Proceedings of the 2004 IEEE International Conference on Robtics L Automation New Orleans, LA 'April 2004
Infinite Dimension System Approach for Hybrid ForcePosition Control in Micromanipulation Jizhong Xiao Wen J. Li Yantao Shen, Ning Xi, and U. C. Wejinya Dept. of Automation and Dept. of Electrical and Dept. of Electrical and ' Computer-Aided Engr. Computer Engr. Computer Engr. Michigan State University The Chinese University of Hong Kong The City College of New York , Shatin, Hong Kong, China New York, USA East Lansing, MI, USA Email: shenya,xin,
[email protected] .edu Emaif:
[email protected] Email:
[email protected]
Absfracf-This paper aims at developing a force-guided micromanipulation technology with in-situ PVDF beam force sensing and hybrid forcdposition control based on an infinite dimensional system model. By using the designed PVDF force sensing cantilever composite structure -with hi& wl~itivity,the micro, contact forcelimpact signa! and its derivative can. be, extracted and processed. As the sensor structure installed at the end
to reduce the large impact effects [SI. In [6], Tanikawa et al. presented a force con@bl system whose task is to keep a proper force during the grasp micmmanipulation, as the authors reported in paper, the high success rate of the grasp task Can not be obtained with a stiffness-like-force-control scheme. It is reasonable to state
.
,
oi an infinite dimension system model. ExperimentaJ results efficient micromanipulation. The objective of this paper is to develop a micro scale force verify the performance of the developed micro force sensing and hybrid control scheme. Ultimately the technology will provide a and con@olscheme. i.e.. modefine and designing a critical and major step towards the deFelopment of automated, highly sensitive force to -the micro manufacturing processes for batch assembly of micro devices. force information, and then enables an on-line regulation of both micro contact force and position during the micromanipuI. INTRODUCT~ON lation. The sensor is designed with a flexible PVDF cantilever Manufacturing ,processes which are capable of 'efficiently beam structure. As the sensor installed at the free end of the assembling micro. devices have not been developed, partially micromanipulator is a rather soft beam, when manipulation because, at the micro-scale, structures are fragile and easily is performed, the beam is necessary to be considered as a breakable. They typically break at .the micro-Newton force flexible link of micromanipulator, .then based on an infinite range that cannot be reliably measured by the most existing dimensional system approach and the feedback of the selfforce sensors [4]. Moreover, so far the most straightforward sensing link, a hybrid micro forcelposition control scheme and flexible operation methods are still to use microprobe is developed on the basis of an infinite dimensional model toiphysically manipulate the micro device [2] and run in a of the sensor. The importance of forcdposition control of open loop format. Thus this method can be inherently risky flexible manipulators was mentioned in, [lo]. However, there without an on-line safety micro force regulation, As a result, are quite a few papers that treat the hybrid control of flexible this situation decreases overall yield and drives up the cost of manipulators on the basis of an infinite dimensional model, micro devices [I]. it is still essentially an open problem due to the distributed For these reasons mentioned above, researches into au- parameter nature of the models [11][12]. In this paper, our tomating the micromanipulation processes have focused on work addresses the micro scale hybrid control using an infinite the micro force sensing and the related control techniques. dimensional system approach. The experiments demonstrate Currently, there exist some developing sensing mechanisms the performances of the developed micro scale hybrid control commonly used in sensing contact forces in micro scale (41. schemes. This could be an important step to make reliable and Among those mechanisms, more suitably, the resolution of high yield batch fabrication and manipulation of micro devices force sensors based on piezoelectric effect is the range a reality. of pN generally [7].Furthermore, the development of force 11. PVDF SENSING MODEL regulation schemes are necessary ,because .big impact and contact forces may break micro structures or may destroy A. Modeling of PVDF composite Ream Sensing micro cell during bio-manipulation. Recently, a low level Fig.1 shows a I-D PVDF sensor beam structure. Following proportional impact force control scheme using nano scale the geometry characteristic of the I-D sensor, since the beam optical beam deflection force feedback, has been implemented is much wider and longer than the thickness, the strain sy ~
-
0-7803-8232-3/04/$17.M) a 0 0 4 IEEE
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Fig. 1 . Illustration of the I-D PVDF cornpasite sensing beam
+
&(t) = IL(d31o(r,t) ~ & @ 3 ( t ) ) W d ~ 0
along the width of the beam can be assumed to be zero. With the above descriptions, based on piezoelectric effect, the unit piezoelectric equation is: (without considering the inverse piezoelectric affection and pyroelectric effects) [13].
D~(T t ) ,= ds,a(r,t)
+ ~:&(t).
(1)
If no charge builds up by the external. force, &(t) in equation (7) will be zero. Then, an equivalent circuit model of a resistor R p in parallel with a capacitor Cp can be used to represent the PVDF film sensor. The output voltage V ( t ) across the PVDF film, can be described by
where D3(?,t ) is the normal electric displacement of PVDF film. is the transverse piezoelectric coefficient. u ( T , ~ ) denotes the unit stress along beam lenglh. E: is the normal dielectrical constant of PVDF film. E3(t) is the normal electrical field of PVDF film. The surface area polarization gives a charge & ( t )across the PVDF surface a e a A (Lx W):
Here the voltage is related to the electric field by’
(9) I
-3
Therefore, &(t) = is the uniform electric field over HI a very small thickness.H,, and then
Using the mechanics of materials for cantilever beam, as shown in Fig.1, the unit stress on the PVDF film strip can be obtained as
Thus we have the following equation to represent the relationship between the generated voltage and the contact force:
V(t) + A V @ ) = B f c ( t ) where X = 2RpCp is a constant, C p =
According to the Fig.1, notice that since two-layer composite beam is in use (we omit the effect of thin electrode layers at the top and bottom surfaces of PVDF layer.), I will be the moment of the transformed section of the composite beam. The neutral axis c, of the composite beam passes through the centroid .of the mansformed cross section. c is the distance between the outside surface of PVDF layer and the neutral axis of the beam. w ( T , ~ )the , elastic deflection of the flexible sensor beam and 0 5 r I L. Here, the neutral axis of the composite beam can be obtained by
W H I C I+ - W H ~ C ~ E1 c, = AT E2
(4)
where E l , E2 are Young moduli of PVDF film and Polyester film, respectively. c1 and c;. are the distances of centroid axes of PVDF layer and Polyester layer with respect to the base
(11) ET3A
- is
RP(IBlA(L0
HI
+ $)c
the
.
capacitance of PVDF film. B = IS a I constant. By Laplace transformation, the electrical transfer function of the sensing beam is given as:
V(s)
B
fc(s)
-X
T ( s )= --
As
lf’
B. Signul Conditioning For signal conditioning, a differential charge amplifier with the same feedback capacitors C f l and C f , is designed for the PVDF force sensor. The differential charge amplifier is based on the chopper stabilized operational amplifier TC765oC with a high input impedance 10”!2 and low bias current 1.5pA. Following the charge amplifier, a differential-to-single-ended amplifier with the gain Kc is added. In this design, the total differential topology can reduce the common mode noises
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niKerenlial charge smplirm ,.__._.__.__...._
Fig. 2.
of the motor base along X and Z axes; w ( L , t ) , the elastic deflection at the free end of the flexible link; and p(r, t ) := z ( t ) - w(r,t). the displacement variable along Z axis. Since we consider to regulate the micro contact force along Z axis, an assumption of small deflection of the heam is made, then we can ignore the effects of centripetal acceleration and axial compression of the beam.
Schematics ai the developed electronic circuit
Y .-->
more effectively. To reject the existing high frequency noises, an active low pass filter with a small time constant TI is used before the voltage output. The integration of the output voltage by time can also be achieved by an integrator unit in the circuit. To further remove.the noises from the data acquisition system, a Gaussian-type low pass filter is added in the data collection program. The simplified~diagramof developed circuit is shown in Fig. 2.
1 I I I
z+ Fig. 3.
C. Svsreni Trunsfer Function
we can obtain the ‘contact force by measuring the output voltage of the sensor system when the initial values %(to) and V&,(to) are known. By preliminary calibration, the sensitivity of the PVDF senso; was estimated to be 4.6602V/pN, the resolution of the sensor was in the range of sub-pN. The output dynamic range of, the sensor is 84.3 dB. The details can be found in [E].
where B ( t ) = w’(L,t ) sinB(t) z= +,t) L ’ Notice that in this paper, a prime represents the displacement derivative and a dot denotes the time derivative. From Fig. 3, at the root end of flexible link, the geometric boundary condition is given w(0,t) =w‘(0,t) = 0
Ptz
. The high sensitive sensor is installed at the tip of the micromanipulator. During manipulation, it is necessary to be considered as an infinite dimensional flexible li+of micromanipulator. In this section, on the basis of an infinite dimensional model of flexible sensor beam, a hybrid force/position control scheme in micromanipulation is proposed.
As shown in Fig. 3, during manipulation, we consider the sensor as a one-link flexible arm with a rigid tip. It is driven by a linear motor along the Z-axis and X-axis in the horizontal and venical direction, respectively. E l , the uniform flexural rigidity of composite beam ( E = El): p. the uniform mass per unit length of the composite beam; A&, the mass of the translational motor base; pt. the uniform mass per unit length of the tip; F,(t), F,(t), the control input forces applied to the linear motor base along X and 2 axes; z ( t ) ,z ( t ) , the positions
@(l.(t),w(L,t),w’(L,t)) Z ( t ) - w(L,t ) - Low’(& t ) L Lo z= .(t) - w ( L , t ) ( 7) =
+
(16)
Based on the system motion (i.e. planar motion), the total kinetic energy is given by
EK A. Dynamic Model of Infinite Dintensional System
(15)
Then, a constraint surface @ ( z ( t ) , w ( L , t ) , w ‘ ( L . t )= ) 0 for the system is found by
111. HYBRIDCONTROL OF FLEXIBLE SENSOR BEAM ’
A flexible l i k with a rigid tip driven by a linear motor
The position vector of contact p i n t of the rigid tip is given
Finally, by considering the whole system, the global transfer function is
e .The function is a bandpass type filter. Based on this equation,
Glass substrate
=
1 -Afm,i2(t) 2
+$
L 0
p2(r,t)dr
1 1 . + -I& + 21tB2(t) 2
(17) . , pL3 . where I b = -IS the moment of inertia of the flexible heam. . 12 Wb = is the angular velocity of the flexible beam.
k
. the moment of inertia of the rigid tip. And the It = PtLo -IS 3 . total potentlal energy E p is
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In the system, the virtual work 6 W is given by
6W = 6z(t)F,(t)
(19)
Substituting the above equations into the Extended Hamiltonk Principle
L r ( 6 E K - 6Ep
+ 6W + E6m)dt = 0
(20)
where let [ be a Lagrange multiplier associated with the above constraint (16). The contact force between the constraint surface and the rigid tip can be represented in the term of the Lagrange multiplier 5. Then we obtain the following dynamic equations of the constrained one-link flexible arm along Z axis.
micromanipulation.) and the desired contact force f," is given as 1 W d ( T ) = -(3LT2 - T 3 + 3Lor2)f,d. (30) 6EI From the constrained condition of system motion in eqn. (16), then the relationship between the zd of the motor base and the desired contact force f: is given
This relationship can be used to set a Zd corresponding to a desired contact force f f . In addition, considering the linear motor moves along X axis, we assume that the motion along X axis (veltical motion) doesn't affect the bending of flexible link,'so we have the dynamics of system along X axis as follows,
Afmi(t)
(32)
where 77th is the mass of the beam, mt the mass of the tip. G is gravity of the system.
and the corresponding boundary conditions as follows
(24)
w(0, t ) = w'(0,t ) = 0
+ (7726 + mt)?(t)= & ( t ) - G
B. Design uf Hybrid Fnrcr/Pr,sitiori Conr&ller Based on the dynamic equations (21). (22) and the boundary conditions (23)-(25), the force controller in the constrained direction Z has the following general form
am
'F,(t)= - k p ( i - - d ) - l i d S - F - + ( f , - S g l l ( f c d i ) f , " ) (33) &(t) (25) where kp, and k d are positive gains. i d can be set according
Moreover, the relationship between the contact force fc and the Lagrange multiplier can be given by
to equation (31) if a desired contact force f," is required. 5 = fJt) can be measured by using the PVDF sensor. ~ ( t ) and i ( t ) can be obtained by the encoder. From equation (32). the position controller in the unconstrained direction X has the following general form
where J, is Jacobian matrix between the Cartesian coordinate and the generalized coordinate [ z ( t ) w ( L ,t ) w ( L ,t)lT.From equation (26), we obtain
f&
= C(t)
(27)
To realize the contact force control, we consider the relation : be the desired contact force, of f c ( t ) . w ( T , t ) . and t ( t ) .Let f W d ( r j the related static deformation of the flexible beam, and z,j, the related static position of the motor base at the equilibrium state. At the equilibrium state (f:, W d ( T ) , z d ) . the relation is found as i ( t ) = i ( t ) = 0, ij(T,t)
=
w ( r , t )= 0
(28)
and based on the above equation and equation (22), we have ,,,, wd ( r ,t ) = 0. (29)
By considering the kinematics of the sensor structure, the relation of the static defokation w ~ ( T(assumed ) the bending of the beam mostly appears in the first shape mode in this
F,(t)
= - k P z ( z - ~ d -) kdz(k - f d j
+G
(34)
where kprr and kdr are positive gains. The controller in equation (34) is a traditional scheme for position control and trajectory tracking, we put less words to describe it. Here, we use the PVDF force sensor to detect the setting desired force, once the detected force approaches the desired value, the position control in the unconstrained direction X will be started. 77ieoreni 1: If the control force applied to the motor base is decided by the controller equation (33). then the original distributed parameter, infinite dimensional system is stable.
Proof: Consider the following Lyapunov function: I
V(t) = E ~ + E ~ + p k ~ ( t ( t ) - z d ) ' + I J f , " ( 2 ( t ) - ~ d (35) )ll In a differential form. we have
+ + k p i ( t ) ( s ( t-) y)+ sgn(f,"t)f,di (36)
V ( t ) = EK E p
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I Connector lo micro robot link I \
connector
I
. . ~ ~ . ~ ~ ~
Fig. 5 .
Fig. 4. The micro robot with the pieiklectric force sensing and conlml system ai MSU.
Substituting the related equations (17, 18, 21-25) into the above equation, yields V ( t ) = i(t)F;(t)
+ (1+ !+(t)(z(t) - id) + sgn(f,di) f,d,dt.
(37) Then substituting the controller (33) into the equation, leads to V ( t )= -k&(t), which means negative semi-definite. So the closed-loop system is stable. .
AX541 1H is lKHz in the experiments. The maximum encoder frequency of micromanipulator motor is 8 x lo6 countds with 14-bit DAC resolution. The loop time of the force sensing and control system is about 2ms. To reduce the vibrations from the environment, an active vibration isolated table was used during the experiments.
B. Force Sensing Calibrafioii Calibration on the contact sensing has been conducted. By virtue of a precisely calibrated Mitutoyo lOOx microscope It is clear that the controller (33) is independent of (with a 50x objective and a 2x zoom), and a Sony CCD camera system parameters, and thus possesses robust stabipy to the system, the set-up for accurately measuring the tiny bending system parameter uncertainties. Based on the force feedback angle @ ( t ) or deflection A ( t ) of the sensor beam under the from the flexible PVDF beam itself, the controller is also microscope was built. Then based on the strain energy method easy to be implemented, no high-order signal measurements of bending beam, The real micro force can be achieved. The are needed. Refemng to the method of Separating Variables detailed results can be found in [SI, the results verify the ([IO], [14], [IS]), the asymptotical-stability of the system can. performance of the force sensor. be proved. C. Hybrid Micro Force/Posirion Confml As shown in Fig. 3, we use a linear motor to move the PVDF IV. EXPERIMENTS sensor tip to contact a glass surface along Z axis horizontally, A. E.xperiinentul Ser-rip the micro contact force regulation on the basis of the infinite The experiments were conducted in a micro robotic system dimension model is tested. In the first experiment, when the shown in Figure 4 at stable room temperature. The micro motor moves from an initial position, assuming the sensor tip robotic system mainly consists of a SIGNATONE Computer continue to contact at a point on the glass surface, the PVDF Aided Probe Station and a Mitutoyo FS60 optical microscope beam starts to bend, like a flexible link of micromanipulator. system. The micro robot is controlled by a PC-based control By using the developed sensing and control method, the micro system. The control system is an open platform which can force of tip is regulated to a desired value. Figure 6 shows easily be integrated with the developed PVDF force sensor and the results of force control of flexible Stmcture. In the force infinite dimensional control system. The PVDF force sensor figure , the dash line represents the desired force f,d. Another is shown in Figure 5. The PVDF force sensor (I-D) has the experimental result shows after a period of tip force regulation following dimensions and parameters: LO = 0.0225m;L = along Z axis, starting from 2.9s, the sensor tip is controlled 0.0192m; zu = 0.0102m; HI = 28pm(PVDF film);R p = to move a straight tine along X direction on the constrained 1.93 x io^; c p = 0.90 x 1 0 - 9 ~ ; = 0.2 x 10-'OF; E = glass surface from the contact point, at the same time, the 2 x 10gN/mZ;E2 = 3.8 x 10gN/mZ;p= 1.911g/m. pt = contact force is still regulated in the contact direction (Z 0.089g/m. direction). Figure I shows the experimental result with the The force and its rate processed by the designed circuit gains kp = 15, kd = 10. The results verify the performance are collected and transferred to the micro robotic system via of the developed hybrid forcelposition control scheme, that a multifunction analogldigital input/output board AX541 1H is, with the position z ( t ) approaches to the desired value zd. installed in a PC. There exists a communication between the the force regulation law makes the force error go to zero PC and the micro robotic system. The sampling frequency of asymptotically. '
L
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V. CONCLUSION
This paper presents the development of a micro force-guided micromanipulation technology with in-situ PVDF beam force sensing and hybrid forcelposition control based on an infinite dimensional model. By using the designed PVDF force sensing cantilever composite structure with high sensitivity, the micro contact force/impact signal and its derivative can be extracted and processed. Since the sensor structure installed at the end of micromanipulator is a soft beam, when manipulation is performed, the cantilever beam is also considered as an infinite dimensional flexible Link. then we developed a hybrid micro contact forcdposition control scheme on the basis of an infinite dimension system approach. Experimental results verify the performance of the developed micro force sensing and hybrid control scheme. Ultimately the technology will provide a critical and major step towards the development of automated manufacturing processes for batch assembly of micro devices.
REFERENCES I l l J. R. Reid, V. M. Bnghl, J. H. Comlois, Aurorrrared Assembly ofFlip-up Micmmirmrr, TRANSDUCERS '97 Chicago.. vol. 1. pp. 347 -390, 1997. 121 E. E. Hui. R. T. Howe, and M. S. Rodgers, Single-Siep Asrevrblj of Compler 3-D Micmrrrunures. IEEE MEMS 2000, pp. 602.607. 131 S . K. Koelemijer Chollet. L. Benmayor. J.-M. Uehlinger and 1. lacot, Corr Eflccriw Micm-Sjsrear Aswnblj Aurontorion, Proceedings of Emerging Technologies and Factory Alomation. Vol. 1. pp. 359.366, 1999.
Hyhrid camml: (a) micro contact force along Z (b) positions z(1) and r(l) in 2 and X.
Fig. I .
141 S. Falikow. J. Seyfned. S. Fahlbusch, A. Buerkle. and E Schmoeckel, A Flexibl~Micmmbor-Based Micmassembly SrorionJoumd of Intelligent and Robotics Systems. Val. 21, pp. 135-169, 2000. [SI Y. Zhau, B. J. Nelson and B. Viliramaditya, Fusing Force and Wsion Feedbock for Micmmanpulalion. ICRA1998. pp. 1220-1225. 1998. 161 T.Tanikawa. M. Kawai. N. Koyachi. T.Arai. T.Ide. S. Kaneko. R. Ohla and T. Hirase, Force Conrml S w e m forduloonomous Micm Monipulorion, ICRA2001. pp. 610.615, 2001. 171 C. K. M. Fmg. 1. Elhajj. W. I . Li. and N. Xi, A 2-D PVDF Force Sensinp S W e m for Micm-nro,iip.lorion orid Micm-ossmbl?, ICRA2002, pp. 1489.1494, 2002. 181 Y. T. Shen, N. Xi. and Wen J. Li. Fore Guided Asrembly ofMicm Mirmm, k c d i n g s of the [EEEIRSJ lotmntional Conference on Intelligent Robots and Systems, Vol. 3, pp. 2149-2154. 2003. 191 T.J. Tam,Y. Y. Wu, N. Xi. and A. Isidori, Force Regulorion and Conroct Tronsirion Conrml. IEEE Control Systems, pp. 32-40, February 19%. [ I O ] F. Matsuno and S. Kasai. Modeling ond Robust Forcc Conrml of Condmined One-Link Flexible Anns, Journal of Robotic Systems. Vol. 15. No. 8, pp. 447-464. 1998. [II] E Chin& D.Wang An ln/i~ire-dimensionoIAnolysis o f . PD-Conrmlled Single Flexible Lbrk in Collision. Proc. of IEEE Internadanal Conference on Robotics and Automation. pp. 419426, 1999. 1121 B. Siciliano and L. Villani, Porollel Force and Posirion Corirml of Flexible Mnnipularors, IEE Proceedings - Control Theory Application, Vol. 147. no. 6. pp. 605-612, 2000. I131 An American Notional Stondord: IEEE Srmdord on Piezoelectrid~, ANSnEEE Standard 176-1987, 1987. 1141 L. Meirovitch. Elemenis of Vlbmlion Anol?sir. New York McCnw-Hill. ch. 5. pp. 218. 1975. .11S1, S . S . Ge. T.H. Lee. and C . Zhu Arvmototicallr Stoble End-Poiru Reeulotion of Flerible SCARA/Caneti& kobor. IEEUASME Tranractians on Mechatronics, Vol. 3. No. 2, 1998.
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