- Email: [email protected]
Shape Memory Alloy Compliant Microrobots
Copyright © IFAC Information Control in Manufacturing, Nancy - Metz, France, 1998
SHAPE MEMORY ALLOY COMPLIANT MICROROBOTS M. Calin", N. Chaillet", J. Agnus", A. Bourjault", A. Bertsch"", S. Zissj"", L.Thiery"""
* Laboratoire d'Automatique de Besanr;on, LAB UMR 6596 (IMFC FR W0067) 25, rue Alain SA VARY, 25000 BESANCON, FRANCE Tel : (33) 03 81 402798 Fax : (33) 0381 402809 Email : [email protected] **DCPR-GRAPP, URA 328 CNRS, 1 rue Granciville, B.P.451, 54001 NANCY, FRANCE ***lnstitut de Genie Energetique, Parc Technologique, 2 avenue 1. Moulin, 90000 BELFORT. FRANCE
Abstract: This paper deals with microrobots actuated by shape memory alloys (SMA). The microrobots must often have a complex 3D geometry and must endure large deformations. Then the mechanical structure of the presented microrobots is realized in polymer by microstereophotolithography (J-lSPL). Different structures, with 2 mm to 700 microns in diameter, have been designed and manufactured, based on elastic pivots and distributed elasticity. Experimental results are given concerning the PID-based motion control of one microrobot. One of our main purposes is the cooperative micromanipulation of micro-objects for micro-assembling tasks. We have developed the impedance model of cooperative microfmgers and identified the design parameters needed for the optimization of our prototypes. Our design method is based on a neural bond graph (N8G) approach. Copyright @19981FAC Keywords: Microrobot, microassembling, shape microstereophotolithography, design, neural bond graph.
I. INTRODUCTION
memory
alloy,
2. DESIGN AND REALIZATION OF MICROROBOTSPROTOTYPES
Microrobotics is an interdisciplinary domain, involving competences from micromechanics, microtechnologies, robotics and control. Our paper describes microrobot actuated by SMA wires, and is composed of three main parts : - design of microrobot prototypes using SMA actuators, with 3D mobility, realized in polymer by J-lSPL, especially microtentacles; - identification and control of these prototypes : because of technological restrictions and characteristics of their actuators, our microrobots are compliant active micromechanisms; - design of such cooperative microrobots with impedance optimization ; we have developed a neural bond graph method (N8G) for adaptive modelling and design optimization.
2.1 The mechanical structure In order to realize microsystems that could be full of interest in microrobotic applications, it is important to be able to produce structures in three dimensions with complex geometries. Moreover, the manufacturing technology has to be collective. Up to now, most micro fabrication techniques, and particularly the ones based on the IC fabrication process, can produce planar microparts, or objects composed of a very small number of layers. Using those techniques, the manufacture of threedimensional parts having curved surfaces and an important number of layers is very difficult. So the IlSPL technique seems to be an attractive alternative
241
2.3 Assembly technique
process to manufacture such kind of 3D microparts with a satisfying accuracy.
To obtain three-dimensional microrobots, an assembly technique is required to integer the SMA wires into the polymer mechanical structure realized by J..lSPL. This technique consists in gluing together the two components, with a controlled initial strain of SMA wire.
In the J..lSPL process, a computer model of the object to build is sliced into horizontal layers. The different slices are then successively manufactured by the space-resolved light-induced polymerization of a liquid monomer in a solid polymer. When a slice of the part is done, the addition of a layer of photopolymerizable resin on the already polymerized part allows to continue the manufacturing process.
When the mechanical structure is designed, clamping areas are provided, in which the SMA wires can be easily inserted. When the SMA wires are correctly positionned in the polymer structure, they are submitted to a mechanical initial stress to store mechanical energy. This step was done by fixing a calibrated weight at one end of the wire, the other end being embeded in a rigid frame . Of course the use of an adapted traction system could improve this operation. Some SMA wires can also be positioned in the structure without initial stress. These passive wires can then have for the future motions a stiffening action.
Two main J..lSPL processes have been developed, the first one is based on a vector by vector tracing of every layer of the object by moving it under a focalized laser beam while manufacturing it (Zissi et al., 1996). It has a typical resolution of 30x30x20 J..lm for every polymerized elementary volume. The second one, called the J..lSPL, gives the most interesting results : it uses a dynamic mask-generator process, and allowed the manufacture of a complete layer by one irradiation only. A liquid cristal display is placed along the optical path (Bertsch, 1996). Its typical resolution is 5 J..lm in the three space dimensions and can be the starting point of a collective fabrication process.
The SMA wires are fixed to the J..lSPL structure by polymerizing a very small amount of photoreactive chemical medium added in the provided holes, with an ultraviolet laser beam, as shown in figure 3. Once the wires are fixed to the polymer structure, the microrobot can nevermore be dismantled. But in fact most microsystems are conceived as objects that can be thrown away after use, and in general, structures that can be dismantled are not really interesting in the micromanufacture field.
2.2 Choice of the actuation solution
Among the physical principles used in the development of miniaturized actuators, the shape memory effect appears to be one of the most attractive. Large deformations and forces can be obtained using shape memory alloys (SMA), and these deformations can be easily converted into flexural or rotative motions by designing adapted mechanical architectures. Different works have already been devoted to this approach, in the field of robotics, but the classical mechanical components used are not well adapted to miniaturization (Bergmasco et al., 1990).
The microassembly process used to manufacture these microrobots is very simple. It requires only two steps which are the addition of a small amount of photopolymerizable resin and a laser irradiation. This technique is then easily adaptable to a collective manufacture of microsystems. Once the wires are fixed to the polymer structure, the ones that are prestressed can be moved by an external heat source, or more efficiently, by Joule effect. In this approach, the SMA wires act as resistors inserted in a current loop.
SMA for microrobot actuation can be obtained in two configurations : wires or thin films . Films can be associated with surface machined silicon structures or with J..lSPL objects to develop micropurnps, movable mirrors or adaptive surface systems (Bush and Johnson, 1990). Nevertheless, using thin films is at present essentially limited to planar applications. To develop microrobots with many degrees of 3D mobility, having a 3D complex geometry, the use of small diameter SMA wires or springs is one of the most suitable configuration.
2.4 Prototypes of microrobots
For the actuation of our current microrobots we chose SMA (NiTi) wires, 120 J..lm in diameter. The advantages of this solution are its low dimensions, a very high energy density and the direct driving of the mechanical structures without intermediary transmission systems. The J..lSPL technology was used to develop deforming mechanical structures. Using this technology, some types of microrobots were built, with 3D mobility from 2 mm to 700 J..lm in diameter. All the prototypes are of serial types,
242
with redundant mobilities. This is a constructive solution well known in macrorobotics, which allows the tracking of complex trajectories by the addition of motions of a large number of modules. All the modules of our prototypes are included in two types of compliant active micromechanisms in kinematical closed-chain : - a compliant dyade type module with a single SMA wire. The active phase corresponds to the Joule heating austenitic transformation. The energy is accumulated in the deformation of the mechanical structure and is released in the return phase, inducing a stress martensitic transformation of SMA wire motor; - a tryade type with one fIrst SMA wire which is the active actuator and a second non heated SMA wire which is only used to amplify the rigidity modulus of the mechanical structure. An example of such a module is presented in fIgure I. Future works are in view to control the microrobot trajectories by heating the two SMA wires. By assembling a great number of modules it is possible to obtain complex mechanisms like the dextrous microgripper presented in fIgure 2.
Fig. I. Pivot type micromodule.
Fig. 2. Prototype of micro gripper.
first phase : laser assisted ~------------------microassembling
SMA prestressed wire IlSPL mechanical structure second phase: laser assisted microassembling after the SMA prestraining manual or automated prestraining device Fig. 3. Assembly principle of a SMA wire microactuator in a polymer IlSPL structure.
Every point of coupling between SMA wires and the polymer structures can be considered as a perfect articulation, because of the flexibility of SMA wires. The compliance of the mechanical structure is made by two types of deformable articulations:
- a hinge type with distributed elasticity, which allows a planar mobility. By the assembling of several modules with different orientations it is possible to realize microrobots with a 3D mobility. This solution allows the parallel coupling of several SMA wires and the variation of the active force by heating a variable number of such micromotors. We have realized such a microrobot, with four parallel assembled SMA wire micromotor and no SMA stiffening wire (dyade type) as shown in fIgure 5. Such microfIngers are able to move a 50 mN. load, i.e. seven times as heavy as the own microrobot. 3
- a pivot type : in fIgure I such a microarticulation with a 2D mobility is presented. We also fabricated modules with a 3D mobility by assembling four SMA wires, distributed 90° by 90° in the polymer structure (see fIgure 4);
243
We also designed a PID-controller to realize a closed-loop control of the position of the microrobot top. This method was tested on several trajectories. Some results of trajectory tracking are given in figure 6 and figure 7. They are very satisfactory in term of performances of the trajectory tracking, especially for the static accuracy of the response, less than 4 Ilm, but can be improved for the dynamic part. Some experiments were also realized with a load of 50 mN in the microrobot top. They also showed good performances. We have also experimented a 3D trajectory generating in open loops. Future experiments will be done to implement the control of this type of trajectory.
mm of magnitude of motion were obtained at the top of a five modules microrobot (total length of the microrobot : 5x4=20 mm).
3. IDENTIFICATION AND CONTROL OF COMPLIANT MICROROBOTS All the physical and technological specifications presented previously showed the difficulty to obtain a theoretical model for our prototypes of microrobots. This fact is due to the difficulty to model and experimentally determine the important physical parameters for the components of the robot. For this reason, in the initial phase an evolutive experimental design of microrobots prototypes is used. In this section we present a neural networks approach for the identification and control of the prototypes. Nevertheless a knowledge model is very important for the design in order to optimize the dynamic behaviour of the system. In the next section some of our results in this field will be presented.
An important problem is the control of the SMA wire behaviour in partial cycles imposed by the microrobotic tasks. It is strongly influenced by the past evolution of microrobot imposing the "return points" in the partial thermomechanical hysteresis cycles of SMA. For this reason, we want to implement and test "memory neural networks" (Sastry et al., 1994). to model and control the dynamic behaviour of the robot. Indeed, in such a network, each neuron is associated with a memory neuron whose output summarizes the history of past activations of the unit. Then, without having to know or to overstimate the order of the system, these memory neural networks allow the identification of the non linear dynamic behaviour of the microrobot in taking into account the thermomechanical history of the system which gives a slow modification of its dynamic behaviour. This approach is a particular case of the neural bond graph models developed in the next section.
It would be very interesting to control with good performances the position of the microrobot top, called the effector, and to track all the desired trajectories in its workspace. In the absence of a knowledge model, we build a control oriented model of our experimental prototypes. Serie-parallel identification by a two-layers network is made. The frrst layer is made by four neurons with a hyperbolic tangent behaviour and the second layer consists in a single linear neuron. The four inputs of this network are the control inputs for two of them values in the two last sampling time - and the measured position of the effector for the other two values in the two last sampling time. The output is the estimated present position of the effector. A back propagation algorithm is used for the learning phase. The experimental tests were realized on a microrobot consisting of five hinged type modules, as shown in figure 4 and figure 5. For the one shown in figure 4, two heated SMA wires are used as the actuator, and the other two are used as elastic springs (tryade type). A single degree of mobility is obtained by the Joule heating of the SMA wire micromotors. The control signal is the current in the wires. The heating is controlled by a PC with an input-output interface. The motion of the microrobot top is measured by a laser sensor with a resolution of I Ilm. After the learning phase, weight and bias of the neural network remain constant for the following tests. The tests realized give good results in term of prediction of the microrobot dynamic behaviour.
Fig. 4. Pivot type microrobot four SMA wires, distributed 90° by 90°.
244
based dynamical model. Our goal is to identify the design parameters involved in these models in order to optimize the microrobot structure.
4.1 Quasi-static model The microrobot is constituted by three physical subsystems: - the compliant closed chain micromechanism; - the SMA wire thermomechanic actuators; - the Joule's type heating control system. The available SMA constitutive equations are generally valid for static behaviour of non cycled samples. We use such a method in an incremental linearized form (Brinson and Lammering, 1993). In this manner, the mechanism behaviour is a static one, valid only for low velocities of input. The dynamic behaviour of the integrated system is introduced by the Joule heating system. The resulting microrobot model is then a quasi-static one : a SMA static behaviour coupled with a thermodynamic model for the heating control system. The problem is now to study the influence of the design parameters for low speed, non cycled, microrobotic tasks, like for instance micromanipulation. In this manner, we can adapt only the desired inertia and stiffness. It is clear that such a model does not allow to act on desired damping microrobot matrix.
Fig. 5. Hinged type microrobot, moving a load of 50 mN (seven times as heavy as the own microrobot). Trajectory tracking 07r-----~----~----_,----_:----_,
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Fig. 6. Response of the microrobot in position closed-loop.
Compliant micromechanism subsystem. Our goal is to calculate the force generated by one SMA wire which is necessary to provide the time evolution of the pivot angle of an elementary micromodule like shown in figure I (two SMA wires are mounted in push-pull positions, one for the actuation and the other for the stiffness). The physical principle of the microrobot motion is based on the Young's modulus evolution during the phase transformation : it is 2.5 time larger in the austenitic phase than in the martensitic phase. This phenomenon is considered in the incremental form of the deformation energy of the microrobot. So, it is possible to determine the incremental form of the global stiffness matrix [K](6x6) in terms of the components of the geometrical model for the pivot angle increment:
Trajectory trackmg ~
i
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:
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10
15
20 25 Time (sec)
30
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Fig. 7. Example of a trajectory tracking.
[K]n = f\ {[k;]n,[I;]n}. (i=3)
(1)
[kiln are the (2x2) component stiffness matrices of the two SMA wires (actuator and stiffness) and of the mechanical structure ; [I;]n are the (I x2) position vectors of the same components ((x,y) incremental values of the mechanism articulations), determined by the geometrical model. The Lagrange model requires the calculation of the incremental kinetic
4. OPTIMIZATION OF MICROROBOT DESIGN: A NEURAL BOND GRAPHS (NBG) APPROACH Only the main phases of our method are presented here. A more detailed presentation is available in (Calin, 1998). Two types of design oriented models are developped : a quasi-static one and a impedance
245
obtain the quasi-static updated incremental model of the microrobot. The design parameters acting on it, are the initial pre-strain in each SMA wire, the wire number and their positions, the current input controlling the SMA phase transition and Young's modulus, and so the stiffness matrix.
energy, which is determined by the kinematical previously deduced model. Only the external load contribution was considered, which is seven times as heavy as the own microrobot weight. The determination of the incremental force in the Lagrange model is realized by imposing the time increment.
In order to identify the validity domain of this quasistatic model, we have realized several experiments on a microrobot prototype, in non loaded task and for current input. Figure 8 presents its cyclic behaviour for a triangle input 0-1 A, with 6 seconds for the widest cycle and 2 seconds of period for the smallest one.
SMA wires sub-system . Our goal is to determine the incremental temperature input needed to produce the wire actuation force previously established. By considering the wire section and length like fixed design parameters, this means to calculate the stress rate (6S) function of strain rate (6E). For the static behaviour of SMA wire, this approach is presented in (Brinson and Lammering, 1993). By the linearization of the weak form of the momentum balance and introducing the SMA one-dimensional constitutive behaviour, one obtains the following closed form expression for the linearized SMA constitutive equations :
~ 12 ,
i
! {S(l1+£JJ}}
= f(Hj}DFTgradjj
1~ o8 ~
(2)
E=O
, 0.4' - - .- -
-0.2
where the first member is the incremental variation of the stress S, induced by a virtual displacement E TI, starting from the precedent known configuration x, and directed along the vector TI . (It is calculated at each iteration by the geometrical model). The deformation gradient F and the displacement gradient grad TI, corresponding to the known configuration x, are obtained from the nodal articulation displacements by N, the matrix of linear shape functions, as defmed in the fmite element method. Hj U=1..6) are the terms introducing the SMA phase transformation characteristics in the classical thermoelastic consitutive equations. They are only functions of SMA constants and the value of stress at which is known for each iteration. "f' is a fonction depending on the type of phase transformation (austenitic or martensitic). The terms Hj preserve quadratic convergence in the solution
0
- -. ..••------~---~~ o_~ 0.2 0.6 0.8 1.2
Fig. 8. Rate influence on cyclic behaviour. The experimental observations, shown in figure 8 have underlined the strong influence of the input rate on the cycle width, the slope of the diagram, and the input-output delay. In the next paragraph a bond graphs (BG) dynamic model is given, which is capable to consider these effects no taken into account in the quasi-static model. They concern the influence of the strain rate on the stiffness (slope) and damping (cycle width) matrices and on the threshold of phase transformation inducing the inputoutput delay. The diagram concerns the dynamic behaviour of the microrobot system : actuator and stiffness SMA wires, polymer compliant structure and SMA-polymer assembling.
x,
5
algorithm. is the SMA Young's tangent incremental modulus for the known configuration. It is function of ~, the current iteration martensite fraction describing the internal phase transition. More informations are available in (Brinson and Lammering, 1993).
, 4.2 Neural bond graph adaptive model.
The classical BG method takes into account hysteresis cycles by the coupling of a storage energy capacitors (C) and dissipating energy resistors R (figure 9) (Kamopp, 1990). For the SMA modelling, Ce is the SMA Young's modulus, in pure austenite or martensite phase (without phase transition). The serial link R-C p represents the dissipation and the storing of energy in a hysteresis behaviour by phase change. Cp represents the equivalent capacitor of the energy stored by of the SMA characteristics.
Joule heating subsystem. The model is based on the heat transfer equations relying the rate of the heat flow induced by the current input, and the rate of the energy change, which depends on the SMA properties and the phase transition. Microrobot model. The linearized relations of the three above mentioned sub-systems are used to
246
Ce
~
R; ... .......,.......: .. .. .
ye1emout
the partial hystersis cycles imposed by a microrobotic task. The static partial SMA hysteresis cycles are controlled by the thermomechanic history by considering the return points of partial cycles [9]. There are no available similar relations for dynamic partial hystersis cycles. We use the memory neural networks (MNN) [9] to go beyond these limits. The MNN are able to identify and control non linear systems, of UTIknown order and changing structure, by considering the whole input-output task history. We use them to adapt both the BG structure and the model parameters. The NBG identified component models are stored in a learning associative design base of compliant microrobots. The general structure of NBG adaptive model is presented in figure 11. u, e, x, cr, T are respectively the input, the error, the position, the stress and the temperature at the increments k or (kI).
Other elements " if higher order
Fig. 9. Classical BG'hysteresis model. The classic BG method is not able to take into account springs with variable stiffness which is the case for SMA wires. The modulation constitutes the BG approach to take into account the variation of physical characteristics of components. It is not valid for physical systems with internal energy source inducing the non conservative behavior of the bond: For this reason we introduce in the BG classical formalism the incremental linearization used in the previous paragraph. The physical characteristic of the resistor R is determined by the influence of the rate evolution on the material properties (see figure 8).
The resulting dynamic behaviour equations, numerical simulations and experimental results are available in (Calin, 1998).
Slope of the diagram. This is determined by the incremental values of tangent SMA Young's modulus (DSMA)' In (Brinson and Lammering, 1993) is deduced the influence of the stress and the temperature on DSMA and in (Shield, 1997) ~xperimental results are given concerning the mfluence of the input rate evolution on the actual stress (and then on DSMA) ' In the same reference is presented the influence of the fatigue and the fissuration on the SMA cyclic dynamic behaviour.
5. CONCLUSION AND FUTURE WORKS We realized several protoypes of microrobots consisting in a mechanical structure in polymer with SMA actuators and the control of the trajectory tracking. We developed a neural bond graph method for design optimization of compliant microrobot. We are about to introduce temperature and force micro sensors in the microrobot architecture to experimentally valid our design models.
Input-output delay. It is determined by the influence of the velocity of the input on the actual stress (rate term 17) and then on the phase transformation threshold.
. O~r future works concerns the following drrectlOns : neural networks control and closed-loop temperature control, integration of sensors into the mechanical structure, multiaxes and force-position control. The potential applications are micromanipulation and microassembly, motions inside tubes and pipes, microcamera and microtool orientation. A main goal is to introduce the NBG model in a experiment-based learning algorithm for the microrobot design with impedance optimization. The microtechnological optimization criterions are introdu.ced in a feature-based form. The coupling of dynamIC NBG models with microtechnological fea~res-based model is the principle of the proposed deSIgn method. Its learning behaviour provides the capability to consider future microtechnologies.
Cycl~ width. It represents the dissipated energy, consIdered by R elements giving the damping matrix.
By coupling all these relations we obtain the design parameters influencing the microrobot dynamics in a bond graph form (figure 10 presents the model for one module of a serial structure like a microfmger). Rand C represent the resistive and capacitive behavi~ur of each component. Cpt and Cel are respectIvely the phase transformation and the elastic ~om~onents . of the stored potential energy.The mertlal term IS introduced by the external load P. TF are BG transformers. Sf are flux sources (mechanical velocities and thermic flux) . We are now interested in the introduction of an adaptive approach in this model, to take into account
247
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~.
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----,r--+l+ SMA Microrobot
+ Sensors (laser sensor, microwelding)
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Fig. 11. Identification of neural bond graph adaptive model using memory neurons.
Karnopp, D. C , D . L. Margolis and R. e. Rosenberg
REFERENCES
(1990). System dynamics : a unified approach, Willey-Interscience. Sastry, P.S., G. Santharam and K.P. Unnikrishnan (1994). Memory Neuron Networks for Identification and Control of Dynamical Systems, IEEE Trans. Of Neural Networks, Vol. 5, No. 2, pp. 306-319. Shield, T. W., P. H. Leo and W. C. Grebner (1997). Quasi-static extension of shape memory wires under constant load, Acta mater. Vol. 45, No. I, pp. 67-74. Zissi, S., A. Bertsch, J. Jezequel, S. Corbel, J.e. Andre and D.J.Lougnot (1996). Stereo lithography and microtechnics, Microsystem Technologies, Vol. 2, pp.97-102.
Bergmasco, M., P.Dario and F.Salsedo (1990). Shape memory alloys microactuators, Sensors and Actuators, Vol. A21-A23, pp. 253-257. Bertsch, A. (1996). Microstereophotolithographie par masquage dynamique, Ph.D Thesis of the INPL, Nancy, France. Brinson, L.C. and R. Lammering (1993). Finite element analysis of the behavior of shape memory alloys and their applications, Int. J. Solids Structures, Vol. 30, No.23, pp. 3261-3280. Bush, J.D. and A.D.Johnson (1990). Shape memory properties in TiNi sputter deposited films, J.Appl.Phys., Vol. 68, pp. 6224-6228. Calin, M. (1998), Etude et realisation de microrobots de type tentacule, Ph.D Thesis of the ENSMM, Besan90n, France.
248
SHAPE MEMORY ALLOY COMPLIANT MICROROBOTS M. Calin", N. Chaillet", J. Agnus", A. Bourjault", A. Bertsch"", S. Zissj"", L.Thiery"""
* Laboratoire d'Automatique de Besanr;on, LAB UMR 6596 (IMFC FR W0067) 25, rue Alain SA VARY, 25000 BESANCON, FRANCE Tel : (33) 03 81 402798 Fax : (33) 0381 402809 Email : [email protected] **DCPR-GRAPP, URA 328 CNRS, 1 rue Granciville, B.P.451, 54001 NANCY, FRANCE ***lnstitut de Genie Energetique, Parc Technologique, 2 avenue 1. Moulin, 90000 BELFORT. FRANCE
Abstract: This paper deals with microrobots actuated by shape memory alloys (SMA). The microrobots must often have a complex 3D geometry and must endure large deformations. Then the mechanical structure of the presented microrobots is realized in polymer by microstereophotolithography (J-lSPL). Different structures, with 2 mm to 700 microns in diameter, have been designed and manufactured, based on elastic pivots and distributed elasticity. Experimental results are given concerning the PID-based motion control of one microrobot. One of our main purposes is the cooperative micromanipulation of micro-objects for micro-assembling tasks. We have developed the impedance model of cooperative microfmgers and identified the design parameters needed for the optimization of our prototypes. Our design method is based on a neural bond graph (N8G) approach. Copyright @19981FAC Keywords: Microrobot, microassembling, shape microstereophotolithography, design, neural bond graph.
I. INTRODUCTION
memory
alloy,
2. DESIGN AND REALIZATION OF MICROROBOTSPROTOTYPES
Microrobotics is an interdisciplinary domain, involving competences from micromechanics, microtechnologies, robotics and control. Our paper describes microrobot actuated by SMA wires, and is composed of three main parts : - design of microrobot prototypes using SMA actuators, with 3D mobility, realized in polymer by J-lSPL, especially microtentacles; - identification and control of these prototypes : because of technological restrictions and characteristics of their actuators, our microrobots are compliant active micromechanisms; - design of such cooperative microrobots with impedance optimization ; we have developed a neural bond graph method (N8G) for adaptive modelling and design optimization.
2.1 The mechanical structure In order to realize microsystems that could be full of interest in microrobotic applications, it is important to be able to produce structures in three dimensions with complex geometries. Moreover, the manufacturing technology has to be collective. Up to now, most micro fabrication techniques, and particularly the ones based on the IC fabrication process, can produce planar microparts, or objects composed of a very small number of layers. Using those techniques, the manufacture of threedimensional parts having curved surfaces and an important number of layers is very difficult. So the IlSPL technique seems to be an attractive alternative
241
2.3 Assembly technique
process to manufacture such kind of 3D microparts with a satisfying accuracy.
To obtain three-dimensional microrobots, an assembly technique is required to integer the SMA wires into the polymer mechanical structure realized by J..lSPL. This technique consists in gluing together the two components, with a controlled initial strain of SMA wire.
In the J..lSPL process, a computer model of the object to build is sliced into horizontal layers. The different slices are then successively manufactured by the space-resolved light-induced polymerization of a liquid monomer in a solid polymer. When a slice of the part is done, the addition of a layer of photopolymerizable resin on the already polymerized part allows to continue the manufacturing process.
When the mechanical structure is designed, clamping areas are provided, in which the SMA wires can be easily inserted. When the SMA wires are correctly positionned in the polymer structure, they are submitted to a mechanical initial stress to store mechanical energy. This step was done by fixing a calibrated weight at one end of the wire, the other end being embeded in a rigid frame . Of course the use of an adapted traction system could improve this operation. Some SMA wires can also be positioned in the structure without initial stress. These passive wires can then have for the future motions a stiffening action.
Two main J..lSPL processes have been developed, the first one is based on a vector by vector tracing of every layer of the object by moving it under a focalized laser beam while manufacturing it (Zissi et al., 1996). It has a typical resolution of 30x30x20 J..lm for every polymerized elementary volume. The second one, called the J..lSPL, gives the most interesting results : it uses a dynamic mask-generator process, and allowed the manufacture of a complete layer by one irradiation only. A liquid cristal display is placed along the optical path (Bertsch, 1996). Its typical resolution is 5 J..lm in the three space dimensions and can be the starting point of a collective fabrication process.
The SMA wires are fixed to the J..lSPL structure by polymerizing a very small amount of photoreactive chemical medium added in the provided holes, with an ultraviolet laser beam, as shown in figure 3. Once the wires are fixed to the polymer structure, the microrobot can nevermore be dismantled. But in fact most microsystems are conceived as objects that can be thrown away after use, and in general, structures that can be dismantled are not really interesting in the micromanufacture field.
2.2 Choice of the actuation solution
Among the physical principles used in the development of miniaturized actuators, the shape memory effect appears to be one of the most attractive. Large deformations and forces can be obtained using shape memory alloys (SMA), and these deformations can be easily converted into flexural or rotative motions by designing adapted mechanical architectures. Different works have already been devoted to this approach, in the field of robotics, but the classical mechanical components used are not well adapted to miniaturization (Bergmasco et al., 1990).
The microassembly process used to manufacture these microrobots is very simple. It requires only two steps which are the addition of a small amount of photopolymerizable resin and a laser irradiation. This technique is then easily adaptable to a collective manufacture of microsystems. Once the wires are fixed to the polymer structure, the ones that are prestressed can be moved by an external heat source, or more efficiently, by Joule effect. In this approach, the SMA wires act as resistors inserted in a current loop.
SMA for microrobot actuation can be obtained in two configurations : wires or thin films . Films can be associated with surface machined silicon structures or with J..lSPL objects to develop micropurnps, movable mirrors or adaptive surface systems (Bush and Johnson, 1990). Nevertheless, using thin films is at present essentially limited to planar applications. To develop microrobots with many degrees of 3D mobility, having a 3D complex geometry, the use of small diameter SMA wires or springs is one of the most suitable configuration.
2.4 Prototypes of microrobots
For the actuation of our current microrobots we chose SMA (NiTi) wires, 120 J..lm in diameter. The advantages of this solution are its low dimensions, a very high energy density and the direct driving of the mechanical structures without intermediary transmission systems. The J..lSPL technology was used to develop deforming mechanical structures. Using this technology, some types of microrobots were built, with 3D mobility from 2 mm to 700 J..lm in diameter. All the prototypes are of serial types,
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with redundant mobilities. This is a constructive solution well known in macrorobotics, which allows the tracking of complex trajectories by the addition of motions of a large number of modules. All the modules of our prototypes are included in two types of compliant active micromechanisms in kinematical closed-chain : - a compliant dyade type module with a single SMA wire. The active phase corresponds to the Joule heating austenitic transformation. The energy is accumulated in the deformation of the mechanical structure and is released in the return phase, inducing a stress martensitic transformation of SMA wire motor; - a tryade type with one fIrst SMA wire which is the active actuator and a second non heated SMA wire which is only used to amplify the rigidity modulus of the mechanical structure. An example of such a module is presented in fIgure I. Future works are in view to control the microrobot trajectories by heating the two SMA wires. By assembling a great number of modules it is possible to obtain complex mechanisms like the dextrous microgripper presented in fIgure 2.
Fig. I. Pivot type micromodule.
Fig. 2. Prototype of micro gripper.
first phase : laser assisted ~------------------microassembling
SMA prestressed wire IlSPL mechanical structure second phase: laser assisted microassembling after the SMA prestraining manual or automated prestraining device Fig. 3. Assembly principle of a SMA wire microactuator in a polymer IlSPL structure.
Every point of coupling between SMA wires and the polymer structures can be considered as a perfect articulation, because of the flexibility of SMA wires. The compliance of the mechanical structure is made by two types of deformable articulations:
- a hinge type with distributed elasticity, which allows a planar mobility. By the assembling of several modules with different orientations it is possible to realize microrobots with a 3D mobility. This solution allows the parallel coupling of several SMA wires and the variation of the active force by heating a variable number of such micromotors. We have realized such a microrobot, with four parallel assembled SMA wire micromotor and no SMA stiffening wire (dyade type) as shown in fIgure 5. Such microfIngers are able to move a 50 mN. load, i.e. seven times as heavy as the own microrobot. 3
- a pivot type : in fIgure I such a microarticulation with a 2D mobility is presented. We also fabricated modules with a 3D mobility by assembling four SMA wires, distributed 90° by 90° in the polymer structure (see fIgure 4);
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We also designed a PID-controller to realize a closed-loop control of the position of the microrobot top. This method was tested on several trajectories. Some results of trajectory tracking are given in figure 6 and figure 7. They are very satisfactory in term of performances of the trajectory tracking, especially for the static accuracy of the response, less than 4 Ilm, but can be improved for the dynamic part. Some experiments were also realized with a load of 50 mN in the microrobot top. They also showed good performances. We have also experimented a 3D trajectory generating in open loops. Future experiments will be done to implement the control of this type of trajectory.
mm of magnitude of motion were obtained at the top of a five modules microrobot (total length of the microrobot : 5x4=20 mm).
3. IDENTIFICATION AND CONTROL OF COMPLIANT MICROROBOTS All the physical and technological specifications presented previously showed the difficulty to obtain a theoretical model for our prototypes of microrobots. This fact is due to the difficulty to model and experimentally determine the important physical parameters for the components of the robot. For this reason, in the initial phase an evolutive experimental design of microrobots prototypes is used. In this section we present a neural networks approach for the identification and control of the prototypes. Nevertheless a knowledge model is very important for the design in order to optimize the dynamic behaviour of the system. In the next section some of our results in this field will be presented.
An important problem is the control of the SMA wire behaviour in partial cycles imposed by the microrobotic tasks. It is strongly influenced by the past evolution of microrobot imposing the "return points" in the partial thermomechanical hysteresis cycles of SMA. For this reason, we want to implement and test "memory neural networks" (Sastry et al., 1994). to model and control the dynamic behaviour of the robot. Indeed, in such a network, each neuron is associated with a memory neuron whose output summarizes the history of past activations of the unit. Then, without having to know or to overstimate the order of the system, these memory neural networks allow the identification of the non linear dynamic behaviour of the microrobot in taking into account the thermomechanical history of the system which gives a slow modification of its dynamic behaviour. This approach is a particular case of the neural bond graph models developed in the next section.
It would be very interesting to control with good performances the position of the microrobot top, called the effector, and to track all the desired trajectories in its workspace. In the absence of a knowledge model, we build a control oriented model of our experimental prototypes. Serie-parallel identification by a two-layers network is made. The frrst layer is made by four neurons with a hyperbolic tangent behaviour and the second layer consists in a single linear neuron. The four inputs of this network are the control inputs for two of them values in the two last sampling time - and the measured position of the effector for the other two values in the two last sampling time. The output is the estimated present position of the effector. A back propagation algorithm is used for the learning phase. The experimental tests were realized on a microrobot consisting of five hinged type modules, as shown in figure 4 and figure 5. For the one shown in figure 4, two heated SMA wires are used as the actuator, and the other two are used as elastic springs (tryade type). A single degree of mobility is obtained by the Joule heating of the SMA wire micromotors. The control signal is the current in the wires. The heating is controlled by a PC with an input-output interface. The motion of the microrobot top is measured by a laser sensor with a resolution of I Ilm. After the learning phase, weight and bias of the neural network remain constant for the following tests. The tests realized give good results in term of prediction of the microrobot dynamic behaviour.
Fig. 4. Pivot type microrobot four SMA wires, distributed 90° by 90°.
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based dynamical model. Our goal is to identify the design parameters involved in these models in order to optimize the microrobot structure.
4.1 Quasi-static model The microrobot is constituted by three physical subsystems: - the compliant closed chain micromechanism; - the SMA wire thermomechanic actuators; - the Joule's type heating control system. The available SMA constitutive equations are generally valid for static behaviour of non cycled samples. We use such a method in an incremental linearized form (Brinson and Lammering, 1993). In this manner, the mechanism behaviour is a static one, valid only for low velocities of input. The dynamic behaviour of the integrated system is introduced by the Joule heating system. The resulting microrobot model is then a quasi-static one : a SMA static behaviour coupled with a thermodynamic model for the heating control system. The problem is now to study the influence of the design parameters for low speed, non cycled, microrobotic tasks, like for instance micromanipulation. In this manner, we can adapt only the desired inertia and stiffness. It is clear that such a model does not allow to act on desired damping microrobot matrix.
Fig. 5. Hinged type microrobot, moving a load of 50 mN (seven times as heavy as the own microrobot). Trajectory tracking 07r-----~----~----_,----_:----_,
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:
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:
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:
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./
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00
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20 30 Time (sec)
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Fig. 6. Response of the microrobot in position closed-loop.
Compliant micromechanism subsystem. Our goal is to calculate the force generated by one SMA wire which is necessary to provide the time evolution of the pivot angle of an elementary micromodule like shown in figure I (two SMA wires are mounted in push-pull positions, one for the actuation and the other for the stiffness). The physical principle of the microrobot motion is based on the Young's modulus evolution during the phase transformation : it is 2.5 time larger in the austenitic phase than in the martensitic phase. This phenomenon is considered in the incremental form of the deformation energy of the microrobot. So, it is possible to determine the incremental form of the global stiffness matrix [K](6x6) in terms of the components of the geometrical model for the pivot angle increment:
Trajectory trackmg ~
i
16 ..... . :- ... . . ~ .. ..
:
.; - - ----~ ----- ~- ----- ~ -----
.. .. i·· ··· ·;· · ···· t······: ......:...... ;..... 04
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····+····i······j--···-i-·····r····· +.... 5
10
15
20 25 Time (sec)
30
35
40
Fig. 7. Example of a trajectory tracking.
[K]n = f\ {[k;]n,[I;]n}. (i=3)
(1)
[kiln are the (2x2) component stiffness matrices of the two SMA wires (actuator and stiffness) and of the mechanical structure ; [I;]n are the (I x2) position vectors of the same components ((x,y) incremental values of the mechanism articulations), determined by the geometrical model. The Lagrange model requires the calculation of the incremental kinetic
4. OPTIMIZATION OF MICROROBOT DESIGN: A NEURAL BOND GRAPHS (NBG) APPROACH Only the main phases of our method are presented here. A more detailed presentation is available in (Calin, 1998). Two types of design oriented models are developped : a quasi-static one and a impedance
245
obtain the quasi-static updated incremental model of the microrobot. The design parameters acting on it, are the initial pre-strain in each SMA wire, the wire number and their positions, the current input controlling the SMA phase transition and Young's modulus, and so the stiffness matrix.
energy, which is determined by the kinematical previously deduced model. Only the external load contribution was considered, which is seven times as heavy as the own microrobot weight. The determination of the incremental force in the Lagrange model is realized by imposing the time increment.
In order to identify the validity domain of this quasistatic model, we have realized several experiments on a microrobot prototype, in non loaded task and for current input. Figure 8 presents its cyclic behaviour for a triangle input 0-1 A, with 6 seconds for the widest cycle and 2 seconds of period for the smallest one.
SMA wires sub-system . Our goal is to determine the incremental temperature input needed to produce the wire actuation force previously established. By considering the wire section and length like fixed design parameters, this means to calculate the stress rate (6S) function of strain rate (6E). For the static behaviour of SMA wire, this approach is presented in (Brinson and Lammering, 1993). By the linearization of the weak form of the momentum balance and introducing the SMA one-dimensional constitutive behaviour, one obtains the following closed form expression for the linearized SMA constitutive equations :
~ 12 ,
i
! {S(l1+£JJ}}
= f(Hj}DFTgradjj
1~ o8 ~
(2)
E=O
, 0.4' - - .- -
-0.2
where the first member is the incremental variation of the stress S, induced by a virtual displacement E TI, starting from the precedent known configuration x, and directed along the vector TI . (It is calculated at each iteration by the geometrical model). The deformation gradient F and the displacement gradient grad TI, corresponding to the known configuration x, are obtained from the nodal articulation displacements by N, the matrix of linear shape functions, as defmed in the fmite element method. Hj U=1..6) are the terms introducing the SMA phase transformation characteristics in the classical thermoelastic consitutive equations. They are only functions of SMA constants and the value of stress at which is known for each iteration. "f' is a fonction depending on the type of phase transformation (austenitic or martensitic). The terms Hj preserve quadratic convergence in the solution
0
- -. ..••------~---~~ o_~ 0.2 0.6 0.8 1.2
Fig. 8. Rate influence on cyclic behaviour. The experimental observations, shown in figure 8 have underlined the strong influence of the input rate on the cycle width, the slope of the diagram, and the input-output delay. In the next paragraph a bond graphs (BG) dynamic model is given, which is capable to consider these effects no taken into account in the quasi-static model. They concern the influence of the strain rate on the stiffness (slope) and damping (cycle width) matrices and on the threshold of phase transformation inducing the inputoutput delay. The diagram concerns the dynamic behaviour of the microrobot system : actuator and stiffness SMA wires, polymer compliant structure and SMA-polymer assembling.
x,
5
algorithm. is the SMA Young's tangent incremental modulus for the known configuration. It is function of ~, the current iteration martensite fraction describing the internal phase transition. More informations are available in (Brinson and Lammering, 1993).
, 4.2 Neural bond graph adaptive model.
The classical BG method takes into account hysteresis cycles by the coupling of a storage energy capacitors (C) and dissipating energy resistors R (figure 9) (Kamopp, 1990). For the SMA modelling, Ce is the SMA Young's modulus, in pure austenite or martensite phase (without phase transition). The serial link R-C p represents the dissipation and the storing of energy in a hysteresis behaviour by phase change. Cp represents the equivalent capacitor of the energy stored by of the SMA characteristics.
Joule heating subsystem. The model is based on the heat transfer equations relying the rate of the heat flow induced by the current input, and the rate of the energy change, which depends on the SMA properties and the phase transition. Microrobot model. The linearized relations of the three above mentioned sub-systems are used to
246
Ce
~
R; ... .......,.......: .. .. .
ye1emout
the partial hystersis cycles imposed by a microrobotic task. The static partial SMA hysteresis cycles are controlled by the thermomechanic history by considering the return points of partial cycles [9]. There are no available similar relations for dynamic partial hystersis cycles. We use the memory neural networks (MNN) [9] to go beyond these limits. The MNN are able to identify and control non linear systems, of UTIknown order and changing structure, by considering the whole input-output task history. We use them to adapt both the BG structure and the model parameters. The NBG identified component models are stored in a learning associative design base of compliant microrobots. The general structure of NBG adaptive model is presented in figure 11. u, e, x, cr, T are respectively the input, the error, the position, the stress and the temperature at the increments k or (kI).
Other elements " if higher order
Fig. 9. Classical BG'hysteresis model. The classic BG method is not able to take into account springs with variable stiffness which is the case for SMA wires. The modulation constitutes the BG approach to take into account the variation of physical characteristics of components. It is not valid for physical systems with internal energy source inducing the non conservative behavior of the bond: For this reason we introduce in the BG classical formalism the incremental linearization used in the previous paragraph. The physical characteristic of the resistor R is determined by the influence of the rate evolution on the material properties (see figure 8).
The resulting dynamic behaviour equations, numerical simulations and experimental results are available in (Calin, 1998).
Slope of the diagram. This is determined by the incremental values of tangent SMA Young's modulus (DSMA)' In (Brinson and Lammering, 1993) is deduced the influence of the stress and the temperature on DSMA and in (Shield, 1997) ~xperimental results are given concerning the mfluence of the input rate evolution on the actual stress (and then on DSMA) ' In the same reference is presented the influence of the fatigue and the fissuration on the SMA cyclic dynamic behaviour.
5. CONCLUSION AND FUTURE WORKS We realized several protoypes of microrobots consisting in a mechanical structure in polymer with SMA actuators and the control of the trajectory tracking. We developed a neural bond graph method for design optimization of compliant microrobot. We are about to introduce temperature and force micro sensors in the microrobot architecture to experimentally valid our design models.
Input-output delay. It is determined by the influence of the velocity of the input on the actual stress (rate term 17) and then on the phase transformation threshold.
. O~r future works concerns the following drrectlOns : neural networks control and closed-loop temperature control, integration of sensors into the mechanical structure, multiaxes and force-position control. The potential applications are micromanipulation and microassembly, motions inside tubes and pipes, microcamera and microtool orientation. A main goal is to introduce the NBG model in a experiment-based learning algorithm for the microrobot design with impedance optimization. The microtechnological optimization criterions are introdu.ced in a feature-based form. The coupling of dynamIC NBG models with microtechnological fea~res-based model is the principle of the proposed deSIgn method. Its learning behaviour provides the capability to consider future microtechnologies.
Cycl~ width. It represents the dissipated energy, consIdered by R elements giving the damping matrix.
By coupling all these relations we obtain the design parameters influencing the microrobot dynamics in a bond graph form (figure 10 presents the model for one module of a serial structure like a microfmger). Rand C represent the resistive and capacitive behavi~ur of each component. Cpt and Cel are respectIvely the phase transformation and the elastic ~om~onents . of the stored potential energy.The mertlal term IS introduced by the external load P. TF are BG transformers. Sf are flux sources (mechanical velocities and thermic flux) . We are now interested in the introduction of an adaptive approach in this model, to take into account
247
Sf*(output 11 : without Mechanical compliant
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'>
(I) 0
~r~
(I~~)
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controlled Joule heating: source
toad-Ip,Cp,Rp)
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. . the module G-I) '..:
Fig. 10. BG dynamic model of the module "j" of the microrobot.
~.
Uk
Power supply
----,r--+l+ SMA Microrobot
+ Sensors (laser sensor, microwelding)
T k• 1
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Fig. 11. Identification of neural bond graph adaptive model using memory neurons.
Karnopp, D. C , D . L. Margolis and R. e. Rosenberg
REFERENCES
(1990). System dynamics : a unified approach, Willey-Interscience. Sastry, P.S., G. Santharam and K.P. Unnikrishnan (1994). Memory Neuron Networks for Identification and Control of Dynamical Systems, IEEE Trans. Of Neural Networks, Vol. 5, No. 2, pp. 306-319. Shield, T. W., P. H. Leo and W. C. Grebner (1997). Quasi-static extension of shape memory wires under constant load, Acta mater. Vol. 45, No. I, pp. 67-74. Zissi, S., A. Bertsch, J. Jezequel, S. Corbel, J.e. Andre and D.J.Lougnot (1996). Stereo lithography and microtechnics, Microsystem Technologies, Vol. 2, pp.97-102.
Bergmasco, M., P.Dario and F.Salsedo (1990). Shape memory alloys microactuators, Sensors and Actuators, Vol. A21-A23, pp. 253-257. Bertsch, A. (1996). Microstereophotolithographie par masquage dynamique, Ph.D Thesis of the INPL, Nancy, France. Brinson, L.C. and R. Lammering (1993). Finite element analysis of the behavior of shape memory alloys and their applications, Int. J. Solids Structures, Vol. 30, No.23, pp. 3261-3280. Bush, J.D. and A.D.Johnson (1990). Shape memory properties in TiNi sputter deposited films, J.Appl.Phys., Vol. 68, pp. 6224-6228. Calin, M. (1998), Etude et realisation de microrobots de type tentacule, Ph.D Thesis of the ENSMM, Besan90n, France.
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