sensors Article
Development and Hybrid Position/Force Control of a Dual-Drive Macro-Fiber-Composite Microgripper Jin Zhang 1 , Yiling Yang 1, * 1 2 3
*
ID
, Junqiang Lou 1, *
ID
, Yanding Wei 2,3 and Lei Fu 2,3
Faculty of Mechanical Engineering and Mechanics, Ningbo University, Ningbo 315211, China;
[email protected] The Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province, Zhejiang University, Hangzhou 310058, China;
[email protected] (Y.W.);
[email protected] (L.F.) State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310058, China Correspondence:
[email protected] (Y.Y.);
[email protected] (J.L.)
Received: 1 April 2018; Accepted: 20 April 2018; Published: 23 April 2018
Abstract: This paper reports on the development, implementation and hybrid control of a new micro-fiber-composite microgripper with synchronous position and force control capabilities. In particular, the micro-fiber-composite actuator was composed of rectangular piezoelectric fibers covered by interdigitated electrodes and embedded in structural epoxy. Thus, the micro-fiber-composite microgripper had a larger displacement-volume ratio (i.e., the ratio of the output displacement to the volume of the microgripper) than that of a traditional piezoelectric one. Moreover, to regulate both the gripper position and the gripping force simultaneously, a hybrid position/force control scheme using fuzzy sliding mode control and the proportional-integral controller was developed. In particular, the fuzzy sliding mode control was used to achieve the precision position control under the influence of the system disturbances and uncertainties, and the proportional-integral controller was used to guarantee the force control accuracy of the microgripper. A series of experimental investigations was performed to verify the feasibility of the developed microgripper and the control scheme. The experimental results validated the effectiveness of the designed microgripper and hybrid control scheme. The developed microgripper was capable of precision and multiscale micromanipulation tasks. Keywords: micro-fiber-composite; microgripper; hybrid control; micromanipulation; position/force
1. Introduction During the past few decades, the piezoelectric actuator has received much attention in the fields of micromanipulation and microassembly [1–3]. This is because piezoelectric material exhibits high resolution and fast response capabilities [4,5]. In particular, piezoelectric actuators are involved in various types of bending actuators (d31 effect, i.e., the material deformation direction is perpendicular to the polarization direction), stack actuators (d33 effect, i.e., the material deformation direction and polarization direction are the same), and macro-fiber-composite (MFC) actuators (d33 effect), as illustrated in Figure 1. When a driving voltage is applied to the piezoelectric bending actuator (PBA), the piezoelectric ceramic (PZT) will elongate or shorten in the length direction [6]. Thus, the material body (e.g., the beryllium bronze and carbon fiber) will cause the bending deformation of the mechanism. Moreover, the piezoelectric stack actuator (PSA) is composed of a multilayer PZT substrate. Its structure is mechanically connected in series and electrically in parallel, as shown in Figure 1b. In addition, the MFC actuator consists of rectangular PZT fibers sandwiched between electrodes, polyimide film,
Sensors 2018, 18, 1301; doi:10.3390/s18041301
www.mdpi.com/journal/sensors
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and layers of adhesive. Therefore, the MFC actuator prevails, owing to its flexible nature, large outputs, and damage tolerance [7]. Sensors 2018, 18, x 2 of 17
do PZT
Electrode
Electrode
Interdigitated electrode
do
V
V
PZT fiber
PZT
Polyimide film V
Structural epoxy
do (a)
(b)
(c)
Figure 1. Schematic diagram of piezoelectric actuators: (a) the PBA; (b) the PSA, and (c) the MFC actuator. Figure 1. Schematic diagram of piezoelectric actuators: (a) the PBA; (b) the PSA, and (c) the MFC actuator.
To effectively manipulate micro-objects ranging in size from micrometers to millimeters, both To effectively manipulate micro-objects ranging in size from to millimeters, both high high resolution and a large workspace range are desirable formicrometers microgrippers in a microhandling resolution and a large workspace range are desirable for microgrippers in a microhandling system [8,9]. system [8,9]. To date, many microgrippers driven by the PBA and PSA have been reported. However, To PBA date,usually many microgrippers driven by the PBA(approximately and PSA have20 been reported. However, thewith PBA the has a small output displacement μm). Even when combined usually has a small output displacement (approximately 20 µm). Even when combined with another another actuation source (e.g., the thermal actuation), the stroke of the PBA-driven microgripper is actuation source (e.g., theAlthough thermal actuation), the stroke of the PBA-driven microgripper is norange, more no more than 100 μm [10]. the PSA-driven microgripper can produce a large gripping than 100compliant µm [10]. mechanisms Although theand PSA-driven microgripper can produce a large complex huge structural dimensions are needed. Forgripping example,range, the complex compliant mechanisms and huge structural dimensions are needed. For example, the authors authors in [11] reported a PSA-driven microgripper based on the double-rocker mechanism where in [11] reported a PSA-driven based on the the output the output displacement wasmicrogripper 427.8 μm. However, thedouble-rocker microgrippermechanism also had where huge geometric displacement was 427.8 However, the microgripper also had huge geometric parameters, parameters, resulting in µm. an inferior displacement-volume performance. Considering that theresulting output in an inferior displacement-volume performance. Considering that the output displacement to be displacement has to be compared with the global size of the microgripper [12], this research has focused compared with the global size of the microgripper [12], this research focused on thewith development of a on the development of a microgripper driven by a MFC actuator. When compared the PBA and microgripper driven by a MFC actuator. When compared with the PBA and PSA, the MFC actuator PSA, the MFC actuator can provide a large output displacement, which simplifies the gripper can provide large output displacement, which simplifies structure and adecreases the number of amplification flexures.the gripper structure and decreases the number of amplification flexures. However, in most studies on MFC actuators, the operation accuracy is lower than the millimeter However, in most studies MFC actuators, the operation lower considered, than the millimeter level. The extension of the MFCon actuator to anultrahigh positionaccuracy control isisrarely except level. The extension of the MFC actuator to anultrahigh position control is rarely considered, except for in [13], where a feed forward control based on the Bouc-Wen model and a linear feedback control for inused [13],to where a feed forward controlnonlinearities based on the arising Bouc-Wen model and a linear feedback control were compensate the hysteresis from the inherent characteristics of the were used to compensate the hysteresis nonlinearities arising from the inherent characteristics of the MFC actuator. However, a single MFC manipulator was investigated, and only the position control MFC actuator. However, single MFC manipulator andand onlythe thegripping positionforce control was conducted. Generally,athe synchronous control ofwas the investigated, gripper position is was conducted. Generally, the synchronous control of the gripper position and the gripping force extremely challenging, but is essential in precision micromanipulation tasks [14]. In [15,16], ais extremely control challenging, but iswas essential in precision micromanipulation tasksforce [14]. In a switching switching scheme proposed to regulate the position and of[15,16], the piezoelectric control scheme proposed to regulate the position and force variables of the piezoelectric microgripper in an microgripper in was an alternate manner. However, the two control were switched successively. alternate manner. However, the two control variables were switched successively. It was difficult to It was difficult to obtain a smooth transition, and only the position or the force could be well obtain a smooth transition, and only the position or the force could be well controlled in each phase. controlled in each phase. The disadvantages of the switching control could be avoided using the The disadvantages of the switching control could be avoided using impedance scheme. impedance control scheme. Based on the Lyapunov approach, [17]the developed a control position-based Based on the Lyapunov approach, [17] developed a position-based impedance control and a sliding impedance control and a sliding mode impedance force control for a PBA-driven microgripper. In mode impedance force control for a PBA-driven microgripper. In [18], a discrete impedance control for [18], a discrete impedance control for both the gripper position and gripping force was proposed, and both the gripper position and gripping force was proposed, and the control stability was verified by the control stability was verified by introducing an appropriate Lyapunov function. introducing an appropriate Lyapunov function. Nevertheless, the impedance control scheme only uses one actuator to regulate two variables. It Nevertheless, the impedance scheme only uses one actuator to regulate two variables. is a typical under-actuated system. control Thus, the control accuracy presents a compromise between the It is a typical under-actuated system. Thus, the control accuracy presents a compromise between position and force [19]. To achieve a balance between the two variables, the control accuracy of the the positioncontrol and force [19].isTo achieve adegraded. balance between two variables, control accuracy impedance scheme necessarily On the the other hand, hybridthe control using two of the impedance control schemefor is necessarily degraded. On of thethe other hand,and hybrid using independent actuators is suitable the simultaneous control position forcecontrol [10]. As for twocontrol independent is suitable the presents simultaneous position and force [10]. the law, theactuators sliding mode controlfor (SMC) great control potentialofinthe stable and precise control applications [20–22]. However, the switching gain in most SMCs is constant or quasi-linear. Concerning system disturbances and model uncertainties in the microgripper, a SMC with a nonlinear adaptive law is desirable [23,24]. To this end, a new MFC microgripper with a large displacement-volume ratio was developed. Meanwhile, a hybrid control scheme was designed to realize the simultaneous control of both the
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As for the control law, the sliding mode control (SMC) presents great potential in stable and precise control applications [20–22]. However, the switching gain in most SMCs is constant or quasi-linear. Concerning system disturbances and model uncertainties in the microgripper, a SMC with a nonlinear adaptive law is desirable [23,24]. SensorsTo 2018, 18,end, x 3 of 17 this a new MFC microgripper with a large displacement-volume ratio was developed. Meanwhile, a hybrid control scheme was designed to realize the simultaneous control of both the position position and and gripping gripping force. force. In In particular, particular, aa new new MFC MFC microgripper microgripper with with two two independent independent MFC MFC actuators is presented. Moreover, the position of the right gripping arm was determined using a actuators is presented. Moreover, the position of the right gripping arm was determined using a fuzzy fuzzy sliding mode control (FSMC), and the force of the left gripping arm was regulated by a PI sliding mode control (FSMC), and the force of the left gripping arm was regulated by a PI controller. controller. Several experimental investigations wereto conducted to demonstrate efficiency and the Several experimental investigations were conducted demonstrate the efficiencythe and the feasibility of feasibility of the developed microgripper and the control scheme. the developed microgripper and the control scheme. The this paper paper is is organized organized as as follows. follows. The The rest rest of of this The description description of of the the MFC MFC microgripper microgripper is is presented presented in in Section Section 2. 2. Section Section 33 shows shows the the hybrid hybrid control control scheme scheme for for regulating regulating the the position position and and the the gripping gripping of of the the microgripper. microgripper. The The prototype prototype development, development, aa series series of of experimental experimental studies, studies, and and the the discussions are outlined in Section 4. In Section 5, the conclusions are described. discussions are outlined in Section 4. In Section 5, the conclusions are described. 2. 2. Description Description of of the the MFC MFC Microgripper Microgripper The is is shown in in Figure 2. As in Figure 2, the The CAD CADdrawing drawingofofthe theMFC MFCmicrogripper microgripper shown Figure 2. illustrated As illustrated in Figure 2, developed microgripper consisted of a pair MFC actuators, a pair aofpair printed circuit circuit board (PCB) the developed microgripper consisted of a of pair of MFC actuators, of printed board cantilevers, a pair of end-effectors, and a support base. Moreover, two identical gripping arms were (PCB) cantilevers, a pair of end-effectors, and a support base. Moreover, two identical gripping arms used to construct the microgripper, andand each gripping arm was composed were used to construct the microgripper, each gripping arm was composedofofone oneMFC MFC actuator actuator (model: Material Corp, Sarasota, FL, FL, USA), one one PCBPCB cantilever, and one (model: M2814-P1, M2814-P1,from fromSmart Smart Material Corp, Sarasota, USA), cantilever, andendone effector. Furthermore, the MFC actuator was attached to the to base the of PCB using end-effector. Furthermore, the MFC actuator was attached theend baseofend thecantilever PCB cantilever epoxy (model:(model: DP460, DP460, from 3M Company, Maplewood, MN, USA). The gripping arm could generate using epoxy from 3M Company, Maplewood, MN, USA). The gripping arm could agenerate large output displacement at the tip end when an input voltage was applied to the MFC actuator. a large output displacement at the tip end when an input voltage was applied to the MFC As the microgripper was drivenwas using two using separate gripping could arm be controlled actuator. As the microgripper driven twoactuators, separate the actuators, thearm gripping could be independently, which provided a more adexterous and reliable micromanipulation operation. In controlled independently, which provided more dexterous and reliable micromanipulation operation. addition, by employing one gripper arm with a MFC actuator as a basic module, a multi-modular In addition, by employing one gripper arm with a MFC actuator as a basic module, a multi-modular gripper gripper could be easily developed. ~ u(t) PCB cantilever
y
Endeffector
Base
Micro-object
MFC actuator
MFC actuator
(a)
(b)
Figure 2. (a) Schematic diagram of the MFC microgripper; (b) Illustration of a micro-object gripping Figure 2. (a) Schematic diagram of the MFC microgripper; (b) Illustration of a micro-object gripping with a microgripper that contains a pair of MFC actuators. with a microgripper that contains a pair of MFC actuators.
The end-effector was glued onto the front end of the PCB cantilever, as shown in Figure 2a. Thus, The end-effector wasof glued onto the end the PCB asthe shown in Figureby 2a. Thus, the structure and material the gripper tipfront could beof adapted to cantilever, the shape of micro-object merely the structure and material of the gripper tip could be adapted to the shape of the micro-object by merely changing the end-effectors. Hence, the microgripper system became simple, and the effectiveness of the changing the applications end-effectors.could Hence, the microgripper system became and theusing effectiveness manipulation be improved. The end-effectors were simple, manufactured a stereo of the manipulation applications could be improved. The end-effectors were manufactured using lithography apparatus (model: RS6000, from Uniontech three-D Technology Co., Ltd., Shanghai, China) a stereo lithography apparatus (model: RS6000, from Uniontech three-D Technology Co., Ltd., along with various materials of a methacrylate photosensitive resin (from Formlabs Corporation, Somerville, MA, USA). Furthermore, the MFC actuator had a very flexible nature and a larger input voltage range from −500 V to 1500 V, while the maximal voltage applied to the conventional piezoelectric actuator was lower than 200 V. In addition, the MFC actuator had a greater electromechanical coupling coefficient than the conventional one. Therefore, the MFC actuator could provide a larger output displacement and a higher actuation force, which makes the MFC actuator suitable for
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Shanghai, China) along with various materials of a methacrylate photosensitive resin (from Formlabs Corporation, Somerville, MA, USA). Furthermore, the MFC actuator had a very flexible nature and a larger input voltage range from −500 V to 1500 V, while the maximal voltage applied to the conventional piezoelectric actuator was lower than 200 V. In addition, the MFC actuator had a greater electro-mechanical coupling coefficient than the conventional one. Therefore, the MFC actuator could provide a larger output displacement and a higher actuation force, which makes the MFC actuator suitable for use in the actuation of a microgripper dedicated to multiscale micromanipulation applications. 3. Hybrid Position/Force Controller Design 3.1. Position Controller Design for the Right Gripping Arm of the Microgripper The purpose of the position controller is to regulate the driving voltages applied to the MFC actuator once the desired position trajectories of the gripping arm are specified. A FSMC based on the dynamic model combined with a fuzzy regulator was used to determine the output displacement of the microgripper. Therefore, the position control performance was guaranteed by the FSMC. It is known that the dynamic model of the piezoelectric system can be presented as follows: (
.. . my(t) + by(t) + cy(t) = c d p u(t) − H(t) + p(t) .
.
H = αd p u − β|u|H|H|n−1 − γu|H|n
(1)
where the parameters m, b, and c denote the equivalent mass, the damping coefficient, and the stiffness of the microgripper, respectively; y is the tip displacement as shown in Figure 1b; u represents the control voltage; t is the time variable; p(t) denotes the perturbation term arising from creep, external force, system disturbances, and model uncertainties; H denotes the nonlinear displacement hysteresis, and its shape and magnitude is determined by parameters α, β, γ, and n; and dp represents the piezoelectric coefficient and the driving voltage of the MFC actuator. Considering that the structure of the microgripper is flexible, the parameter n was assigned as one [13]. Supposing that the position error ey (t) = yd (t) −y(t), where yd (t) is the desired signal and y(t) denotes the actual signal. Then, the sliding function can be defined as s ( t ) = λ P ey ( t ) + λ I
Z t 0
.
ey (τ )dτ + ey (t)
(2)
where λP and λI are designated positive parameters. . Note that the equivalent control ueq is the solution to sr (t) = 0, the equivalent control can be derived by combining Equations (1) and (2). ueq
h
m c b m − λ I y + m − λP cd p . +λ P yd +λ I yd + mc H − pmest
=
. .. y + yd
(3)
where pest (t) represents the estimation value of the perturbation term p(t), which can be acquired by its one-step delayed estimation [17]. pest (t)
..
.
= my(t − T ) + by(t − T ) + cy(t − T ) −cd p u(t − T ) + cH(t − T )
(4)
Considering that sometimes the initial force of the microgripper does not lie on the sliding surface, and system disturbances and uncertainties always exist, an extra reaching law usw is needed. Thus, the total control can be expressed as
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= ueq h+ usw . .. . = cdmp mc − λ I y + mb − λ P y + yd + λ P yd +λ I yd + mc H − pmest + ηsgn(sr ) + δsr
uy
(5)
where δ (δ>0) is a control gain; η (η> 0) denotes a positive switching gain; T is the sampling time; and sgn(·) represents the sign function. Theorem 1. For the system (1) with the sliding function (2), the sliding mode will occur in afinite time if control law (5) is used. Proof. The Lyapunov function candidate is chosen as
L=
1 2 sr 2
(6)
Then, the following conditions are required: .
.
L = sr sr < 0
(7)
The first derivate of the sliding function s can be written as .
sr
c m
=
. .. . − λ I y + mb − λ P y + yd + λ P yd
+λ I yd +
Pest c mH − m
−
Perr m
−
cd p m uy
(8)
where perr (t) is the perturbation estimation error, i.e., perr (t)= p(t) −pest (t). Combining Equations (2), (6), and (8), we have .
.
L = sr shr = sr
. .. . − λ I y + mb − λ P y + yd + λ P yd i cd +λ I yd + mc H − pmest − pmerr − mp uy = sr −ηsgn(sr ) − δsr − pmerr = −η |sr | − δsr 2 − pmerr sr c m
(9)
When the switching gain η is designed to meet the condition as follows η>
| Perr | +κ m
(10)
where κ (κ> 0) denotes an arbitrary constant. Then, the following equation is derived .
.
L = sr sr = −η |sr | − δsr 2 − < −η |sr | − pmerr sr < −κ | sr | < 0
perr m sr
(11)
Therefore, Equation (7) can be satisfied using Equations (9)–(11). According to the Lyapunov stability theorem, the control system is stable, and the states reach the sliding surface in a finite time. When using the SMC to conduct the position tracking, the chattering phenomenon may occur, since the function sgn(sr ) in Equation (5) is discontinuous. Thus, a saturation function was used to substitute the sign function to suppress the chattering. The saturation function is given by
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sat(sr ) =
sr > ε | sr | < ε −1 sr < − ε
1
sr ε
(12)
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where ε (ε > 0) denotes the thickness of the boundary layer. It was observed that a linear feedback where (ε> used 0) denotes thickness of boundary the boundary It was observed thatwas a linear feedback controlεwas when sthe within the layer,layer. and the switching control only employed r was control was used when s r was within the boundary layer, and the switching control was only if sr was outside the boundary layer. employed if sr was outside the boundary layer.to adjust the switching gain η in terms of the system Moreover, a fuzzy regulator was used Moreover,According a fuzzy regulator wascontrol used to adjustthe theswitching switchinggain gainη η in terms of thewhen system uncertainties. to the SMC process, should increase the . uncertainties. According to the SMCthe control switching η should increasethe when theη position trajectory has not reached idealprocess, sliding the surface (i.e., sgain Furthermore, gain r sr > 0). . position reached ideal the sliding surface (i.e.,𝑠 Furthermore, the again η needs to trajectory decrease ifhas the not trajectory hasthe crossed sliding surface (i.e., Consequently, fuzzy 𝑟 𝑠̇𝑟s>r s0). r < 0). needs to decrease if the trajectory has crossed thegiven sliding regulator can be developed. The fuzzy sets are by surface (i.e., 𝑠𝑟 𝑠̇𝑟 < 0). Consequently, a fuzzy regulator can be developed. Thenfuzzy sets are given by o . ss = ∆η = NB (13) PS PM PB NM NS ZO ss NB NM NS ZO PS PM PB (13) .
.
.
where parameter parameter 𝑠𝑠̇ ssisisthe thelinguistic linguistic variable , and k1 the is the normalizing factor), where variable ( 𝑠𝑠̇(s = s= k1 𝑠k𝑟 𝑠̇1𝑟sr,srand k1 is normalizing factor), the the incremental ∆η denotes the output linguistic variables; NB, NM, and NS represent negative incremental Δη denotes the output linguistic variables; NB, NM, and NS represent negative big, big, negative medium negative small, respectively; is zero; PM, andPB PBare arepositive positivesmall, small, negative medium and and negative small, respectively; ZOZO is zero; PS,PS, PM, and positive medium and positive big, respectively. positive medium and positive big, respectively. The membership membership functions functions for for the the input input and and the the output output linguistic linguistic variables variables are are illustrated illustrated in in The Figure 3. 3. As As shown shown in the purpose of Figure in Figure Figure 3, 3, Gaussian-shaped Gaussian-shapedmembership membershipfunctions functionswere wereused usedforfor the purpose smooth transition. of smooth transition. NM
NS
ZO
PS
PM
NB
PB
1
0.8
0.8
Degree of membership
Degree of membership
NB 1
0.6
0.4
0.2
NS
ZO
PS
PM
PB
0.6
0.4
0.2
0
0 -1
NM
-0.5
0
0.5
-1
1
-0.5
0
0.5
1
Δη
sds
(a)
(b)
Figure 3. Membership functions for (a) the input linguistic variable, and (b) the output linguistic variable. Figure 3. Membership functions for (a) the input linguistic variable, and (b) the output linguistic variable.
In addition, the complete rule base of the fuzzy regulator can be designed as follows In addition, the complete rule base of the fuzzy regulator can be designed as follows R1: IF ss is PB THEN is PB . R1 : R 2 :IF IFss ssis is PB PB PM THEN THEN ∆η isis PM . R2 : IF s s is PM THEN ∆η R3 : IF ss is PS THEN is isPSPM . : R3 PS ZO THEN THEN ∆η isis ZO (14) R 4 :IF IFss. ssis is PS (14) R4 : R5 :IF IFss ss is is ZO THEN ∆η is NS ZO NS THEN is . R5 : IF ss is NS THEN ∆η is NS R6 : IF . ss is NM THEN is NM R6 : IF s s is NM THEN ∆η is NM R7 : IF . ss is NB THEN is NB R7 : IF ss is NB THEN ∆η is NB To convert the degrees of membership of the output linguistic variable, the center of gravity defuzzification method was used, because it could calculate the best compromise among multiple output terms [25]. Then, the switching gain was acquired using the following equation t
M dt 0
(15)
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To convert the degrees of membership of the output linguistic variable, the center of gravity defuzzification method was used, because it could calculate the best compromise among multiple output terms [25]. Then, the switching gain was acquired using the following equation η=M
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Z t 0
∆ηdt
(15)
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where M (M> denotes theschematic scale factor.diagram of the FSMC for the position control of the Figure 4 0)shows the Figure 4 shows the schematic diagram of the FSMC for the position control of the MFCmicrogripper. MFCmicrogripper.
FSMC controller
yd
M
k1
y
sr sr Sliding function
Disturbance
DSM controller u f ueq u sw
MFC
Fuzzy regulator ss
Microgripper
Figure4.4.Schematic Schematicdiagram diagramof ofthe thetrajectory trajectorycontroller. controller. Figure
3.2. Force ForceController ControllerDesign Design for for the the Left Left Gripping Gripping Arm Arm of of the the Microgripper Microgripper 3.2. In precise precise micromanipulation micromanipulation applications, applications, the the driving driving voltages voltagesapplied applied to to the the MFC MFC actuator actuator In needed to to be be regulated regulated once once the the desired desired force force trajectories trajectories of of the the gripping gripping arm arm were were specified. specified. needed Considering that the micromanipulation progress is usually very slow [26], and the model errors Considering that the micromanipulation progress is usually very slow [26], and the model errors alwaysexist, exist, aa simple simple proportional-integral(PI) proportional-integral (PI)controller controllerwas wasused usedtotocompensate compensatethe theforce forceerrors. errors. always Based on thethe control algorithm could eliminate the steady error and respond rapidly. Based on the theforce forceobserver, observer, control algorithm could eliminate the steady error and respond The force controller output isoutput given is bygiven by rapidly. The force controller
K K T p T0 u fu(kf )(k= +KKpp[[ε(k ) −ε((kk−1)]1 )] +p 0 (kε)(k) ) uuf (f k(k−11)) Ti Ti
(16) (16)
where kk denotes denotes the the sampling sampling number; number; εε is is the the position position tracking tracking error error between between the the desired desired force force where trajectory and the actual one; K and T represent the proportional gain and integral time, respectively; p trajectory and the actual one; Kp and Ti represent the proportional gain and integral time, respectively; i and TT00isisthe thesampling samplinginterval intervaland andTT0 0isisequal equaltoto0.0005 0.0005s.s. and 3.3. Hybrid HybridPosition/Force Position/ForceController Controller Design Design for for the the MFC MFC Microgripper Microgripper 3.3. In this this section, section, the the hybrid hybrid position position and and force force control control of of the the two two gripping gripping arms arms of of the the MFC MFC In microgripper are are considered. considered. To To carry carry out out aa precision precision micromanipulation micromanipulation application, application,aa procedure procedure microgripper similar to the studies in [10,17] was used. To begin with, the two end-effectors were in contact with similar to the studies in [10,17] was used. To begin with, the two end-effectors were in contact with the micro-object. Then, several concurrent position and force trajectories were used to grip the object. the micro-object. Then, several concurrent position and force trajectories were used to grip the object. After that, that, the the desired desired position position and and force force return return to to zero zero to to release release the the micro-object. micro-object. After Finally, the FSMC for the position and the PI controller for the gripping forcewere wereused usedtogether. together. Finally, the FSMC for the position and the PI controller for the gripping force The output of the right and the left gripping arms were measured by the laser sensor. Then, the gripping The output of the right and the left gripping arms were measured by the laser sensor. Then, the force of the leftofgripping arm wasarm estimated using a popular force observer (see Section Figure gripping force the left gripping was estimated using a popular force observer (see4.3). Section 4.3).5 gives the schematic diagram of the hybrid position and force control scheme. Figure 5 gives the schematic diagram of the hybrid position and force control scheme.
NI 9234
y
Laser sensor
f
yd fd
FSMC
uy
Gripper NI 9263
f
PI Observer
uf NI 9234
Power amplifier
Laser sensor
MFC1 MFC2
similar to the studies in [10,17] was used. To begin with, the two end-effectors were in contact with the micro-object. Then, several concurrent position and force trajectories were used to grip the object. After that, the desired position and force return to zero to release the micro-object. Finally, the FSMC for the position and the PI controller for the gripping force were used together. The output of the right and the left gripping arms were measured by the laser sensor. Then, the Sensorsgripping 2018, 18, 1301 force of the left gripping arm was estimated using a popular force observer (see Section 4.3).8 of 18 Figure 5 gives the schematic diagram of the hybrid position and force control scheme.
NI 9234
y
Laser sensor
f
yd fd
FSMC
uy
Gripper Power amplifier
NI 9263 PI
f
uf
Observer
NI 9234
MFC1 MFC2
Laser sensor
Figure 5. Schematic diagram of the hybrid position/force control scheme.
Figure 5. Schematic diagram of the hybrid position/force control scheme.
4. Experimental and Discussions Sensors 2018, 18,Results x
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4.1. Prototype Development 4. Experimental Results and Discussions The prototype and the experimental setup of the MFC microgripper are presented in Figure 6. 4.1. Prototype Development Two MFC actuators (model: M2814-P1, from Smart Material Corp) were driven by a power amplifier The prototype and the experimental setup of the MFC microgripper are presented in Figure 6. (model: PZD700A, from Trek Corporation, Waterloo, WI, USA). The power amplifier had a maximal Two MFC actuators (model: M2814-P1, from Smart Material Corp) were driven by a power amplifier voltage of 700 V and an amplification ratio of 70. A laser displacement sensor (model: LK-G30, (model: PZD700A, from Trek Corporation, Waterloo, WI, USA). The power amplifier had a maximal from voltage Keyence Osaka, Japan) was used to measure the output of from the MFC of Corporation, 700 V and an amplification ratio of 70. A laser displacement sensor displacement (model: LK-G30, microgripper, which had a Osaka, 50-nm resolution 10measure mm. Asthe the output range of the displacement Keyence Corporation, Japan) waswithin used to displacement of the was MFCat the micron level, whilewhich the range the gripping at the level, another laser sensor microgripper, had a of 50-nm resolutionforce withinwas 10 mm. Asmillinewton the range of the displacement was at the LK-G150, micron level, while the range of the gripping was resolution at the millinewton level, another laser (model: from Keyence Corporation) with aforce 500-nm was used to evaluate the force LK-G150,Moreover, from Keyence Corporation) withand a 500-nm resolutionfor wasdata usedacquisition to evaluate and of thesensor MFC (model: microgripper. four-channel A/D D/A modules theoutput force were of theprovided MFC microgripper. Moreover, four-channel A/D and chassis D/A modules for data with control by a National Instruments (NI) cDAQ-9174 in combination acquisition and control output were provided by a National Instruments (NI) cDAQ-9174 chassis in an analog input module NI-9234 and an analog output module NI-9263. Furthermore, the control combination with an analog input module NI-9234 and an analog output module NI-9263. system was implemented using a personal computer (PC) with Labview software. In addition, a wire of Furthermore, the control system was implemented using a personal computer (PC) with Labview the single-mode optical fiber (the diameter is 750 µm) was chosen as the micro-object to be manipulated, software. In addition, a wire of the single-mode optical fiber (the diameter is 750 μm) was chosen as as illustrated in the magnified view inas Figure 6. in the magnified view in Figure 6. the micro-object to be manipulated, illustrated
Laser sensor Support
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4.2. Output Displacement Test
4.2. Output Displacement Test
Using alaser displacement sensor, the output displacement of the MFC microgripper can be
Using alaser displacement the output displacement of the MFC microgripper can be experimentally measured. Duesensor, to the symmetric structure, the output displacement was tested by experimentally measured. Due to the symmetric structure, wasoftested exerting amulti-amplitude sine-wave voltage (ranging from the 0 to output 9 V) to displacement the MFC actuator the by rightgripping arm, as illustrated in Figure 7. The maximal output displacement of one gripping arm was approximately 1221.3 μm. When compared with the reported microgrippers in [10,11,17,19], the proposed MFC one presented a much larger output displacement, which is preferable for multiscale micromanipulation tasks. Moreover, significant hysteresis loops, which arose from the inherent characteristics of the piezoelectric actuators, are exhibited in Figure 7b. It was observed that the maximal hysteresis accounted for 17.3% of the output displacement. To compensate for the piezoelectric
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exerting amulti-amplitude sine-wave voltage (ranging from 0 to 9 V) to the MFC actuator of the rightgripping arm, as illustrated in Figure 7. The maximal output displacement of one gripping arm was approximately 1221.3 µm. When compared with the reported microgrippers in [10,11,17,19], the proposed MFC one presented a much larger output displacement, which is preferable for multiscale micromanipulation tasks. Moreover, significant hysteresis loops, which arose from the inherent characteristics of the piezoelectric actuators, are exhibited in Figure 7b. It was observed that the maximal hysteresis accounted for 17.3% of the output displacement. To compensate for the piezoelectric hysteresis in the assembly and manipulation tasks, a precise control strategy for the MFC microgripper was required. Sensors 2018, 18, x 9 of 17 1400
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4.3. Force Observer Development 4.3. Force Observer Development To estimate thethe force signal ininthe variousforce forceobservers observers have been developed. To estimate force signal themicrogripper, microgripper, various have been developed. For example, a linear force observer using a simple dynamic modelisisreported reportedin in[27]. [27]. However, However, this For example, a linear force observer using a simple dynamic model this linear observer exhibited a low accuracy, owing to the piezoelectric hysteresis and creep linear observer exhibited a low accuracy, owing to the piezoelectric hysteresis and creep phenomenon. a nonlinear force estimator combining the hysteresisand andcreep creepmodels models was phenomenon. AfterAfter that,that, a nonlinear force estimator combining the hysteresis was proposed in [28]. Nevertheless, model errors are inevitable. Hence, a more effective force observer proposed in [28]. Nevertheless, model errors are inevitable. Hence, a more effective force observer was developed [29] that could be carried out without the hysteresis and creep models. In previous was developed [29] that could be carried out without the hysteresis and creep models. In previous work [29], a fourth-order model was employed to construct the force observer. Alternately, a simple work [29], a fourth-order model was employed to construct the force observer. Alternately, a simple second-order model could also be used in the recent work [17]. second-order model also be used in the recent [17]. the gripping force between the left In this paper,could a force observer in [17] was used work to estimate In this paper, a force observer inThe [17] wasobserver used toinestimate the gripping gripping arm and the micro-object. force the time domain is givenforce by between the left gripping arm and the micro-object. The force observer in the time domain is given by F (t) =
F (t )
dp 1 −1 n −1 o L G (s) [y(t) − y1 (t)] − d [u(t) − u(t − T )] 1s p 1 1 s pp
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where sp denotes the elastic constant of the gripping arm; L is the inverse Laplace transform operator; G s(s) is the plant model constant (with unity DC gripping gain) under theL−1 excitation of theLaplace driving transform voltage; y is the where p denotes the elastic of the arm; is the inverse operator; position output excited by the driving voltage u and the gripping force F, whereas y represents 1 G (s) is the plant model (with unity DC gain) under the excitation of the driving voltage; ythe is the position output underby thethe excitation of voltage the driving voltage alone; andforce u(t) and u(t−T) are driving the position output excited driving u and the ugripping F, whereas y1the represents voltage at the time instances t and t−T.
position output under the excitation of the driving voltage u alone; and u(t) and u(t−T) are the driving voltage at the time instances t and t−T. The plant model can be identified using the sweep-sine method when the excitation voltage is applied to the left gripping arm alone. Figure 8 shows the frequency response of the microgripper derived from the spectral analysis. As shown in Figure 8, the identified second-order model was consistent with the system dynamics in low frequencies. Moreover, the microgripper had a first natural
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The plant model can be identified using the sweep-sine method when the excitation voltage is applied to the left gripping arm alone. Figure 8 shows the frequency response of the microgripper derived from the spectral analysis. As shown in Figure 8, the identified second-order model was consistent with the system dynamics in low frequencies. Moreover, the microgripper had a first natural frequency of 74.2 Hz and a second natural frequency of 211.5 Hz. According to recent studies [30,31], the effect of the high-frequency modes was usually very small, and the dynamic characteristics of the flexible structure mainly depended on its first transverse bending mode; thus, the higher modes could be ignored. Thus, only the first mode was selected (i.e., a second-order model) to demonstrate the feasibility Sensors 2018, 18, xof the designed control scheme in this paper. 10 of 17 60
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The The elastic constant sp was determined knownweight weight mN) acquiring elastic constant sp was determinedby byhanging hanging aa known (10(10 mN) andand acquiring the the caused displacement, i.e., s p = 40.32 μm/mN. Moreover, the piezoelectric coefficient d p was identified caused displacement, i.e., sp = 40.32 µm/mN. Moreover, the piezoelectric coefficient dp was identified as the gain (i.e., dpd=p 132.9 theplant plantmodel model G with unity dc could gain could be derived as DC the DC gain (i.e., = 132.9μm/V). µm/V).Then, Then, the G with unity dc gain be derived by , whichisisgiven given by by by GG= =GG p/d p, p which p /d 2.174 × 1055 G (s) = 2 (18) 2.174 10 G( s) s 2 + 8.609s + 2.174 × 1055 (18) s 8.609s 2.174 10 In addition, to evaluate the characteristics of the force observer, the input voltage shown in Figure 9a was to exerted to thethe power amplifier to drive theforce left MFC actuator, thevoltage externalshown force in In addition, evaluate characteristics of the observer, thewhile input was set to be zero. The measured position and force are depicted in Figure 9b,c, respectively. It wasforce Figure 9a was exerted to the power amplifier to drive the left MFC actuator, while the external the maximal error of the force observer wasare approximately mN,9b,c, which indicated that was found set to that be zero. The measured position and force depicted in0.354 Figure respectively. It was the gripping force could be accurately estimated.
found that the maximal error of the force observer was approximately 0.354 mN, which indicated that the gripping force could be accurately estimated. 6
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In addition, to evaluate the characteristics of the force observer, the input voltage shown in Figure 9a was exerted to the power amplifier to drive the left MFC actuator, while the external force was set to be zero. The measured position and force are depicted in Figure 9b,c, respectively. It was found2018, that18,the maximal error of the force observer was approximately 0.354 mN, which indicated Sensors 1301 11 of 18 that the gripping force could be accurately estimated. 6
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4.4. Experimental Results for the Hybrid Position/Force Control 4.4. Experimental Results for the Hybrid Position/Force Control 4.4.1. Experimental Experimental Results Results for for the the Single Single Position Position Control Control 4.4.1. In this thissection, section,only onlythe thesingle singleposition position control right gripping for microgripper the microgripper In control of of thethe right gripping armarm for the was was performed. For various practical micromanipulation operations, the overall manipulation performed. For various practical micromanipulation operations, the overall manipulation process process can be classified threethe phases: the gripping (I), thephase holding (II),releasing and the can be classified into threeinto phases: gripping phase (I),phase the holding (II),phase and the releasing phase (III). Accordingly, the trapezoidal trajectory is usually used in such applications. phase (III). Accordingly, the trapezoidal trajectory is usually used in such applications. However, However, this trajectory also presents an unwanted overshot at the turning points, which would this trajectory the Sensors 2018, 18, x also presents an unwanted overshot at the turning points, which would damage 11 of 17 damage the fragile micro-objects [13]. Hence, an improved cycloid trajectory was proposed to fragile micro-objects [13]. Hence, an improved cycloid trajectory was proposed to suppress the
overshoot, asovershoot, shown in phase I and in Figure illustrated Figure 10,inthe desired suppress the as shown in phase phase III I and phase 10. III inAsFigure 10. Asinillustrated Figure 10, trajectory was accurately in the three phases. In thephases. gripping (I), the gripping the desired trajectory wastracked accurately tracked in the three In phase the gripping phase (I),arm the moved as arm the driving increased. In the holding phase position trajectory wasposition kept at gripping movedvoltages as the driving voltages increased. In (II), the the holding phase (II), the 300 µm. Inwas the releasing phase the releasing trajectory phase returned to zero. As the position error trajectory kept at 300 μm.(III), In the (III), the trajectory returned to was zero.random, As the the normally tracking result demonstrated the reliability of the positionthe tracking result. position errordistributed was random, the normally distributed tracking result demonstrated reliability of Moreover, cycloidresult. tracking error presented antracking approximately normal distribution, and the 95% the positionthe tracking Moreover, the cycloid error presented an approximately normal confidence −0.034 ± 2.513interval µm. Therefore, the±RMSE of theTherefore, cycloid trajectory tracking distribution,interval and thewas 95% confidence was−0.034 2.513 μm. the RMSE of the error was calculated as 1.282 µm.was Thecalculated value wasas0.43% than thewas0.43% maximal amplitude of the cycloid trajectory tracking error 1.282smaller μm. The value smaller than desired The experiments indicatedThe thatexperiments the output displacement the right gripping arm maximaltrajectory. amplitude of the desired trajectory. indicated thatof the output displacement could precisely tracked usingbe theprecisely positiontracked control using scheme. of the be right gripping arm could the position control scheme. 10
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4.4.2. Experimental Results for the SingleForce Control In this section, only the single force control of the left gripping arm for the microgripper was performed. According to the force control strategy, the input voltages of the left MFC actuator were regulated. To begin with, acycloid force trajectory with a 6.5-mN amplitude was applied to the left gripping arm. The corresponding tracking result of the gripping force is presented in Figure 11. It was observed that the actual force tracked the desired force trajectory accurately. Moreover, the
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tracking error; and (c) Histogram of position tracking error.
4.4.2. Experimental Experimental Results Results for for the the SingleForce SingleForce Control Control 4.4.2. In this this section, section, only only the the single single force force control control of of the the left left gripping arm for for the the microgripper was In gripping arm microgripper was performed. According to the force control strategy, the input voltages of the left MFC actuator performed. According to the force control strategy, the input voltages of the left MFC actuator were were regulated. Towith, beginacycloid with, acycloid force trajectory with aamplitude 6.5-mN amplitude wastoapplied regulated. To begin force trajectory with a 6.5-mN was applied the left to the left gripping arm. The corresponding tracking result of the gripping force presented gripping arm. The corresponding tracking result of the gripping force is presented in is Figure 11. It in Figure 11. Itthat wasthe observed that the actual tracked the desired force trajectory accurately. was observed actual force tracked theforce desired force trajectory accurately. Moreover, the Moreover, the trajectory tracking error and its histogram are depicted in Figure 11b,c. It was found trajectory tracking error and its histogram are depicted in Figure11b,c. It was found that the force that the force error presented a normaland distribution and that the 95%interval confidence −5 ± tracking errortracking presented a normal distribution that the 95% confidence was interval 7.144×10was −5 ± 0.201 mN. Since the force error was random, the normally distributed tracking result 7.144 × 10 0.201 mN. Since the force error was random, the normally distributed tracking result demonstrated demonstrated thethe reliability of the force result. Furthermore, the arbitrary error the reliability of force tracking result.tracking Furthermore, the arbitrary force trackingforce errortracking had a RMSE had a RMSE of 0.103 mN, which was 1.58% smaller than the maximum of the arbitrary force trajectory. of 0.103mN, which was1.58% smaller than the maximum of the arbitrary force trajectory. Thus, the Thus,microgripper the MFC microgripper also presented force control accuracy. MFC also presented good forcegood control accuracy. 0.6
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Figure 11. Force control results of a cycloid trajectory. (a) Force tracking result; (b) Force tracking Figure 11. Force control results of a cycloid trajectory. (a) Force tracking result; (b) Force tracking error; error; and (c) Histogram of force tracking error. and (c) Histogram of force tracking error.
4.4.3. Experimental Results for the Hybrid Position/Force Control In this section, the hybrid position/force control of the microgripper was investigated. In particular, the FSMC (see Figure 4) for the position and the PI controller for the force of the microgripper were simultaneously used. First, the cycloid trajectory was tracked, and the control results are shown in Figure 12. It was observed that the actual output displacement and gripping force could track the desired trajectories accurately and the significant hysteresis as the properties of the MFC actuator was reduced to a negligible level. Moreover, the histograms for the position and the force tracking errors are presented in Figure 12c,f. The concurrent arbitrary trajectories tracking errors exhibited normal distributions, and the 95% confidence intervals of the position and the force tracking errors were −0.039 ± 2.727 µm and 6.976×10−5 ± 0.224 mN. Hence, the RMSEs of the position and force tracking errors were calculated as 1.391 µm and 0.114 mN, which were 0.46% and 1.76% smaller than the peak-to-peak amplitude of the desired trajectories. The MFC microgripper presented good position and force control accuracy simultaneously.
the force tracking errors are presented in Figure12c,f. The concurrent arbitrary trajectories tracking errors exhibited normal distributions, and the 95% confidence intervals of the position and the force tracking errors were−0.039 ± 2.727 μm and 6.976×10−5 ± 0.224 mN. Hence, the RMSEs of the position and force tracking errors were calculated as1.391 μm and 0.114 mN, which were0.46% and 1.76% smaller than Sensors 2018, 18, the 1301peak-to-peak amplitude of the desired trajectories. The MFC microgripper presented 13 of 18 good position and force control accuracy simultaneously. 10 500
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Figure 12. Hybrid position/force control results of a cycloid trajectory. (a) Position tracking result; (b) Figure 12. Hybrid position/force control results of a cycloid trajectory. (a) Position tracking result; Position tracking error; (c) Histogram of position tracking error; (d) Force tracking result; (e) Force (b) Position tracking error; (c) Histogram of position tracking error; (d) Force tracking result; (e) Force tracking error; and (f) Histogram of force tracking error. tracking error; and (f) Histogram of force tracking error.
To further demonstrate the control performance of the FSMC, another tracking experiment with To further demonstrate the control and performance of the FSMC, another tracking experiment with an arbitrary trajectory was performed, the corresponding control results are depicted in Figure an arbitrary trajectory was performed, and the corresponding control results are depicted in Figure 13. 13. It was observed that the position and force tracking errors of the trajectory presented It was observed that the position and force tracking errors of the trajectory presented approximately approximately normal distributions. Furthermore, the 95% confidence interval of the position normal Furthermore, theand 95%the confidence intervalinterval of the position tracking errors was trackingdistributions. errors was−0.178 ± 2.973 μm, 95% confidence of the force tracking errors − 0.178 ± 2.973 µm, and the 95% confidence interval of the force tracking errors was 0.001 ± 0.327 was 0.001 ± 0.327 mN. Hence, the RMSEs of the cycloid trajectory were calculated to be 1.517 μm mN. and Hence, the respectively. RMSEs of theThe cycloid trajectory were calculated be 1.517 µmthe and 0.167 mN, respectively. 0.167 mN, values were 0.51% and 2.57% to smaller than peak-to-peak amplitude The values weretrajectories. 0.51% and 2.57% smallerdemonstrated than the peak-to-peak of the desired trajectories. of the desired Experiments that the amplitude MFC microgripper exhibited good Experiments demonstrated that the MFC microgripper exhibited good position and force position and force control accuracy simultaneously. Therefore, the hybrid position and force control control accuracy simultaneously. Therefore, the hybrid positionand andeffective. force control scheme adopted for the scheme adopted for the MFC microgripper was feasible MFC microgripper was feasible and effective.
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Figure 13. Hybrid position/force control results of an arbitrary trajectory. (a) Position tracking result; Figure 13. Hybrid position/force control results of an arbitrary trajectory. (a) Position tracking result; (b) Position tracking error; (c) Histogram of position tracking error; (d) Force tracking result; (e) Force (b) Position tracking error; (c) Histogram of position tracking error; (d) Force tracking result; (e) Force tracking error; and (f) Histogram of force tracking error. tracking error; and (f) Histogram of force tracking error.
4.5. Discussion 4.5. Discussion While the displacement obtained by one of the arms was indeed higher than the other While the displacement obtained by one of the arms was indeed higher than the other piezoelectric piezoelectric drives, it was still necessary to demonstrate that the gripper could be used to manipulate drives, it was still necessary to demonstrate that the gripper could be used to manipulate small-scale small-scale objects (about 10 microns or smaller in size). Thus, a sinusoidal position trajectory with objects (about 10 microns or smaller in size). Thus, a sinusoidal position trajectory with multiple multiple amplitudes was applied to the microgripper. The corresponding tracking results are shown amplitudes was applied to the microgripper. The corresponding tracking results are shown in Figure 14. in Figure 14. It was observed that the actual position tracked the desired force trajectory accurately, It was observed that the actual position tracked the desired force trajectory accurately, as illustrated as illustrated in Figure 14a. Moreover, Figure 14b,c shows that the control error basically decreased in Figure 14a. Moreover, Figure 14b,c shows that the control error basically decreased with the with the trajectory amplitude, and the maximal control error was approximately 0.6 μm when the trajectory amplitude, and the maximal control error was approximately 0.6 µm when the trajectory trajectory amplitude was 10 μm. In fact, the control accuracy was heavily affected by the detection amplitude was 10 µm. In fact, the control accuracy was heavily affected by the detection resolution resolution of the microgripper system [12]. Thus, the gripper could be used to manipulate small scaleof the microgripper system [12]. Thus, the gripper could be used to manipulate small scale-objects. objects. Furthermore, the position tracking error was plotted together with the mean of the desired Furthermore, the position tracking error was plotted together with the mean of the desired trajectory trajectory in Figure 14a. According to Figure 14d, the plots of the signal/noise for a wide range of in Figure 14a. According to Figure 14d, the plots of the signal/noise for a wide range of displacements displacements are presented. Accordingly, the developed microgripper could be used for multiscale are presented. Accordingly, the developed microgripper could be used for multiscale manipulation. manipulation. 300
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(c) of a multi-amplitude trajectory. (a) (d) Position tracking result; (b) Figure 14. Position control results Figure 14. Position control results of a multi-amplitude trajectory. (a) Position tracking result; Position tracking error; (c) Position error versus trajectory amplitude; (d) Position error versus 14.tracking Positionerror; control of error a multi-amplitude trajectory. (a) and Position (b) (b)Figure Position (c)results Position versus trajectory amplitude; and (d) tracking Position result; error versus mean of the desired trajectory. Position (c) Position error versus trajectory amplitude; and (d) Position error versus mean of thetracking desirederror; trajectory. mean of the desired trajectory.
In order to demonstrate that the microgripper could handle multiscale micro-objects, several In dimensions order to demonstrate that the microgripper could handle multiscale micro-objects, several typical of micro-objects between 100 μm could to 900handle μm were used tomicro-objects, perform manipulation In order to demonstrate that the microgripper multiscale several typicalasdimensions of micro-objects between 100 µm to 900 µm were used to perform manipulation tasks, in Figure 15. typicalshown dimensions of micro-objects between 100 μm to 900 μm were used to perform manipulation tasks, as shown in Figure 15. tasks, as shown in Figure 15.
Figure holding aa single single mode modefiber fiberofof125 125μm; μm;(b)(b) Figure15.15.Cases Casesofofmicromanipulation micromanipulation tasks: tasks: (a) (a) holding Figure 15. Cases ofμm micromanipulation tasks: (a) holdingofaa single mode fiber (d) of clamping 125 µm; manipulation of a 200 diameter solder ball; (c) manipulation 440 μm resistance; manipulation of a 200 μm diameter solder ball; (c) manipulation of a 440 μm resistance; (d) clamping (b) irregular manipulation of a 200 µm diameter solder ball; (c)amanipulation of a 440 µm resistance; (d) clamping an crystal 700 μm μm microcomponent; microcomponent; and(f)(f) manipulating an irregular crystalofof550 550μm; μm;(e) (e)manipulation manipulation of of a 700 and manipulating an irregular crystal of 550 µm; (e) manipulation of a 700 µm microcomponent; and (f) manipulating a a wire cable ofof 860 μm. a wire cable 860 μm. wire cable of 860 µm.
Table 1 summarizes MFCmicrogripper. microgripper.According According Table Table 1 summarizesthe theperformances performancesof of the the developed developed MFC to to Table 1, 1, MFC microgripperexhibited exhibitedaalarge large workspace workspace range accuracy. thethe MFC microgripper range and and high highposition/force position/forcecontrol control accuracy. Hence, microgripperwith withthe thedesigned designed hybrid hybrid control Hence, thethe microgripper control scheme schemewas wassuitable suitablefor foruse useinprecision inprecision micromanipulation.Furthermore, Furthermore, the the input input voltage voltage employed its its micromanipulation. employed in in this thisstudy studywas was50% 50%less lessthan than nominal maximum voltage(−500 (−500V~1500 V~1500V) V) and and only only one each gripping nominal maximum voltage one MFC MFCactuator actuatorwas wasglued gluedonto onto each gripping
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Table 1 summarizes the performances of the developed MFC microgripper. According to Table 1, the MFC microgripper exhibited a large workspace range and high position/force control accuracy. Hence, the microgripper with the designed hybrid control scheme was suitable for use inprecision micromanipulation. Furthermore, the input voltage employed in this study was 50% less than its nominal maximum voltage (−500 V~1500 V) and only one MFC actuator was glued onto each gripping arm, so the MFC microgripper was capable of multiscale micromanipulation and microassembly tasks. Nevertheless, a higher resonant frequency was expected to derive a much larger operation bandwidth [32]. Table 1. Performances of the MFC microgripper. Parameter
Value
Dimension Output displacement First resonant frequency Arbitrary position/force RMSEs Relative RMSEs (Arbitrary) Cycloid position/force RMSEs Relative RMSEs (Cycloid)
86.8 mm×10.8 mm×(20−5)mm 1221.3 µm 74.2 Hz 1.517 µm/0.167 mN 0.51%/2.57% 1.391 µm/0.114 mN 0.46%/1.76%
In addition, the MFC microgripper also had a large global size, as shown in Table 2. It is well known that the output displacement of the microgripper has to be evaluated with its total structural dimensions. Therefore, for a clear view, the displacement-volume ratios of the reported piezoelectric microgrippers [10,11,17,19] were compared in Table 2. It was observed that the developed MFC microgripper outperformed the others in terms of having a higher displacement-volume ratio and a larger gripping range. Moreover, the manipulation accuracy of the microgripper could be guaranteed by the hybrid control scheme. Table 2. Comparisons with reported piezoelectric microgrippers. No.
Actuation Principle
Output Displacement
Displacement-Volume Control Ratio Variables
Independent Regulation
Relevant Literature
1 2 3 4 5
Piezoelectric bimorph Thermo-piezoelectric Piezoelectric stack Piezoelectric stack MFC actuator
20 µm 80 µm 328.2 µm 427.8µm 1212.4 µm
0.049 µm·mm−3 0.003 µm·mm−3 0.016 µm·mm−3 0.019 µm·mm−3 0.101 µm·mm−3
No Yes Yes — Yes
[17] [10] [19] [11] Current
Both Both Both — Both
5. Conclusions The above sections presented the development, implementation, and hybrid position/force control of a new MFC microgripper with a large displacement-volume ratio. Based on the MFC actuator, the proposed microgripper was actuated and designed. Through the FSMC, precision position control of the microgripper was obtained. Meanwhile, gripping force control was guaranteed by the PI controller. Note that the microgripper was driven by two independent MFC actuators; the right actuator was used to position the micro-object and the left one was used to control the force. A series of experimental investigations were carried out to test the characteristics of the microgripper and to validate the designed hybrid control scheme. The main conclusions of this study can be summarized as follows: (1)
The proposed MFC microgripper presented a large output displacement and a high displacement-volume ratio, which demonstrated that the microgripper was capable of multiscale micromanipulation;
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The designed hybrid control scheme, which employed the FSMC combined with the PI controller, was feasible. The control scheme was able to regulate both the position and the gripping force simultaneously, and its effectiveness and simplicity make it suitable for industry systems.
In the future, other force sensing techniques will be performed to achieve a more compact size. Moreover, parameter optimization will be conducted to obtain a higher natural frequency. Acknowledgments: The authors would like to thank the support of the Zhejiang Provincial Natural Science Foundation of China (No. LQ18E050003), the Zhejiang Provincial Education Department Project (No. Y201737055), and the National Natural Science Foundation of China (No. 51505238, No. 61703217, and No. 51375433). This work is also sponsored by the K.C. Wong Magna Fund in Ningbo University and the Open Research Project of the State Key Laboratory of Industrial Control Technology, Zhejiang University, China (No. ICT1800377). Author Contributions: Yiling Yang and Yanding Wei conceived and designed the experiments; Junqiang Lou performed the experiments; Lei Fu contributed analysis tools; and Jin Zhang analyzed the data and wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.
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