, heat production = 0.00906 W

Figure 3.3 shows the temperature distribution through the different tissues. The most strik- ing characteristic is the high gradient (g) in the insulation material and in the tissues that are well provided by blood. During the simulation the SMA wire and insulation is located between the bone and the muscle part. The bone has almost no blood flow and has therefore no high gradient. Locating the SMA wire on another place, will have influence on the temperature distribution. It may also be clear that ,especially by the effect of blood perfusion, the high temperatures caused by the heating are a local effect.

Now it is clear that insulation is needed to prevent tissue damage, real time experiments can be performed. The SMA wire is placed in a perspex insulation tube, with an inner radius of 1.5 [mm] and an outer radius of 3 [mm]. The wire is not directly in contact with the insulation material and the total setup is placed outside the body. The wire is heated with an input of 1 [A] and the outer side of the insulation is touched by the index finger. During the heating time, the insulation material is touched without experiencing an uncomfortable feeling.

3.3 Temperature simulation outside the human body

The heat balance of the wire can be defined as in equation 3.3, with the thermal parameters c [%]and T [s], depending on the surroundings but here treated as constants, see appendix A for more information.

From equation 3.3, the temperature of the wire can be computed as function of the input current I. However, the constants (T and c) are different in an insulated environment from the ones in a non-insulated environment. Next to insulation, forced cooling will also influence the thermal behavior and therefore the thermal parameters. The thermal parameters that are used in a non-insulated, non-cooled environment are shown in table 3.2.

3.4. FORCED COOLING

Table 3.2: Values for the thermal parameters

Of course, if one wants to know the exact temperature at a certain time point, the temperature should not be simulated but measured. The most common way to measure the surface temperature of an object is with the use of an thermocouple. However, this method will cause errors, due to the small dimensions of the wire. The measured input-output relation of current and temperature can probably be described by a first order differential equation. But the measured value will be lower then the real temperature, since it is an average between the temperature of the wire and its surroundings. A better method to find the real temperature will be by using an indirect or a non contact measurement. For instance by measuring the electric resistance of the wire for different temperatures in an oven. During such experiments, the measured resistance is a measure for the temperature. The resistance of a smart memory alloy is not only dependent on the temperature of the wire but also on the strain, or in other words the resistance is also a function of the shape of the material. Therefore, the wire should be placed with different strains and temperatures in an oven and a relationship of resistance as function of both stress and temperature can be derived. In this report the values that were shown in tabel 3.2 are used, and only the temperature simulation is used.

3.4 Forced cooling

A direct result of the time that is needed for a SMA actuator to cool down, is the low bandwidth. By using an antagonistic SMA actuator the actuation speed of the first 3 B 4 cycles will be higher, the second wire will heat higher and will pull at the still warm but cooling wire and vise versa. But at a certain point the maximum temperatures and maximum forces are reached. The only solution to increase the bandwidth of a SMA actuated system is to actively cool the wires. Initial experiments with the cooling of the wires were performed; the wires were placed into tubes with a constant air flow. The strain was held constant and a step input of 1 ampere was applied during 5 seconds. It was not possible to measure the temperature of the wires directly and therefore the force is measured which is an indication of the temperature. In figure 3.4(a) the measured force is plotted with different air flows against time.

The results can be divided in two parts: the heating and the cooling of the wire. It is clear that a higher air flow leads to more heat loss to the surrounding and therefore a lower temperature and a slower increase in temperature, (different rate of c and 7). In the second part it is clear that the cooling velocity, the gradient g, is higher when the air flow increases.

However another interesting and reproducible phenomenon, that can be noticed when heating the wire, is shown in figure 3.4(b). In this case a step input of 1.5 ampere was applied to the actuator during 5 seconds and removed at this point. Two strange effects take place, the first is the decrease in force at f 1 [s] and the second is the increase in force when the current is removed. Apparently, too high temperatures are leading to a decrease in force, since cooling of the material (after removing the current) will lead to an increase in force. This effect is most unwanted when controlling a mechanism using a SMA actuator, simply because the system can easily become unstable. Therefore, it is important and necessary that safety margins and boundaries on the maximum temperatures or inputs, are used to prevent the system to come in such an potentially unsafe configuration.

3.5. DISCUSSION: SMA FOR MEDICAL APPLICATIONS IN A HUMAN BODY

I 5 10 15

time [s] "0 5 10 15

time [s]

(a) Force delivered by SMA wire during (b) Measured force with high current input forced cooling

3.5 Discussion: SMA for medical applications in a human body

In this chapter different subjects with respect to the heating of SMA wires have been discussed. Using SMA actuators in different setups, with or without insulation, with or without cooling leads already to a change in behavior and response. Using the wires in the human body leads to even more difficulties. The temperature in the human body is around 37 "C, this has to be taken into account when using SMA wire, for examp le the transformation temperature has to be higher to actively make use of the SMA. By performing simulations, where a SMA wire was placed inside a human abdomen it became clear that, the insulation capacity of the human tissue, leads to a local heating effect. The blood perfusion causes a fast transport of heat trough the rest of the body. The total produced heat by the wire, that is transported is negligible in respect to the total produced heat by the human body. It can be concluded that insulation is necessary if active use over the complete temperature range is needed. And secondly to keep the tissue temperature below the coagulation temperature of 55 "C. An experiment showed that a perplex tube, with outer radius of 3 [mm], can be a good insulator. Active cooling to increase bandwidth of a SMA and to decrease the surrounding tissue temperature is promising. These simulations and small experiments showed also that it may be possible to use SMA as actuators in medical applications. They also showed that more experiments and simulations are needed to discover the exact temperature behavior, by for instance performing temperature measurements.

Chapter

Design of a 2-SMA actuated slave system

A complete new gripper, that is suitable for medical robotics, has to be designed. In this chapter the design criteria are discussed with respect to a list of demands and requirements. According to these criteria, a final design of a gripper is made and presented in paragraph 4.2.

4.1 Demands and requirements

The main design criterion for making a gripper that is suitable for medical robotic goals, is the demand that the gripper must be very small. The diameter of the tool need to be less then 12 mm, since it is inserted in the human body through holes that have such a diameter. Because a SMA wire can only be active in one direction, an antagonistic force is necessary to move in the opposite direction. A second SMA wire is chosen as antagonistic actuator, a passive spring could also serve as counter force but eliminates the possibility to move actively in both directions and will probably be slower. Actuation by 2 SMA wires need a different scissor mechanism than the current mechanism used in 1121, which has two moving blades actuated by one SMA wire and a passive spring. The scissor-like movement of the blades consists now of one, to the world fixed, blade and one moving blade that has connection points for the SMA wires. The moving blade is running in bearings to minimize friction and contact area between the moving and fixed blade. This mechanism is more difficult then the one of the conventional gripper but has the big advantage of low friction and no play, which is positive regarding the actuation.

To make it possible to control the position of the moving blade, a measurement of its position is needed. A possible position sensor that is small enough for this application is a small sensor based on the Giant Magneto Resistive (GMR) effect. The sensor consists of 4 magnetic sensitive resistances, placed in a Wheatstone bridge. The voltage output of the Wheatstone bridge varies due to magnetic field changes. The sensor (651x1231 [pm]) is located on the fixed blade while the magnet (0 1.5 x 1.5 [mm] ) is attached to the moving blade. Output saturation is reached when the magnet moves outside the dimensions of the sensor. This means that the maximum displacement is 615 [pm], which results in a maximum possible angle displacement of the grasper of 10". Secondly, a force sensor with an actuation range from 0 to 30 [N] is needed, to measure the force that is acting on the environment by the gripper. The typical lifetime of a SMA wire is 150000 cycles with a load of 150 [MPa] [20]. This

4.2. FINAL SLAVE SYSTEM

lifetime will be enough for minimal one operation and certainly enough for the experimental setup, the lifetime will not be a restriction for the design.

A summery:

desired real small, diameter less then 12 [mm] diameter 6 [mm] 2-SMA actuated 2-SMA actuated minimai friction ball bearings bio-compatible stainless steel measurement of the angle displacement GMR sensor measurement of the acting forces force sensor with actuation range from 0 to 100 [N] desired minimum opening of 2-3 [mm] opening 3.5 mm = 10 "

With an opening angle of 10 ["I and a radius R = 0.003 [m], the total elongation is & 2 ; r ~ = 5.236010-~[m]. The maximum strain of the wire is em,, = 4 %, which leads to a minimum wire length of 0.0131 [m]. For purely practical reasons a longer wire of 0.2 [m] was used during the experiments.

4.2 Final slave system

The final slave system that is designed conform the design aspect determined in the previous paragraph, is shown in figure 4.1.

Figure 4.1: Total slave system


The two force sensors are situated in the center of the picture. The SMA wires are connected between the force sensors and a connection with rigid steal ribbons. A permanent magneet is placed on the steal ribbon, in such way that the magnet moves over the fixed GMR position sensor confirming the movement of the grasper tip. A detailed figure of this system is shown in figure 4.2(a). It can be seen that the Wheatstone bridge in the GMR sensor needs four supplying wires, which can be placed parallel with the SMA wires and do not lead to problems. Since this is an experimental setup, the GMR sensor is still placed on a small print circuit board (pcb) .

Figure 4.2: A detailed photo of the gripper

A current flux will have a negative influence the measurement of the magnetic sensitive sensor and will lead to measurement errors. To prevent this, the current is tapped before it is reaching the sensor. Finally, it can be concluded that the gripper is as small as the nowadays used graspers, with a diameter of 6 [mm] , that can be seen in figure 4.2(b).

Chapter 5

A model of the 2-SMA actuated slave system

In this chapter a constitutive material model for a SMA wire [ll] is used to derive a system model. The SMA actuator is part of the dynamic slave system and needs to be included in the model. Therefore, a material model is needed for solving the differential equations that represent the dynamical system. Since the material behavior is non-linear, an iterative solving algorithm is derived in section 5.3. With the material model it is also possible to reconstruct the generated force of the wire from the temperature and strain, this will be discussed in section 5.4.

5.1 Constitutive material model for a SMA

In paragraph 2.1 an introduction to the working principle of shape memory alloys was given. The phase of the material depends on the temperature, stress and strain. To get a better understanding of the dynamic behavior of smart memory alloy and to implement it in a simulation, a model is needed. In [Ill, a geometrical model for a SMA wire has been derived, in which the behavior is described with the help of measured stress-strain curves at different temperatures. The typical measured hysteresis curve (figure 5.1 on the left) was divided in 4 parts on a physical basis.

Figure 5.1: rnt relation with stress and strain

5.1. CONSTITUTIVE MATERIAL MODEL FOR A SMA

1: A The alloy is completely in its austenite phase (A) and deforms elastically. The elastic deformation starts at point AF (Austenite Finish) up to point MS (Martensite Start).

2: A M The phase of the material starts to change at point MS from austenite to martensite (AM), this is a plastic deformation with a relatively horizontal plateau, this will continue until the deformation reaches point MF (Martensite Finish), where the phase is completely martensite.

3: M Unloading the material leads to a hysteresis loop, starting with an elastic deformation (M), where the ratio MartensiteIAustenite does not change from point MF to AS (Austenite Start).

4: M A Further unloading leads to a plastic deformation from AS to AF, with a phase change from martensite to austenite (MA).

If the deformation is not large enough to reach point MF, the elastic deformation during unloading just starts earlier, represented in figure 5.1 by points 2 and 8 or 3 and 7.

These four points in the (e,p)-plane are mapped on an alternative (m,J)-plane, with the alternative dimensionless parameters m (martensite fraction) and J is such that the quadri- iateral, connecting points 1, 4, 6 and 9, is a square in the (m,J)-plane. Both parameters are restricted: 0 5 m 5 1 and 0 5 J 5 1, this is showed in figure 5.1 on the right. In this way a temperature independent scale is created that simplifies the relation between stress and strain. Secondly, this mapping leads to the assumption that the deformation always proceeds in this square field, so or m or J is changing, leading to equation 5.1

The bilinear relation between the strain e and the stress p on one side and the martensite fraction m and J on the other side is given by equations 5.2 and 5.3 :

or alternatively by equations 5.4 and 5.5:

e = el + e2J + e3m + e4Jm

The parameters pl , pa, p3, p4, el, e2, e3, e4 are assumed to be lineair dependent of the temperature.

5.1. CONSTITUTIVE MATERIAL MODEL FOR A SMA

The values for the parameters are chosen by placing fits on the measured stress-strain curves, the final values are shown in table 5.1.

strains stresses parameter

ela e2a e3a e4a elb e2b e3b e4b

value 0.05715.10-~

0 1.805.10-~

0 4 .797.10~~ 3.621.10-~ -52.60.10-~ 45.14.10-~

parameter value K-l Pla 13.57 K-l P2a 0 K-: P3a 11.85 K-1 P4a 0

Plb -523.9 p2b 244.0 P3b -466.7 p4h 277.9

Table 5.1: Constitutive parameters of the SMA wire

This relationship is plotted in figure 5.2(a) at temperatures 20, 30, 40, 50 and 60 PC]. Comparing this model with the schematic representation in figure 5.2(b) and the physical background, some remarks have to be made.

(a) Schematic representation of the real (b) Fitted stress-strain curves according to stress-strain curves the model parameters

Figure 5.2: stress-strain curves at different temperatures according to the constitutive material model

0 Negative stress (pressure) can not be delivered by a small SMA wire, therefore all negative forces are set to zero. 0 Negative strain is physically impossible, all strains smaller then zero are set to zero. o The assumption in equation 5.1 leads to a discontinuous model. In reality the phase transformation will be a continuous process. 0 When using this model, one has to know the position in the (-m plane, in other words the

5.2. MODEL OF THE DYNAMIC SYSTEM

history has to be known. During every step the constraints 0 5 m I: 1 and 0 5 J 5 1 have to be checked. There is a wide variety of smart memory alloys available, which all have different material

properties. If one wants to use this model for a different material, new stress-strain curves have to be measured and new fits have to be made, leading to 16 new values for the parameters pla to e4b. A solution for this time consuming process could be the derivation of a parameter estimation algorithm, that optimizes the choice of the 16 parameters.

5.2 Model of the dynamic system

Figure 5.3 shows a schematic representation of the gripper that was designed in chapter 4. The two antagonistic SMA wires are represented by fsma, (closing), that pulls the mass to the right and fsma, (opening), that pulls the mass to the left.

Figure 5.3: Schematic representation of the system dynamics of the gripper

The equation of motion of this system can be represented by equation 5.7, where M is the mass of the system and b the viscous damping in the bearings and the wires. fez represents all other disturbances, for instance friction and the reaction force delivered by the touched environment.

The displacement of the mass corresponds with a rotation of & ~ T R which is the same as 1 [deg] = 5.2360 [m].

5.3 A solving method for the non-lineair system

The non-linear equation 5.7 is iteratively solved, since fsma has a non-linear relationship with f (E, 0). First, the system is simplified to equation 5.8. It is quite reasonable to assume that the mass-term due to the small dimensions can be neglected and the viscous damping is assumed to be small, due to the bearings. At this point the dynamic differential equation is transformed in a static one. At every time-step, formula 5.8 is solved, in this way a time depending system is created.

fsmal - f sma, = fez

Engineering stress fsma = pSm,ATef and engineering strain e,,, = - - I 1 are used. A lref

Newton Raphson algorithm is used to solve this equation, which is in this case based on small

5.3. A SOLVING METHOD FOR THE NON-LINEAIR SYSTEM

changes in stress (6p) and strain (6e):

Rewriting leads to the residu that has to be minimized during every time-step in equation 5.10.

In section 5.1, a relation between stress and strain of a SMA wire is described. Differentiating equation 5.3 (m = constant) and equation 5.2 (t= constant) leads to:

Otherwise, if j = 0 it is easy to see that:

or shortly:

With p,t the partial differential of p to J etc. The assumption is made that Aref is constant. Secondly, it is assumed that the temperature does not change during a time step and that it is prescribed by equation 3.3. This assumption is made to simplify the system equations. In reality, the temperature, which is dependent on resistance, will change during a time step. This leads to a non-linear coupled system of two differential equations, which is rather difficult to solve.

- From the design of the slave tip it can be concluded that usma, = us,,, and that the neA=f and reference length of both wires is the same. Using 6e = leads to Mu = ire f

Me = Ite A,, f. Writing equation 5.13 in equation 5.10 gives the final equation 5.14

Within each time step, this iterative solving algorithm is used to minimize the error in the force and to calculate a force equilibrium. When the new variation in displacement is found, the delivered forces can be calculated with the material model. At each iteration point is checked whether 0 5 m 5 1 and 0 5 J 5 1. When the the residue r, is small enough, the iteration procedure for the next time step can be started. It should be noted that this solution procedure is a static solution, hence the force equilibrium is calculated (in appendix B this model is elaborated for one SMA wire). It is not possible to implement friction or damping in the system, which will lead to differences in simulations and experiments (shown in paragraph 6.2).

5.4. CONSTITUTIVE MATERIAL MODEL FOR FORCE SIMULATION

5.4 Constitutive material model for force simulation

The solving method presented in section 5.3, calculates the new position after a change in temperature of one of the two wires, or a change in external force. The solving method in this section will not be used to calculate a new position but will be used to calculate a new force after implying a change in position or temperature. This method will be extremely useful during experiments, where the position is measured and the temperature of the wire is measured or simulated. With the assumption in equation 5.1, it is assumed that the m = constant. Using equations 5.3 and 5.2, with known temperature and strain, < and the stress p can be calculated. How- ever it has to be checked if 0 < < < l, if this is not the case, a recalculation with f = 0 or f = 1 is needed.

This algorithm is implemented in C and can be used in real-time and off-line experiments. The results of online experiments are shown in figure 5.4. However, to use this model in a way that the results are reproducible and are corresponding with the measured forces, it is important to start the simulation at the correct point in the m-< plane, with the correct initial conditions. The implemented algorithm is given in appendix C.

14, I - simulated force 1

ib A 30 i o 50 & i o Jo time [s]

lb 40 30 i 0 50 i 0 ;O i0 time [s]

(a) Force of left wire (b) Force of right wire

Figure 5.4: Simulated and measured forces

In figure 5.4, the simulated and measured forces are plotted. The inputs, strain and temperature, are taken from a reference track that will be discussed in chapter 8. Figure 5.4(a) represents the delivered force of the left wire (opening) and figure 5.4(b) represents the force of the right wire (closing).

Several adaptations were made to the algorithm with respect to the original parameter values. Because the simulated force was often negative or zero while the measured force was positive, the parameter plb was increased from plb = -532.9 [MPa] to plb = -400.9 [MPa]. Furthermore the reference length was decreased from 0.2 [m] to 0.1 [m] and the initial strain was set at 0.02 [-I. This resulted in a force that is positive but too high during experiments, the force was scaled down by using a reference cross section of ATef = 0.02 [mm2]. The differences that are present are caused by the choice of the 16 material parameters. Another fact is that the physical force has a certain maximum, that depends on for instance, the material properties,


cross section, and pre-strain. As can be seen in figure 5.4(b), the simulation model can predict higher forces then are physically achieved. This is caused by the linear dependency of the temperature, while in reality this will be probably a more asymptotic relationship.

Chapter 6

Controller tuning in frequency and time domain

Tuning controllers can be performed in the frequency domain, a common tune criterion is the bandwidth of the system. The tuning of a controller will result in a better performance of the system. However, before frequency domain analysis of a non-linear system is possible, the system has to be linearized. Since no transfer function of the system can be measured during experiments, the system model has to be used to find the linearized transfer function.

6.1 Linearized system transfer function

With the equation of motion, equation 5.7, and the actuator dynamics, equation 3.3 and 5.13, a linearized transfer function, equation 6.1, can be derived [ll].

The system is linearized around working point x = 0, with Lo = ArefIIe and I%, = ArejIIe. The subscripts . and represent the active and the passive wire, respectively. Since phase transformation leads to different values of ke and k, (table 6.1), different system dynamics can be present. Therefore, only two cases are calculated, the first is the case with both wires are in their elastic phase, the second case is the one when both wires are in their transformation phase. The other possibilities will be located between these two cases.

Table 6.1: Values of .ire and .ire in elastic and transformation region.

, IIe

The linearized system makes it possible to represent the SMA wires as linear springs, with a stiffness that depends on the phase. The lSt order differential equation that represents the temperature behavior in combination with the 2nd order differential equation that represents the system dynamica, resulting in a 3rd order transfer function. Figure 6.1 shows the resulting transfer function of the system with values for the parameters shown in table 6.1.

elastic transformation 16.4 2.9 1.5 6.5

GPa MPU.K-'

6.1. LINEARIZED SYSTEM TRANSFER FUNCTION

Table 6.2: System parameter values

At w = 0.59[rad] the thermal parameter T is located, which results in a phase delay up to 90 O.

..... .... q (. .................. ....................... : :.- -..rr-.-ryrr-.---." .. .....,...... " "..." --. ......-..-......- . . . . . . . , . . , : . : . . . . . . . . . . . . . . . . . . . . . . , , . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . .

. . . . . . . . . . . . . . . .

is 2. a, u + .- $ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C

.< , , . . . . . . . . . . . . . . ,.

m . . . . . . . . . . . . . . . . rn -2i'r' : ............. ...;.;...i..*.Lii-.. -- -... - ..-:.. ;.i :.-..-:..->....a ..>. ..! ................ H ,, . - - - transformation

Frequency (radlsec)

Figure 6.1: Transfer function of dynamic system

To position this system, a linear PI feedback controller is chosen based on the control law from equation 6.2. An integrating action is necessary to prevent the system from having a steady state error and to suppress noise in the low frequency range. Since an integrating action leads to a phase delay of 90 ", it is important that it has no influence around the bandwidth, in this case at 1 [Hz].

Therefore 7-i = 0.80 is chosen, in this case the integrating action ends at 0.4 [Hz]. Afterwards the gain is increased until the highest bandwidth with sufficient phase margin is realized. The open loop transfer function is shown in figure 6.2, with final values for the controller Kp =

955 [$I and 7, = 0.80 [s], which results in a bandwidth of 6.5 [rad/s] and a phase margin of 30 [deg].

6.2. TIME RESPONSES IN EXPERIMENTS AND SIMULATIONS

Frequency (radlsec)

Figure 6.2: Open loop transfer function

The control parameters that were used during experiments were slightly different from the ones that were theoretically derived. The gain was used in [g] instead of [GI, this is achieved

after a multiplication with A 2 7 r ~ which is the same as 1 [deg] = 5.2360 lW5 [m]. To get a

better performance the gain was increased to Kp = 0.12 6, further increase of Kp leads to instability for certain trajectories.

Adding an integrating action to the system results in a larger overshoot, which can be seen during simulations. Whenever the system control saturates, the integrating action causes a windup of the input. The integrator will keep integrating, and this charge must be removed later, resulting in substantial overshoot. The solution to this problem is an anti-windup, which avoids saturation. [17]

6.2 Time responses in experiments and simulations

The PI controller is implemented Matlab Sirnulink, this software is coupled with hardware such as the PC and Dspace. As reference trajectories for the experiments in the time domain, a 1 sinusoid and a step function are used. The model derived in chapter 5 is used to simulate the output responses on these inputs. The results of the time responses and input signals on the sinusoid are shown in figure 6.3.


12 - reference angle measured anale

5 I

10 15 20 tlme [s]

(a) Simulated time respons on sinus

0~0

(b) Measured position and error

0.41 I

-0 41 5 10 15

I -04 4 20 0 10 15 20

m e [s] itme [s]

(c) Simulated input (d) Input from experiment

1 -

0 5 -

tlme [s] bme [s]

( e ) Simulated forces (f) Measured forces

Figure 6.3: Simulated and measured time responses on a sinusoid reference trajectory


15 - measured angle

.- - reference angle

-1 5; I 5 10 15 20

time [s]

I 5 10 15 20

time Is]

(a) Simulated time response on step (b) Measured time response on step

time [s]

( c ) Simulated input (d) Input from experiment

5 10 15 20 time [s]

6 - measured force SMAr ,-.- measured force SMAl

I 5 10 15 20

time [s]

(e) Simulated forces (f) Measured forces

Figure 6.4: Simulated and measured time responses on a step input reference trajectory

As can be seen in figure 6.3 and figure 6.4, the position error is quite large, especially when the velocity is changing sign. Using a feedforward friction compensation does not lead to an improvement in the performance. Of course this relatively large error is a direct effect of controlling a non-linear system with a linear controller. An improvement of the performance will be obtained by designing a non-linear controller. In [12] and [ll] a model based non-linear feedforward controller is designed and implemented. In this report the focus is to

6.2. TIME RESPONSES IN EXPERJMENTS AND SIMULATIONS

couple the master and slave system and only a PI-controller is implemented. However, it is recommended to implement a non-linear controller in future research.

It takes time to heat a wire as well as it needs time to cool it. A maximum input of 1 ampere is used and when a step input is applied to the system, it leads to a large error. One advantage is that during surgery the movements of the opening and closing of the tip will be more fluent and the errors will be smaller. Another possibility is to increase the maximum input value, this will lead to faster heating but again some boundaries on the temperature should be taken into account to prevent the wire to break. The force of the wire starts to increase within 0.05 seconds after the step is applied to the system, it takes up to 0.3 seconds to reach an accuracy of 95 % with respect to the final reference position, which is quite fast for a smart memory alloy. Fast opening and closing of the tip results in a fast raise in temperature of both the wires, e.g. the left wire will need a higher temperature then the right that had no time to cool down yet. The first two times, the opening and closing will be fast until the maximum force and temperature are reached, which means that no more movement is possible until the wires are cooled. Attention has to be paid to the stability during cooling because of the phenomena showed in 3.4(b). This already solved by using a maximum input that is smaller then 1 ampere.

Differences in measured and simulated forces are located in figures 6.3(e) and 6.3(f) and figures 6.4(e) and 6.4(f). These differences can be attributed to the solving method of the simulation model. The static force equilibrium is solved, in the simulations the external force is set to zero. This results in an equality of the left and right wire forces. During experiments, the friction and damping will cause a non-zero value for the external force, which results in a difference between measured force of the left and the right wire.

From figure 6.3(c) and 6.3(d) it is clear that there is no saturation of the actuator, which leaves room for the implementation of an additional non-linear controller. In figure 6.4(d) the anti-windup part of the controller is obvious.

Part I1

A Master Slave system with haptic feedback

Chapter 7

Haptic feedback in medical robotics

The current master slave system in medical robotics, do not provide the human operator any kind of feeling. The new 1 DOF slave system have been made operational in Part I, it can be integrated in a master slave system that does provide the human operator with a kind of feeling. However, before coupling the master and slave system in Part I1 of this report, it is useful to investigate why touch is such an important sense and what kind of feedback can be established.

7.1 Haptic Sensing

A sense that is sometimes underestimated is touch, while touch is very important in most situations. For example, when there is little or no light, we can walk because we can feel around with our hands, or when sensing the back of an object only touch can help you out. But even more handful is touch to examine whether an object is cold or warm or to help determine stiffness, viscosity, weight and roughness. But how does this touch works? For not going to much in detail, only a few definitions are given and not the whole biological background of sensing. [l8]

tactile sensory: The definition of a tactile sensor is :'a device that measures parameters of a contact interaction between the device and some physical stimulus'. So tactile sensing provides data on the size, shape, position, thermal conductivity or distribution of forces of a contacting object and torque. Human tactile sensing can be divided in two groups of sensing, which are known as kinesthetic and cutaneous components.

kinesthetic sensing: The kinesthetic information arises out of muscle and joint signals. The whole hand and arm contribute information concerning the nature of the touched object. So by knowing the position of the links the shape is recovered.

cutaneous sensing: The cutaneous information is derived from sensors on the fingertips, for example pressure, thermal conductivity.

haptic sensing: Haptic sensing is the combination of kinesthetic and cutaneous sensing.

As we see, haptic sensing provides us a lot of information, especially when we talk about surgery: the surgeon can feel his way around the tissue, can cut where he/she thinks the tissue is the less vulnerable and so on. However, it is still not completely clear how the sense 'touch' exactly works. Holding an object requires a certain DC-offset value; when this DC value is reached it warns that a certain object is touched. If the surgeon wants to gain more

7.1. HAPTIC SENSING

information about the touched object he will press harder and will have information about stiffness and damping, or more general about the impedance. It is also not clear what kind of differences in touch humans can feel. Experiments with a master-slave system with haptic feedback, can help to answer these questions.

The deviation of haptic feeling in kinesthetic and cutaneous feeling can also be used for a qualification of haptic feeling, for instance in the form of bandwidth [21]. The bandwidth of kinesthetic sensing is up to 10 [Hz] and the bandwidth for cutaneous sensing is up to 320 [Hz]. The bandwidth of human motion is up to 10 Hz with a tremor signal between 8 and 12 Hz. It should be noted that these bandwidths are maxima, most of the times the movement will be much slower, especially when working as surgeon. It is however desired to have a system that can meet this maximums. Furthermore it is desired that the grasper is fully closed within 0.5

Is1 . In literature [19], values for the delivered torques, that are needed for grasping an object are around 0.3 [Nm], but with lower torques it is also possible to grasp objects. A comfortable force level for one finger is up to 7 [N] and no individual finger should be higher loaded then 30-50 [N]. Feeding back the forces in medical robotics, will result in a large recovery of haptic sensing, since part of kinesthetic and a part of cutaneous feeling are based on forces. In the next chapter the forces/torques are being fed back to the master manipulator, to restore a part of the haptic sensing.

Chapter 8

Coupling the master and slave manipulators

In this chapter we describe the integration of the slave system, developed in Part I, in a master- slave system. First, the master manipulator is presented and its properties will be discussed. Then, the coupling of both the systems into a master slave system will be described. This system has been made operational by means of a control strategy for a bilateral actuation, hence presented in section 8.2. Finally, the system responses will be presented in the last section.

8.1 The master manipulator system

The master manipulator, (figure 8.1) that was used to be coupled with the slave system, was already designed in [13]. The master system has an electro motor that is capable of delivering torques up to 0.15 [Nm]. Two scissor handles are used to manipulate the master system:

Figure 8.1 : The master manipulator

the displacement initiated by the handles is measured by a position sensor. The system is controlled by an "ideal" control strategy, which means that the input current corresponds to a certain static torque. The relation between current and torque is derived in 1131 and is 0.033 [?I.

8.2. CONTROL STRATEGIES FOR BILATERAL ACTUATION

8.2 Control strategies for bilateral actuation

If only the master's motion and/or forces are transmitted to the slave, the system is called unilateral. If, in addition, slave motion and/or forces are transmitted to the master, the system is called bilateral. Several strategies for a bilateral coupling of a master to a slave are possible: an overview is given in [14]. In this chapter the master and slave are coupled through direct force feedback, which means that the measured (or estimated) force is direct fed back to the master system. In figure 8.2, a schematic representation of a digitally coupled master slave system is shown.

Figure 8.2: A schematic representation of the master slave system

The computer contains the software to compute and transfer motions and forces and controls both the systems. The master position is used as reference position for the slave manipulator. Direct force feedback, or kinesthetic force feedback (KFF), needs a force to be fed back to the master system. In this case, there are two possibilities to gain the force that is acting on the environment: either the force is measured, or the force is estimated. A control scheme of the coupled system is shown in figure 8.3. The human operator delivers a force or position to the

Figure 8.3: Control architecture of the KFF control strategie

e

master system and the measured position x, is used as reference position for the slave. The difference between the reference position and the measured position of the slave x, is the error signal e that is used as input for the slave controller to control the slave system. The slave system interacts with the " environment" (i.e. the operational area inside the human body) and the reaction force Fen, is measured/simulated and fed back to the master controller. This results in an actuation of the master system that delivers the desired force to the human operator. Furthermore, a camera or view on the slave system gives visual feedback to the human operator.

Master - System

- -

Master Slave Controller C- 4 Controller

Human

Slave system

* 4

Environment I Operator

L - - - - +--I.-- Camera I --

Fenv

8.3. TIME RESPONSES OF THE COUPLED MASTER SLAVE SYSTEM

8.3 Time responses of the coupled master slave system

The control scheme is implemented in Matlab Simulink and linked with a Dspace system. Both the master and slave system are linked with a current amplifier to apply the correct current at a certain voltage. The intern controllers of the master and slave systems that were derived earlier have been used. The motion of the master is scaled down by a factor 5: i.e. an angle displacement of 50 "of the master will result in a maximum angle displacement of 10 "of the slave. The estimated forces of the SMA wires are recalculated to a torque by multiplying the difference of the two wires by the radius of the tip (R = 0.003 [m]). Squeezing an object with the far end of the tip will result in a different torque then squeezing the same object at the beginning of the tip. However, this effect is completely natural when grasping an object with a gripper.

An experiment is performed with a human operator manipulating the master system. During this experiment 3 phases are present: 1) a non-contact move (0-20 and 70-80 seconds ), 2) establishing contact (20-30 seconds), 3) contact move (30-70 seconds).

In figure 8.4, the resulting reference and measured angle of the slave system are plotted.

12

10

8

6

- 4 =

a, - p 2

0

-2

-4

-6 0 10 20 30 40 50 60 70 80

time [s]

Figure 8.4: Tracking of slave system on master reference

The corresponding implied force is shown in figure 8.5: this signal is the difference between the forces of both SMA-wires. The velocity during non-contact movement is limited by the cooling time of the wire. Only slow repetitive movements of less then 1 [Hz] can be tracked well, if there are signals with a higher frequency they are being tracked for only 2 or 3 cycles. In figure 8.4 and 8.5, phase 1 from 0-20 seconds, the movement is a non-contact move, the tracking error is quite small during slow movements and increases with fast movements. No

8.3. TIME RESPONSES OF THE COUPLED MASTER SLAVE SYSTEM

time [s]

1 .

Figure 8.5: Implied force: measured and estimated

- 30

external force, except friction, is present which results in a small difference of the left and right force.

- . ' l ! 1

................................................ . . . . . . . . . . . . . . . . . . . . . . . - . i . . I ! . . j . . .- 8 . - measured force

I I I I I t - - estimated force

At time 20 seconds, phase 2, contact is established with the environment (a rubber tube). The position then varies with the reference position because of the interaction with the environment.

-35 0 10 20 30 40 50 60 70 80

When the contact with the environment is established, the tube is squeezed several times, during phase 3 from 30-70 seconds. This results in an increase in active force. The estimated force corresponds to the measured force and force feedback is established.

Secondly, it can be concluded that the position error increases: the reference position can not be followed by the slave system. This problem is caused by 2 facts: the first is that the human can squeeze through the force delivered by the master system; the second is that the slave system is too slow to follow the reference immediately. The solution for this problem can be to scale further down the reference position and to scale up the force when there is contact. The estimated force can be made larger then the measured force by means of an automatic up scaling. But since the current amplifier for the master system was already at its maximum this solution could not be implemented.

Finally, at 70 seconds the free movement is re-established: the force is again well predicted (figure 8.4), while the position error increases with fast movement (figure 8.5).

Chapter 9

Conclusions and recornmendat ions

Smart memory alloys (in this case nitinol) are commonly being used in passive medical applications. The superelasticity property makes the material very useful for stents, flexible graspers and retrieval backs. The possibility to use SMA as an actuator, using the thermal shape memory behavior, is not broadIy accepted. Even though, research on this topic has been widely performed and has lead to promising results. One possible reason for the non- acceptance may be the high working temperature of SMA, especially for applications in the human body. Simulations have been performed for cases in which heated SMA wires are used as actuators inside the human body. This resulted in a very local heat development that could be lowered by insulating the wires. Real time experiments with insulated wires have been performed and showed that no damage due to the high temperature was done to the human index finger. Another negative effect is the low bandwidth of the SMA wire. How- ever, forced cooling may increase the bandwidth and will cool down the surrounding tissues. Together with the advantage of high force-to-weight ratio, it can be concluded that SMA, if insulated, can be a promising possible actuator for medical applications inside the human body.

A new small 1 DOF slave system for a medical robotic master-slave system has been designed. By using 2 antagonistic SMA wires, it is possible to actively actuate the grasper in two directions, i.e. the opening and closing of the tip. A non-linear model has been used to describe the relation between the temperature, stress and strain of the wire. This numerical mode1 does represent the system behavior relatively good. Unfortunately, for computing the force, the temperature of the wire is needed. This is gained by simulating the temperature in open air. But for an insulated SMA wire or for the situation in which the SMA wire is placed inside a human body, this computation will not be an accurate one. Hence, more research with respect to this temperature issue has to be done, by for instance performing temperature measurements.

The force that is delivered by the sIave system has been reconstructed with an algorithm that is on-line, implemented using the non-linear model with the strain and temperature as inputs. This reconstruction algorithm has shown good results and hence, can be used instead of the large force sensors. The (small) differences between the measured and reconstructed force are due to the chosen values of 16 material model parameters. It is recommended to write an identification algorithm for finding the optimal set of values for these parameters.

The slave system has been controlled by a PI-control algorithm, which has resulted in small tracking errors during slow movement. However, fast movement has lead to larger error signals. This performance can probably be improved by adding a non-linear controller to the

system, for instance a model based feedforward controller.

Finally, the master and slave system have been coupled by direct force feedback: the position of the master is the reference position for the slave and the reconstructed force at the slave side is fed back to the master manipulator. Using this control strategy, the human operator is able to feel the touched "environment7'. In this way, a part of the haptic feedback has been restored, which is the major drawback in the current medical robotic master-slave systems. During contact movement, large position errors occur that can be decreased by scaling the position and forces. The specs of the system are still too low to fulfil the needs of the surgeon in terms of maximum bandwidth, so only slow movement (1 [Hz]) is possible. With the small 1 DOF master-slave system being made operational, it is now possible to continue the research in more degrees of freedoms.

Literature

[I] Pennes, H.H., "Analysis of tissue and arterial blood temperatures in the resting human forearm", J. Appl. Physiol, Vol. 1, pp. 93-121, 1948

[2] Fiala, D, J . Lomas and M. Stohrer, A computer model of human themnoregulation for a wide range of environmental conditions: the passive system, Institute of Energy and Sustainable Developent, De Montfort University leicester and University of Applied Sciences Stuttgart, 1999

[3] Janssen, F.E.M. Development of a model for rewarming patients during surgery.WET 2003.3 master thesis, University of Technology Eindhoven, 2003

[4] L6pez Fernhdez, R.F, L.M.T. Balibrea, PID control of SNIA fibers. Hysteresis comid- eration, and time extension reduction using electrical resistance measurement, Rev. T i c . Ing. Univ. Zulia., Vol. 23, No. 3, pp. 195-205, 2000

[5] The International Organization on Shape Memory and Superelastic Technologies, http://www.smst.org

[6] Park K. and M. Esashi A Multilink Active Catheter with polyimidi-Based Integrated CMOS Interface Circuits, Journal of Microelectromechanical systems, Vol. 8, No. 4, pp. 349-357, December 1999

[7] Troisfontaine, N., Ph. Bidaud and P. Dario, Control Experiments on two SMA based micro-actuators, in proceedings of the fifth international symposium on experimental robotics (ISER'97), 1997

[8] Hoshimoto, M., T . Tabata and T. Yuki, Development of Electrically Heated SMA Active Forceps for Laparoscopic Surgery, in IEEE International Conference on Robotics and Automation, 1999

[9] Pfeiffer, C., DeLaurentis and C. Mavroidis. Shape Memory Alloy Actuated Robot Pros- theses: Initial Experiments. master thesis, Robotic and Mechatronics Laboratory, De- partment of Mechanical and Aerospace Engineering, Rutgers university, 1999

[lo] Aalsma, A.M.M.,E.E.G. Hekman, J. Stapert and H. Grootenboer , A completely in- tramedullary leg lengthening Device, in Proceedings of the 20th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Vol. 20, No. 5, 1998

[ll] Wijst, W.M. van der Shape Control of Structures and Materials with Shape Memory Alloys. phd. thesis, University of Technology Eindhoven, 1998

[12] Peeters, J.M. Medical robotics, A S M A actuated laparoscopic forceps with force feedback. master thesis DCT report 01.2002, University of Technology Eindhoven, 2002

LITERATURE

[13] Ranken, M. Design of a master manipulator for a laparoscopic forceps, report DCT 2002.07, University of Technology Eindhoven, 2002

[14] Rovers, A.F. Haptic Feedback: A literature study o n the present-day use of thaptic feedback in medical robotics. DCT Report nr. 2002.57, University of Technology, 2002

[15] Intuitive Surgical @, http://www.intuitivesurgical.com

[16] Computermotion, http://www.computermotion.com

[i7] Franklin, G.F.J.D. Powell, A.E. Naeini Feedback contrd of dgmmzc s.;stems. Addism- -Wesley Publishing Company, Inc., New York, 1994

[I81 Howard, E. and R. Nicholls Advanced tactile sensing for robotics, Series in Robotics and Automated Systems, Vo1.5, University College of Wales Aberystwyth, UK, 1992.

[19] Cavugo~lu,M.C., W. Williams, F. Tendick and S. S. Sastry Robotics for felesurgery : second generation berkele/UCSF laparoscopic telesurgical workstation and looking towards the future applications, in Proceedings of the 39th AZZerton Conference on Cummunica- tion, Control and Computing, 2001

[20] Reynaerts, D., H. van Brussel, Design aspects of shape memory actuators, Mechatronics , Vol. 8, pp. 635-656, 1998

[21] Dong-Soo Kwon, Se-Kyong ong. A microsurgical telerobot system with a 6-DOF haptic master device, in Proceedings of the 2000 International Symposium o n Mechatronics and Intelligent Mechanical System for 21 Centurey, pp. 65-71, 2000

[22] Bejan, A., Heat Dansfer, 1993

Appendix A

First order DV for heat development in wire

The temperature of the wire that is placed in the open air, cannot be controlled directly, but is a consequence of the heat balance between stored, lost, conducted and generated power [22]. The easiest way to heat SMA wires is by means of electric current. The generated power is then:

where I is the electric current, R the total electric resistance of the wire, rel the specific electric resistance and 1 and A the length and the cross-sectional area of the wire respectively. The lost power is due to convection.

where h is the heat transfer coefficient, depending on environmental circumstances, 8 the surface temperature of the wire, 8, the temperature of the environment, d, the circumference and 1 the length of the wire. The stored energy follows from:

where p and cp are the density and the specific heat capacity of the wire. The conducted power at the ends is not taken into account, because of the ratio between the length and the cross-sectional area of the wire. The wire is seen as a wire of infinite length. Equations A.l, A.2 and A.3 together form the heat balance of the wire, which results in:

The thermal parameters c and r are treated as constant, but they change when surroundings change or when the crystal structure of the wire changes. The specific electric resistance, thermal conductivity and the specific heat capacity are different for the martensite and austenite structure [4]. .

Appendix B

Simulation results for 1 SMA wire

The stress strain behavior of one wire during actuation is schematically represented in figure

starting at point (0,O) m =0, ksi = zero

applying load, point AS (e1,pl) m = 0, 0 <ksi < 1

P O<m 1 and ksi = 1, temperature increases

curve starting to shift up, m = constant, O<ksi 1

point MS (el+e2, pl+p2) martensite formation start ksi =1, O<rn<l

when the temperature is even higher the curve shifts further up, ksi = 0, 0 < rn < 1, and the

strain is recoverd e

Figure B.l: the actuation loop of one wire, represented in stress strain curves

This behavior can be simulated in time with a numerical model. The equation:

~ s m a A r e f = f e 03.1)

has to be iteratively solved for every time step. This is done by the shown algorithm:

Temp0 = 20; %293; % s t a r t i n g temperature Tempomg = 20; % 293; % Temperature surroundings c = 250; % thermal parameter [C/Ae21 t a u = 1 .7 ; % thermal parameter [sl

e l a = 0.05715e-3; e2a = 0; e3a = 1.805e-3; e4a = 0; e l b = 4.797e-3; e2b = 3.621e-3; e3b = -52.6e-3;

for i = 1:1000; % Input Current

% Temperature model dTemp= (-Temp0 + Tempomg +c*I(i)-2)/tau ; Temp(i) = Temp0 + dTemp*dt;

% Initializing parameters depended on temperature

+ elb; + e2b; + e3b; + e4b; + plb; + p2b; + p3b; + p4b;

% calculation of the AF, MS, MF, AS eAF = el; eMS = el+e2; eMF = el+e2 + e3 + e4; eAS = el + e3; pAF = p1; pMS = p1 + p2; pMF = pl+p2+p3+p4; PAS = pl+p3;

% assumption mdot = 0; j = 1; residu(i, j)=l; while abs(residu(i,j)) > 1e-10 ;

if j > 10 break;

end if eO < eAF; % first we have to go to point AF

m = 0; ksi = 0; piE = pAF/eAF; piTemp = 0 ; p = pO + piE*de;

elseif eO > eMF; % if the maximum strain is exceeded we move with the following gr m = 1; ksi = 1; piE = (pMF-PAS) / (eMF-eAS) ; piTemp = 0;%?? p = pO + piE*de;

else

m = mO; ksi = (eO-el-e3*m)/(e2+e4*rn); p = p1 +p2*ksi + p3*m + p4*ksi*m; p2ksi = p2 + p4*m; e2ksi = e2 + e4*m; e2Temp = ela + e2a*ksi + e3a*m + e4a*ksi*m; p2Temp = pla + p2a*ksi + p3a*m + p4a*ksi*m;

if ksi > 1 ; % checking if ksi and m are between 0 and 1 ksi = 1; m = (eO-el-e2*ksi)/(e3+e4*ksi); p = p1 +p2*ksi + p3*m + p4*ksi*m; e2m = e3 +e4*ksi; e2Temp = ela + e2a*ksi + e3a*m + e4a*ksi*m; p2m = p3 + p4*ksi; p2Temp = pla + p2a*ksi + p3a*m + p4a*ksi*m; piTemp = p2Temp - (e2Temp*p2m/e2m); piE = p2m/e2m; if m > 1;

m = 1; ksi = 1; piE = ( p ~ ~ - p ~ S ) / (eMF-eAS) ; piTemp = 0;%?? p = pO + piE*de;

end end if ksi < 0;

ksi = 0; m = (e0-el-e2*ksi) / (e3+e4*ksi) ; p = pl +p2*ksi + p3*m + p4*ksi*m; e2m = e3 +e4*ksi; e2Temp = ela + e2a*ksi + e3a*m + e4a*ksi*m; p2m = p3 + p4*ksi; p2Temp = pla + p2a*ksi + p3a*m + p4a*ksi*m; piTemp = p2Temp - (e2Temp*p2m/e2m); piE = p2m/e2m; if m < O ;

m = 0; ksi = 0; piE = pAF/eAF; piTemp = 0 ; % ?? p = pO + piE*de;

end end

end

du = (f e (i) - ref *p-~teta*dTemp*dt) / (Mu) ;

unew = uO + du; enew = unew/lref; %updating varibles de = enew - eO; mO= m;

ksiO = ksi;

PO = p; eO = enew; uO = m e w ;

residu(i, j) = du; % the residu end

fa (i)= Aref *pc (i) ; % force delivered by active SMA engeneering stress end

The inputs that are used during a simulation, extern force and current, are defined in figure B.2. A load is applied, released, again applied and hold at a constant level. When the force has reached it constant niveau, current is applied.

(a) Extern force (b) Input current

Figure B.2: Input signals on one SMA wire

With these inputs the following results are obtained in figure B.3

strain 0.04 r I

, , 08 stress-strain 4

2..... . . . . . .

o..... . . . .

time [s] m & k s ~

"0 0.5 time [s]

strain [-I Temperature

0.5 time [s]

Figure B.3: resulting responses of the simulation

If the load is applied, the strain is increasing form zero to point AF, point (e1,pl) in the (e,p)-plane. Until this point is reached m and J are both zero. When the load increases further, the strain is also increasing which leads to an increase in J, until point MS is reached, point (el+e2, pl+p2) in the (e,p)-plane. From that point the martensite fraction, m, will start to change. Unloading, will first cause a decrease in J, due to the hysteresis effect, and a decrease in strain due to the elastic deformation. Since the load is not complete zero, the line connecting point AS and AF, is not crossed and m will stay unchanged. Applying a load, will again lead to an increase in strain, { and m (when the line MS-MF is crossed). When the load is left constant, the input current is increased and the temperature is raising. This causes the stress-strain curve to shift up, which means that with a constant force the strain is decreasing. This result in a decrease in J and when the temperature is high enough in a decrease in the fraction m.

Appendix C

Control scheme implementation in Simulink

enablecontroller D? I I error I

Figure C.l: Simulink block schema of the total master slave system with the force simulation algorithm

/* S-function t o pred ic t t h e force of a SMA with known s t r a i n * crea ted by Martijn Franken (January 2003)*/

#define t s ( S ) ssGetS~cn~aram(S,O) #define Aref s (S) ssGetSFcnParam(S, 1) #define mOSMAs (S) s s ~ e t ~ ~ c n ~ a r a m ( S , 2) #define ksiOSMAs (S) ssGetSFcnParam(S ,3) #define eOSMAs (S) ss~etSFcnParam(S ,4) #define pOSMAs (S) ss~etSFcnParam(S, 5) #define fOSMAs(S) s s G e t ~ ~ c n ~ a r a m ( S ~ 6 )

// sample time / / o f f s e t s t r a i n SMAl // i n i t i a l m

// i n i t i a l k s i / / i n i t i a l s t r a i n SMA

// k s i SMA 1 // i n i t i a l force SMAl

#define NPARAMS 7

#define U(element1 (*uPtrsCelementl) /* Pointer t o Input Port0 */

s t a t i c real-T ela=5.715420891685447e-5; s t a t i c real-T e2a=0.0; s t a t i c real-T e3a=0.00180458780072; s t a t i c real-T e4a=-4.336808689942018e-19; s t a t i c real-T elb=0.00479667192759; s t a t i c real-T e2b=0.00362091582487; s t a t i c real-T e3b=O. 0526; s t a t i c real-T e4b=0.04513944349761; s t a t i c real-T pla=13.57341130001205e6; s t a t i c real-T p2a=3.55271367880050le-9; s t a t i c real-T p3a=11.84546171464848e6; s t a t i c real-T p4a=-2.486899575160351e-8; s t a t i c real-T plb=-400.9e6; s t a t i c real-T p2b=2.439963202145598e+8; s t a t i c real-T p3b=-466700000; s t a t i c real-T p4b=2.778529052362479e+8;

* S-function methods * *====---------------- ---------------- */

/* Function: mdlIn i t ia l izeSizes ...................................

* Abstract: * The s i z e s information is used by Simulink t o determine t h e S-function * block's c h a r a c t e r i s t i c s (number of inputs , outputs , s t a t e s , e t c . ) . * /

s t a t i c void mdlInitializeSizes(SimStruct *S)

ssSetNumSFcnParams(S, NPARAMS); /* Number of expected parameters */ i f (ssGetNumSFcnParams (S) ! = ssGetSFcnParamsCount (S) ) (

r e tu rn ; /* Parameter mismatch w i l l be reported by Simulink */

i f ( ! ssSetNumInputPorts (S, 1 ) ) r e tu rn ; ssSetInputPortWidth(S , 0, 2) ;

i f ( ! ssSetNumOutputPorts (S , 1) ) r e tu rn ; ssSetOutputPortWidth(S, 0 , 5) ;

/* Take care when specifying exception free code - see sfuntmpl.doc */ ssSetOptions(S, SS-OPTION-EXCEPTION-FREE-CODE);

1

/* Function: mdlInitializeSampleTimes ............................. * Abstract: * Specifiy that we inherit our sample time from the driving block. */ static void mdlInitializeSampleTimes(SimStruct *S) <

ssSetSampleTime (S, 0, *mxGetPr (ts (S) ) ) ; ssSetOf f setTime (S, 0, 0.0) ;

1

static void mdlInitializeConditions (SimStruct *S)

// InputRealPtrsType uPtrs = ssGetInputPortRealSignalPtrs(S,O); real-T eO = *mxGetPr (eOSMAs (S) ) ; real-T pO= *mxGetPr (pOSMAs (S) ) ; real-T *xO = ssGetRealDiscStates (S) ;

xO [O] =*mxGetPr (mOSMAs (S) ) ; // initial martensite concentration xO [I] =*mxGetPr (ksiOSMAs (S) ) ; // initial ksi xO [2] =*mxGetPr (eOSMAs (S) ; // initial strain SMA xO [31 =*mxGetPr (pOSMAs (S) ; // initial stress SMA 1 x0 [4] =*mxGetPr (f OSMAs (S) ) ; // initial force SMAl

static void mdloutputs (SimStruct *S , int-T tid)

/* Return t h e current s t a t e a s t h e output */

y C01 =x C01 ; // martensi t y C11 =x Cll ; // k s i y C21 =x C21 ; // s t r a i n y C31 =x Dl ; // s t r e s s y C41 =x C41 ; // force

1

#define MDL-UPDATE /* Function: mdlupdate ..........................................

s t a t i c void mdlupdate (SimStruct *S, int-T t i d )

real-T *x = ssGetRealDiscStates (S) ; InputRealPtrsType uPt rs = ssGetInputPortRealSignalPtrs(S,O);

real-T dt=*mxGetPr ( t s (S) ; real-T Aref =*mxGetPr (Aref s (S) ) ; real-T eO; /* declara t ion parameters f o r two antagonist ic wires */ real-T e l ; real-T e2; real-T e3; real-T e4; real-T p l ; real-T p2; real-T p3; real-T p4; real-T eAF; real-T eMS; real-T eMF; real-T eAS; real-T pAF; real-T pMS; real-T pMF; real-T PAS; real-T ks i0 ; // k s i of l a s t s t e p real-T e ; real-T dp; real-T PO;

real-T p ; real-T f a ; real-T mO; real-T m; real-T k s i ; real-T temp ;

//mO=x COI ; //save last k s i and m

temp = U(0); //temperature input // stress-strain temperature dependent parameters for both wires // SMA 1 el=ela*temp+elb; e2=e2a*temp+e2b; e3=e3a*temp+e3b; e4=e4a*temp+e4b;

e = U(1) ; // strain measured/simulated // calculation of the AF, MS, MF, AS eAF = el; eMS = el+e2; eMF = el+e2 + e3 + e4; eAS = el + e3; pAF = pl; pMS = p1 + p2; pMF = pl+p2+p3+p4; PAS = pl+p3;

// ..................................................... if (e < eAF) {

dp = pAF/eAF; p = pO + dp*(e-e0) ; m = 0; ksi = 0;

1 else if (e > eMF) {

dp = (pMF - PAS)/ (eMF-eAS) ; p = pO + dp* (e-e0) ; m = 1; ksi = 1;

1 else { ksi = (e-el-e3*m) / (e2+e4*m) ; p = pl +p2*ksi + p3*m + p4*ksi*m;

if ( ksi > 1) {

// CASE 2 ksidot = zero ksi = 1;

C m = 1; ksi = 1;

if (ksi < 0) C

ksi = 0 ; m = (e-el-e2*ksi) / (e3+e4*ksi) ; p = p1 +p2*ksi + p3*m + p4*ksi*m; if (m< 0)

< m = 0; ksi = 0;

p = pO + dp* (e-e0) ; // dteta*dt; 3

3 3

// ......................................................

// Now we need to check if e according to e = el + e2*ksi + e3*m + e4*m*ksi is the s // e according to our dynamical system equation.

x[Ol=m; // from strain to displacement angle xClI=ksi ; // force SMAl x[21= e; // martensite concentration SMAl x[31= p; // ksi SMAl xC41= fa; // temp SMAl

3

static void mdlTerminate (SimStruct *S)

#ifdef MATLAB-MEX-FILE /* Is this file being compiled as a MEX-file? */ #include "simu1ink.c" /* MEX-file interface mechanism */ #else #include I' cg-sf un . h" /* Code generation registration function */ #endif

Appendix D

Smart memory alloy selling companies

Online shop (tip):

www.memory-met alle.de Am Kesselhaus 5 D-79576 Weil am Rhein Tel.: f49. (0)7621 799 121 Fax: f49. (0)7621 799 244 E-Mail: [email protected] Contact: Robert Ploetz [[email protected]] Dr. Matthias Mertmann [[email protected]] Dutch Suppliers:

www.2spring.com 2SPRING Industrieweg 38 5688 DP Oirschot Netherlands T +31 499 42 5588 F +31 499 577 337 Contacts: Chris van den Boom [[email protected]]

Acknowledgement

I want to use this opportunity to thank everybody who helped me in any possible way. Ivonne and Maarten, thank you for your critical remarks, the coaching work and for offering me the possibility to do my master's thesis at the bio-robotics group. Piet, thank you for your ex- cellent help with the smart memory material behavior. Furthermore I want t o compliment Rob who did a tremendous 'small' job by helping to create the slave system. And I enjoyed working in the lab, making use of the knowhow of Renz, Harry, Peter and Karel. And I hope that the other members of the bio-robotics group liked working with me as much as I liked working with them. And thanks to the room mates of Whoog -1.131, for the fine company during though days.

Ren6 and Lea, special thanks for all the possible support you gave me. And last but certainly not least, thank you Agnes, for your patience, interest and lots of help!

eindhoven university of technology master smart …meester slaaf robot systemen worden ontworpen om...

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