Design and Control of Shape Memory Alloy Actuated Grippers

Third International Conference on Advances in Control and Optimization of Dynamical Systems March 13-15, 2014. Kanpur, India

Design and Control of Shape Memory Alloy Actuated Grippers S. Krishna Chaitanya* K. Dhanalakshmi** 

*Vignan University, Vadlamudi, PIN 522213 INDIA (Tel: +91-9440485456; e-mail:[email protected]) **National Institute of Technology, Tiruchirappalli, PIN 620015 INDIA (Tel: +91-431-2503360; e-mail:[email protected]) Abstract: Design, investigation and control of two novel Shape Memory Alloy (SMA) wire based gripping systems one operated in open mode and another in closing mode is presented in this paper. A unified design is chosen for both the gripping systems. The gripping systems use SMA wire with a counteracting torsion spring to generated two way motion. Models of the gripping systems are experimentally determined from the open loop step response. Pulse width modulation control (PWM) controller is designed to control the tip displacement of gripping finger. These controllers are compiled to track various stationary and variable (dynamic) trajectories to suit applications that can manipulate objects of varied dimensions. Experimental results show that the grippers are able to track the position rapidly and precisely. Keywords: Shape Memory Alloy wire, Gripper, Pulse Width Modulation, Control. 

unknown parameters, discouraging further attempts to design a model based control system. System identification is a better means for modelling such systems in comparison with the above mentioned modelling techniques followed by other researchers Dhanalakshmi et al. (2008), Chaitanya et al. (2013), Ghasemi et al. (2013). Over the year’s system identification technique gained popularity because of its advantage in estimating more appropriate model.

1. INTRODUCTION Smart materials such as electro-rheological fluids, magnetorheological fluids, piezoelectric materials, and shape memory alloys (SMAs) have gained high importance recently. Among these SMAs gained a great deal of attention due to its high strength to weight ratio. Additional good characteristics such as ductility, fast response, anti-corrosion resistance, large stable displacement, good controllability, reliable for large cycles of operation and bio-compatibility probed them in multitude applications. Some major applications include actuation, sensing, shape control and vibration control. Until 1984 SMA prime actuation was only by thermal heating i.e., by conduction or convection. SMA started becoming popular after 1984, when Honma et al. (1984) demonstrated that it is possible to control the actuation by electric heating, thus opening their use in several engineering applications such as robotic and actuator applications. Strain in the SMA wire is modulated with temperature, generally by an applied voltage difference across the length. These features put together to develop electric actuators more direct and simple in actuation eliminating power transmission devices such as gears, lead screws and other frictional moving parts used in conventional actuators.

This work aims at design and control of SMA actuated gripping systems which feature simple and flexible design, ease of fabrication and optimal utilization of SMA wire to achieve larger displacement. 2. CONSTRUCTION AND PRINCIPLE OF WORKING As pointed earlier, two modes of gripping operations exist: the open mode and the closed mode. The objective here is to apply a single configuration of SMA wire and the bias spring for gripping in both modes of operation. The proposed gripping designs are based on the work presented as in Filippo et al. (2004).

Despite these special features, SMAs are non-linear, uncertain and time-varying scenery, which makes it difficult to identify the relationship between heat conditions and the strain/force generated. Therefore, many intelligent control techniques are employed to tackle above mentioned problems to improve the performance of SMA systems. During last four decades immense modelling techniques based on mathematical and phenomenological models are developed to control SMA actuated systems Schiedeck et al. (2011). It is difficult to choose the proper model for a particular application. In addition, these models may contain many 978-3-902823-60-1 © 2014 IFAC

Fig. 1 CAD model of the grippers 400

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Construction of the grippers is similar, but for differing design of the rotatable finger and the point of connection of the SMA wire to the finger to aid open/close operation. Each gripper is fabricated with an aluminium body consisting of two fingers - one fixed to the base and the other movable i.e., rotatable about a pivot point along with torsion spring, which is architecturally placed on two supporting beams also fixed to the base. Providing only one movable finger simplifies the gripper design and enhances the grasping accuracy. The joint has a large range of motion that is achieved by attaching the SMA wire very close to the revolute joint axis. The high force requirement is achieved by using the SMA wire in a loop like in a bundle of two. Integration of SMA wire is seen from the CAD model developed in COMSOL Multiphysics in Fig. 1.

The generated force, Fg by the SMA wire is a function of the gripper geometry, given by

 M L F  F  b  1 g  c L L 1  2 

(1)

The overall force, Fg is obtained by the contribution of parallel SMA wire having a force of, Fs each is Fg  2  Fs

(2)

The SMA wire length, L depends on the opening angle of the gripper,  and the distance between pivot point and the grip, L1 and is given as L

The principle involved is conversion of linear stroke of SMA wire into angular movement of the rotatable finger. During electric actuation the SMA wire contracts and pulls the rotatable finger by exerting a compression force on the spring. This finger rotates to open (or close) the gripper when the contraction force generated by the SMA wire exceeds the restoring force exhibited by the bias spring thereby accumulating potential energy. During deactivation the SMA wire stretches with the help of the elastic recovery force exhibited by the spring thus aids the gripping finger to close (or open) to perform grasp and hold operations.

L2   5 

(3)

SMA wire contracts 5% of its overall length, which contributes opening of the finger by an angle,  . The influence of L2 has a profound effort on the force exhibited by the gripper. Larger L2 contributes higher forces, Fc with the same number of wires as in (1), but at the same time shorter L2 reduces the length of the SMA wire as in (3). Corresponding to the desired design specifications (Fc = 2 N and  = 30°), geometric constraints of the supporting structure (L1 = 9.48 cm and L2 = 3.5 cm) and a suitable selection of SMA wire (Ø 0.15 mm and L = 36.65 cm) the bias spring is dimensioned.

3. DESIGN OF GRIPPERS Choice of suitable components and their dimension for the mechanism is the primary step in design. It is easier to design the resilient biasing element for a selected configuration of the SMA wire actuator and an angle of rotation of the movable finger. The design is such that for 30° rotation angle of the movable finger about the pivot point the finger should open/close. 38 cm long SMA wire housed in ‘U’ shape at the trailing edge of the movable finger and fixed to the base provides angular movement of the finger.

The restoring force, Rf necessary to revert back the gripping finger to its initial position which could be restored by a minimum restoring force, Rfsma to its cold state (martensite) (from Mondotronics Inc.) is given by: R f  2  R fsma  2  0.62  1.24N

(4)

The bending moment, Mb of the spring is given by M b  R f  L1  11.75Ncm

(5)

This is the minimum value of the torque necessary to deform the SMA wire. When the jaw is open the torque increases generating a maximum torque, Mbmax. With the gradual closing of the jaw, the spring moment decreases. The wire diameter of the torsion spring loaded only by the bending moment of the spring is expressed mathematically as

d  4 64M b maxDN ET

 2.1mm

(6)

where N is the number of coils, d is the wire diameter of the spring, D is mean diameter of the spring, Ø is the preload angle and ET is the Young’s modulus of the steel spring.

Fig. 2 Free body diagram of the movable gripping jaw

Fixing D = 3.5 mm, N = 3, Ø = 180°, ET = 200 GPa and substituting maximum bending moment, Mbmax in the (6) results in the torsion spring wire diameter, d to be approximately 2.1 mm; this is the estimated diameter of the spring to revert back the movable finger after rotation by 30° upon actuation.

The bias spring is dimensioned to provide the force necessary to recover pseudo-plastic strain in SMA wire in the cold wires (in martensitic phase); the required closing force of the clamp is Fc = 2 N. Fig. 2 presents a schematic of the static model of the gripper.

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cooling. As these actuators are very easy to sense its state of motion precisely, they find multitude control applications where cost and size (eliminating additional sensing devices) of the system are defining factors. 4.1 Design of Driving Electronics Fig. 5 shows a simple current amplifier circuit designed to control the amount of current flow through the wire. It is a voltage-controlled current-output circuit. The current flow in the SMA wire can be easily measured from the voltage across the series resistance. This data is processed to provide sufficient information regarding the state of the SMA wire. In particular, the electrical resistance of SMA wire and the power input to the SMA wire can be measured using simple circuit laws for modeling and control design purpose.

Fig. 3 Free body diagram of movable jaw with positioned laser sensor Fig. 3 shows the laser sensor positioning for measuring the jaw displacement, l. Angle of open (closing) and separation between the two fingers are obtained using the relations

 

Angle of open (closing)

:

  tan1 l 34

Separation angle

:

  37.72  tan1 l 34

 

4. MODEL ESTIMATION The experimental facility shown in Fig. 4 to implement closed loop control of the smart grippers is developed. A noncontact type laser displacement sensor is engaged to measure the displacement of the movable gripping finger when the SMA wire is actuated.

Fig. 5 Amplifier circuit to drive SMA actuator VC is the control signal feed from the DAQ card (0-3.3 V) RA is the input resistance of Op-Amp (40 Ω) RB is the feedback resistance Op-Amp (100 Ω) RSMA is the resistance of the SMA wire (Dynamic) (30 Ω) RS is the resistance connected in series with the SMA wire (10 Ω) V0 is the voltage across the SMA wire and the series resistance VS is the voltage across the series resistance Current through the SMA wire, ISMA ≅ current through the series resistance, IS i.e. I S 

Fig. 4 Experimental setup - photograph

VS RS

(7)

Assuming the ideal behaviour of operational amplifier, the current through the inverting terminal of Op-Amp, I- ≅ 0.

Data Acquisition Toolbox in MATLAB SIMULINK™ is used to interface the DAQ card to the PC. The DAQ card acquires the displacement data from the sensor; the respective control is given to the SMA actuator. The combination of SMA wire providing one way action (angular movement) with the bias spring (torsion) enables two way movement (open and close operation). In this work it is shown that SMA actuator can also be used as a sensor because of its inherent change in electrical resistance upon actuation. This sensor cum actuator behaviour is addressed as self-sensing property. When energized (heated) the SMA wire shrinks in its length their by showing a change (fall) in resistance, retains its original length under the presence of biasing force during

Voltage across the SMA wire, VSMA  V0  VS

(8)

Hence SMA wire resistance RSMA 

V0  VS I SMA

(9)

The input power consumed by SMA, 2 PSMA  I SMA  RSMA

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4.2 Influence of SMA wire diameter

decrease in time response cannot be obtained with increasing excitation current. Excitation of the SMA wire beyond its safe heating current hardly influences the response time of the gripper.

Diameter of SMA wire is considered to have a profound effect on the angular displacement of the movable finger, closing time, opening time and total response time of the gripping device. Initial tests are carried to investigate these influential factors by exciting the SMA with currents varied in steps of 25 mA until the safe heating current prescribed by the manufacturer Modotronics Inc. Table 1 presents the results on opening and closing time (i.e. heating and cooling time) for the grippers. Results show that SMA wires of Ø 0.076 mm and Ø 0.1 mm are too fragile and cannot generate enough pull force to act as the actuator of the gripper. Apart from being extremely prone to breaking, they are also very difficult to handle resulting in installation difficulties. Converse effect is observed for Ø 0.25 mm SMA wire. It absorbs higher power during actuation because of its low resistance compared to other sizes of SMA wire.

Fig. 6 Angular response of the grippers 4.4 Influence of Excitation Current

Table 1 Reaction time recorded for various sizes of SMA integrated in the grippers

Fig. 8 shows a bar graph of the maximum cyclic tip angular displacement of the gripping devices for current controlled pulse signals of various amplitudes at 50% duty cycle and same action frequency 1/10 Hz.

NiTi size (mm)

Th (s)

Tc (s)

Th (s)

Tc (s)

0.076

NA

NA

NA

NA

Fragile and Installation difficulty

0.1

NA

NA

NA

NA

Fragile and Installation difficulty

0.13

1

2.25

0.88

3.1

Utilizable

0.15

1.2

2.63

1.05

3.24

Utilizable

7.6

High power consumption, larger cooling time

0.25

Open mode

1.08

7.8

Closing mode

1.1

Remarks

SMA wires of Ø 0.13 mm and Ø 0.15 mm are suitable for use in the gripper because of their advantage in providing large angular displacement of the movable finger consuming less power (< 500 mA).

(a)

It is found that the tip displacement of gripper increases with the excitation current. For Ø 0.13 mm SMA wire, an excitation current of 320 mA is required for the grippers to close (open). The maximum tip displacement recorded at this current level averaged to 13.48 mm (44.56 mm) from multiple readings. With incremental steps of 25 mA, the average tip displacement increased approximately linear at 0.1194 mm/mA (0.3628 mm/mA) respectively. The correlation coefficients (R-values) obtained from the curves in Fig. 6 for Ø 0.13 mm and Ø 0.15 mm SMA wires are 0.9475 and 0.9138 (0.9021 and 0.8935) respectively. However, it is seen that the tip displacement of gripper cannot increase unlimitedly for any increase in the excitation current beyond phase transformation.

(b) Fig. 7 Time response of gripper (Ø 0.13 mm) (a) open mode (b) closing mode Experimental results show that increase in heating current correspondingly increases the cyclic displacement amplitude of SMA grippers, due to the increase in cyclic strain of SMA wires.

4.3 Investigation of Gripper Characteristics

4.5 Influence of Action Frequency

Fig. 7 shows the opening, closing and total time response of the grippers corresponding to varying heating current, for the preferred sizes of SMA wire. Faster response is achieved when the heating current increases. However, unlimited

Generally SMAs are actuated using current controlled pulsed signals due to their unavoidable cooling phase, wherein the

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operational frequency plays a major role in attaining cyclic response.

Efficiency

:

P 100  94.79 P o

0

0

i

The efficiency achieved with this driving circuit is good in comparison as in Zhong et al. (2006). The life of SMA wire will be reduced due to overheating. However, an additional burn-up resistor in series to SMA wire is employed to tackle sudden current surges thereby protecting from overheating. 4.7 System Identification Experiments are performed using the setup shown in Fig. 4 to acquire the open loop step response of an SMA wire actuated gripper i.e. tip displacement for an input current. The model structure of the SMA actuated systems is chosen to be first order with time delay. The time domain open loop response to 0.1V steps of input voltage ranging from 2.6 to 3.3V are applied to the open and closed mode grippers as presented in Fig. 10. The initial slope of the responses change with the magnitude resulting in faster response for larger input, also the close mode gripper is faster than the open mode gripper. Fig. 11 shows the experimental and estimated step response of the grippers and their respective position errors. These responses are using to obtain the first order time delay transfer function for the grippers using Prediction-error minimization technique from the system identification toolbox in Matlab.

Fig. 8 Influence of excitation current (Ø 0.13 mm) Hence any actuator devised using SMA where fast response matters should work satisfactorily with high frequency switching inputs. Fig. 9 shows a bar graph of the cyclic angular displacement amplitudes of the SMA grippers for driving frequencies of 1/2, 1/4, 1/6, 1/8 and 1/10 Hz with a duty cycle of 50% for safe heating current limits. The experimental results show that the displacement amplitudes of the SMA grippers are restricted by the action frequency. Upon increasing the action frequency, the cyclic displacement amplitude of the actuator decreases. If the action period is long enough (i.e., short action frequency) complete heating and cooling cycles can be observed and hence the cyclic angular displacement amplitude increases. Moreover, with the increase in action period the cyclic angular displacement amplitude of the SMA wires will not increase unlimitedly. Once if the SMA wire is completely transformed into its austenite phase, further elongation cannot be observed with additional heat supply.

(a)

Fig. 9 Influence of action frequency 4.6 Driving Power

(b) Fig.10 Open loop response of the smart grippers (a) Closed mode gripper (b) Open mode gripper

It is important to know the efficiency of driving circuit in order to effectively exploit the actuator’s functionality. Driving circuit power test is conducted by powering SMA wire with an input voltage Vi = 9 V, input current Ii = 320 mA and noting down output current Io = 318 mA. The power input to the gripper and the power consumed by the SMA wire can be worked-out as shown below. Subsequently, the efficiency of the driving circuit can be determined. Input power

:

Output power

:

The simulation showed 99.79% and 96.31% best fit with less than 1% and 4% mismatch between the experimental position and simulated model outputs for the close mode and open mode grippers respectively. The first order time delay transfer function of closed mode gripper: G p(s)

Pi V i  I i  2.88W 2 Po  I o  RSMA  2.73W

12.19  e-0.7 s 1  0.47 s

(11)

4.17  e-1.1s 1  0.69 s

(12)

open mode gripper : G p( s)

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where Gp(s) is the transfer function of the system, Kc and Tc are gain and time constant respectively.

The position tracking response, respective control action and power consumed by the system while tracking a step trajectory of amplitude 40 mm (13 mm) with 50% duty cycle having action period 20 s is shown in Fig. 13 for closed mode (open mode) gripper. Fig. 14 and 15 respectively show position tracking response, respective control action and power consumed for triangular and sinusoidal trajectories of amplitude 40 mm (13 mm) and frequency 1/20 Hz for closed (open) mode gripper. The position tracking response closely matches with the desired response, although smooth, never reaches the set point i.e., percentage steady state tracking error of 0.14 (0.05). These results clearly show the PWM controller is effective in tracking the position of grippers. The closed loop step tracking response for closed mode (open mode) gripper to a series of set points from 20-40mm (5-13mm) in steps of 5mm (2mm), actuated (energized) for a duration of 10 s and cooled (relaxed) for a duration of 10 s are shown in Fig. 16 and 17 with their corresponding position errors.

5. RESULTS AND DISCUSSIONS 5.1 Control of Grippers In this section PWM control technique is designed and employed for the purpose of position tracking of SMA actuated gripping systems. The block diagram of the control schemes is shown in Fig. 12. The design of a PW modulator involves determination of the threshold of the bang–bang trigger, the output of the bang– bang trigger and the amplitude & the frequency of the carrier wave. Whenever the difference between command signal and carrier wave is negative in magnitude, subsequently the output of the PW modulator switches to 11.385 V from 0 V, which energizes the SMA wire. The frequency and amplitude of the carrier wave are selected to be greater than the maximum value of command signal.

15

Tip displacement (mm)

Tip displacement (mm)

45

30

15

10

5

Simulated position Measured position 0

0

2

4

0

6

Time (s)

Simulated position Measured position 0

2

6

(b) 0.8

0.4

0.4 Error (mm)

Error (mm)

(a) 0.8

0

0

-0.4

-0.4

-0.8

4 Time (s)

0

2

4

6

Time (s)

-0.8

0

2

4 Time (s)

(c) (d) Fig. 11 Match and mismatch between the measured and simulated outputs (a, c) Closed mode gripper (b, d) Open mode gripper

Fig. 12 Schematic block diagram of PWM controlled SMA actuated gripper

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(a)

(c)

(b)

(d)

Fig. 13 Position response and control action with PWM control for stationary trajectory tracking: (a, b) closed mode gripper (c, d) open mode gripper With the average control action provided by PWM control, compromise in accuracy is inevitable which can be visualized from the series of step tracking responses. It is also observed that peak overshoot and the ringing of response around the

set point during the heating cycle increases with the decrease in set point. This peak overshoot in the response is a result of sudden heating of SMA wire with high control action provided by controller and thus the ringing.

(a)

(c)

(b)

(d)

Fig. 14 Position response and control action with PWM control for triangular trajectory tracking: (a-b) closed mode gripper (c-d) open mode gripper

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(a)

(c)

(b)

(d)

Fig. 15 Position response, control action and power consumed with PWM control for sine trajectory tracking: (a, b) closed mode gripper (c, d) open mode gripper

(a)

(b) Fig. 16 Closed mode gripper PWM controller response for different set points (a) Position response (b) Position error

(a)

(b) Fig. 17 Open mode gripper PWM controller response for different set points (a) Position response (b) Position error

REFERENCES Dhanalakshmi, K., and Umapathy, M. (2008) Active Vibration Control of SMA Actuated Structures using Fast Output Sampling Based Sliding Mode Control. Instrumentation Science and Technology, 36, 180-193. Grant, D. (1997) Variable structure control of shape memory alloy actuators, IEEE Control Systems., 17, 80-3. Honma, D., Yoshiyuki, M., and Nobuhiro, I. (1984) Micro robots and micro mechanisms Using shape memory alloy. The third Toyota conference-In integrated Micro Motion Systems, Micro-machining, Control and Application, Nissin, Aichi. Krishna Chaitanya, S., and Dhanalakshmi, K. (2013) Demonstration of Self-Sensing behaviour of Shape Memory Alloy actuated Gripper, IEEE Multi-

Conference on Systems and Control, 28-30 August, 218-222. Morra, Filippo., Molfino, Rezia. and Francesco, Cepolina. (2004) Miniature gripping device, Proceedings of IEEE International Conference on Intelligent Manipulation and Grasping IMG (Genova, Italy). Schiedeck, F., and Mojrzisch, S. (2011) Frequency-domain control design for shape memory alloy actuators, Sens. Actuators A Phys., 169, 133-140. Zhong, Z.W. and Yeong, C.K. (2006) Development of a gripper using SMA wire, Sens. Actuators A Phys., 126, 375-81. Ghasemi, Z., Nadafi, R., Kabganian R., and Abiri, R. (2013) Identification and Control of Shape Memory Alloys, Measurement and Control, 46, 252-56. 407