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REGULAR PAPER Design and control of a 3-chambered fiber reinforced soft actuator with off-the-shelf stretch sensors Pham Huy Nguyen 1 Saivimal Sridar 1 Wenlong Zhang 1 Panagiotis Polygerinos 1 Received: 16 November 2016 / Accepted: 7 April 2017 / Published online: 18 April 2017 Ó Springer Singapore 2017 Abstract The necessity for efficient control of soft actu- ators has recently resulted in the development of complex physical models that are actuator geometry and material type dependent. In this paper, we address the ability to do closed-loop control with a simplified model independent of material properties and material characteristics of a soft robotic system. We demonstrate this by using a P-con- troller on a new 3-chambered, fiber-reinforced elastomeric actuator (3CA) that utilizes off-the-shelf stretch sensors. A motion capture system is used to calibrate and generate two different quasi-static models (a general linear regression model and an input dependent model) that map the varying chamber pressure readings with the actuator’s end effector position, effectively represented by the stretch sensor cur- vature. Simulations using a closed-loop controller, with both models, provide further insight on the quality of the models and corresponding control performance. We use this information in an experimental study that yields comparable performances to the simulated results. More- over, we demonstrate that the input-dependent model based controller can provide better results than that of the general model based controller. Finally, we demonstrate that our soft actuator can be closed-loop controlled with off-the- shelf stretch sensors with repeatable results. This opens a way to design new control concepts for multi-chambered actuators that can produce more complex motions in the future. Keywords Soft actuator Soft robot Soft sensor Linear regression model Input dependent model Control 1 Introduction Compliance, high-power-to-weight ratio, and low fabrica- tion costs are some of the many advantages associated with the fast growing interest in soft robotics. These traits make soft actuators and robots suitable for use in a number of applications, including manipulation (Calisti et al. 2012; Marchese and Rus 2015; Homberg et al. 2015; Brown et al. 2010), wearable and human-robot interfaces (Asbeck et al. 2015; Haines et al. 2014; Polygerinos et al. 2015; Galiana et al. 2012; Park et al. 2014; Menguc et al. 2014; Subra- manyam et al. 2015; Gafford et al. 2014; McMahan et al. 2005; Roche et al. 2015), and also search and rescue (Lin et al. 2011; Marchese et al. 2014; Tolley et al. 2014; Morin et al. 2012; Ramezani et al. 2017). These robots with their soft actuation and soft-bodied nature allow safe interac- tions with unstructured environments and the people involved and show a great potential in replacing rigid robotic manipulators utilized in industrial environments (Fitzgerald 2013; Bischoff et al. 2010). Further exploration of their capabilities could soon enough lead to robotic systems that offer better and safer methods in handling sensitive objects with the ability to work closely with humans. Fluidic actuators made with elastomeric materials is one of the most common types of soft actuators encountered in literature (Ilievski et al. 2011; Polygerinos et al. 2013; Suzumori et al. 2007; Moseley et al. 2016; Firouzeh et al. 2015). They typically consist of a hollow chamber, or network of chambers, which when pressurized with a fluid, provide mechanically programmed-type motions, such as Pham Huy Nguyen and Saivimal Sridar contributed equally to this work. & Panagiotis Polygerinos [email protected] 1 The Polytechnic School, Ira A. Fulton Schools of Engineering, Arizona State University, Mesa, AZ 85212, USA 123 Int J Intell Robot Appl (2017) 1:342–351 DOI 10.1007/s41315-017-0020-z

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REGULAR PAPER

Design and control of a 3-chambered fiber reinforced soft actuatorwith off-the-shelf stretch sensors

Pham Huy Nguyen1 • Saivimal Sridar1 • Wenlong Zhang1 • Panagiotis Polygerinos1

Received: 16 November 2016 / Accepted: 7 April 2017 / Published online: 18 April 2017

� Springer Singapore 2017

Abstract The necessity for efficient control of soft actu-

ators has recently resulted in the development of complex

physical models that are actuator geometry and material

type dependent. In this paper, we address the ability to do

closed-loop control with a simplified model independent of

material properties and material characteristics of a soft

robotic system. We demonstrate this by using a P-con-

troller on a new 3-chambered, fiber-reinforced elastomeric

actuator (3CA) that utilizes off-the-shelf stretch sensors. A

motion capture system is used to calibrate and generate two

different quasi-static models (a general linear regression

model and an input dependent model) that map the varying

chamber pressure readings with the actuator’s end effector

position, effectively represented by the stretch sensor cur-

vature. Simulations using a closed-loop controller, with

both models, provide further insight on the quality of the

models and corresponding control performance. We use

this information in an experimental study that yields

comparable performances to the simulated results. More-

over, we demonstrate that the input-dependent model based

controller can provide better results than that of the general

model based controller. Finally, we demonstrate that our

soft actuator can be closed-loop controlled with off-the-

shelf stretch sensors with repeatable results. This opens a

way to design new control concepts for multi-chambered

actuators that can produce more complex motions in the

future.

Keywords Soft actuator � Soft robot � Soft sensor � Linearregression model � Input dependent model � Control

1 Introduction

Compliance, high-power-to-weight ratio, and low fabrica-

tion costs are some of the many advantages associated with

the fast growing interest in soft robotics. These traits make

soft actuators and robots suitable for use in a number of

applications, including manipulation (Calisti et al. 2012;

Marchese and Rus 2015; Homberg et al. 2015; Brown et al.

2010), wearable and human-robot interfaces (Asbeck et al.

2015; Haines et al. 2014; Polygerinos et al. 2015; Galiana

et al. 2012; Park et al. 2014; Menguc et al. 2014; Subra-

manyam et al. 2015; Gafford et al. 2014; McMahan et al.

2005; Roche et al. 2015), and also search and rescue (Lin

et al. 2011; Marchese et al. 2014; Tolley et al. 2014; Morin

et al. 2012; Ramezani et al. 2017). These robots with their

soft actuation and soft-bodied nature allow safe interac-

tions with unstructured environments and the people

involved and show a great potential in replacing rigid

robotic manipulators utilized in industrial environments

(Fitzgerald 2013; Bischoff et al. 2010). Further exploration

of their capabilities could soon enough lead to robotic

systems that offer better and safer methods in handling

sensitive objects with the ability to work closely with

humans.

Fluidic actuators made with elastomeric materials is one

of the most common types of soft actuators encountered in

literature (Ilievski et al. 2011; Polygerinos et al. 2013;

Suzumori et al. 2007; Moseley et al. 2016; Firouzeh et al.

2015). They typically consist of a hollow chamber, or

network of chambers, which when pressurized with a fluid,

provide mechanically programmed-type motions, such as

Pham Huy Nguyen and Saivimal Sridar contributed equally to this

work.

& Panagiotis Polygerinos

[email protected]

1 The Polytechnic School, Ira A. Fulton Schools of

Engineering, Arizona State University, Mesa, AZ 85212,

USA

123

Int J Intell Robot Appl (2017) 1:342–351

DOI 10.1007/s41315-017-0020-z

elongation, contraction, bending, twisting, or combinations

of these different motions. These types of soft elastomeric

actuators either utilize a pneumatic or hydraulic pressur-

ization stimulus, while the ease of customization and

scaling is dependent on the physical properties of the

materials used to manufacture the actuator.

Some soft elastomeric actuators such as the PneuNets

(Polygerinos et al. 2013), fiber reinforced actuators (FRAs)

(Polygerinos et al. 2015; Cianchetti et al. 2013; Agarwal

et al. 2016; Galloway et al. 2013), and HydroMuscles

(Sridar et al. 2016) have been developed and utilized for a

variety of applications. While there has been a tremendous

increase in the fundamental understanding and the design

methods of specific types of soft actuators, not enough

progress has been made on the modelling and control

aspects of these actuators, mainly due to hindering factors

such as the non-linearity that is demonstrated by elas-

tomeric materials when pressurized. In recent studies, soft

actuators have been modeled as Ogden hyper-elastic solids

(Luo et al. 2015), hyper-elastic incompressible Yeoh and

Neo-Hookean materials (Polygerinos et al. 2015), standard

linear solid (SLS) (Sridar et al. 2016), etc., which are

mathematically intense, and are specific to the geometry

and material properties of the actuator design that is ana-

lyzed. Therefore, these models become design specific and

computationally expensive to solve in real-time.

Hence, there is a need for simpler, more computationally

efficient control methods for soft actuators. Towards this

direction, a small number of past works have demonstrated

simple control techniques that rely on previously modeled

soft actuator designs (Skorina et al. 2016; Kadowaki et al.

2011; Svetozarevic et al. 2016). This paper introduces a

new design of a soft actuator based on FRAs (Fig. 1) that

incorporates inexpensive, off-the-shelf soft-stretch sensors

to help sense elongation and contortion of the actuators

during pressurizations. The soft 3-chambered actuator

(3CA) design comes with a minimal number of passive

rigid components, where position control is achieved

through a control algorithm that is independent of the

material properties and geometrical characteristics.

Section 2 presents the design and manufacturing steps

of the 3CA. Section 3 illustrates the mechanical charac-

terization and integration with the actuator of the stretch

sensors. Modeling the behavior of the system is detailed in

Sect. 4. The controller development, and controller per-

formance, in simulation and experiments, of the 3CA are

detailed in Sects. 5 and 6.

Fig. 1 The 3-chambered actuator (3CA). It is embedded with

conductive rubber stretch sensors along the sides of each chamber.

The end effector position is marked by a visual marker

Fig. 2 a Mold for a single chamber; b mold for fusing the 3 chambers; c process of fabricating the 3-chambered actuator (3CA)

Design and control of a 3-chambered fiber reinforced soft actuator with off-the-shelf… 343

123

2 Design and manufacturing

The 3CA consists of three independent cylindrical FRAs in

a parallel formation that requires a three-step fabrication

process as seen in Fig. 2 to generate the final prototype of

the multi-articulate design.

2.1 Single chamber fabrication

The molds for the single FRA were fabricated in three

separate parts using a high spatial resolution rapid manu-

facturing 3D printer (Objet30, Stratasys, MN). The single

actuator mold is designed to incorporate helically extruded

features that are imprinted on the silicone to facilitate

thread winding on the actuator in both clockwise and

counterclockwise directions. These windings prevent the

radial expansion of the actuators and are identical in pitch

to ensure axial elongation of individual chambers as

opposed to bending. As shown in Fig. 2a, two of the mold

pieces contain the helical feature while the top part is used

as a guide for the core of the actuator. The parts of the mold

are secured together and silicone mixture is poured into the

mold cavity. The chambers were made using a two-part

silicone elastomer material with shore hardness 20A

(Dragonskin 20, Smooth-On Inc., Macungie, PA) mixed in

equal proportions by weight. A centrifugal mixer and a

vacuum chamber were utilized to produce a homogeneous

silicone mixture, free of trapped air bubbles that could

compromise the life span of the soft actuator.

The central hollow cavity within the single soft actuator

was generated with the use of a low friction surface acrylic

tube, which was inserted into the mold during the curing

process of the elastomer. A dowel pin attached in the center

of one of the core sides and the top core support piece

together achieve the desired concentricity within the mold.

The mold-core setup was placed in an oven at 70 �C to

expedite the silicone curing process. The mold was then

dismantled leaving the silicone and the core. Kevlar thread

of 3.556 9 10-4 m is then wrapped around the silicone to

act as the radial reinforcement. A symmetrical winding was

used in order to ensure constant strain over the length of

each of the chambers ensuring actuation only along the

center axis of actuator when pressurized. A total of three

soft actuators (chambers) were prepared having the exact

same dimensions, following the same molding process.

2.2 Fusion of the three chambers

A second mold was digitally printed to integrate the three

previously developed chambers and fuse them together.

The three-part mold was assembled and secured in place

and silicone elastomer was poured into the mold. The three

FR-actuators were then immersed into the mold as seen in

Fig. 2c and centered using the top core support piece. The

mold is heated in the oven until the silicone is cured. The

mold and cores were removed after the curing process is

completed and vented screws were inserted to one side of

the actuator, in each one of the chambers, where the dowel

pins have left a small orifice to the silicone. Seal tape was

applied to the external side of the actuator circumference

and dipped into a shallow container with uncured silicone

to seal the exposed sides of the chambers. The silicone

mixture was allowed to cure and the excess material that

did not adhere to the actuators’ surfaces due to the presence

of the tape, was cut off of the finished 3CA.

2.3 Sensor integration

An off-the-shelf stretch sensor (conductive rubber cord

stretch sensor, Adafruit, NY) was attached along each side

of the chambers of the 3CA, allowing sensing in 3

dimensions. The sensor was placed on the external surface

of the chambers along the axial direction as silicone

adhesive (Sil-Poxy, Smooth-On Inc., Macungie, PA) was

applied to seamlessly fuse it with the silicone body of the

3CA. The stretch sensors were placed 120� apart, in a

symmetric fashion to ensure that each strain combination

would lead to a unique end effector position of the actuator.

The ends of the sensors were left exposed for the electrical

connections that measure changes in resistivity when

stretched. The newly integrated sensors were allowed to

cure and adhere ensuring a strong and flexible bond.

3 Stretch sensor characterization

Each of the stretch sensors offers a resistivity of approxi-

mately 13.8 X mm (Adafruit, https://www.adafruit.com/

product/519), with the resistance able to increase when

transitioning from a relaxed to a stretched state. The

working range of the sensor is reported to be up to 50–70%

strain from its resting length. Higher strains deform the

sensor temporarily and require around 1–2 min of settling

time to return to its initial relaxed resistive value.

To characterize the stretch sensor, cord samples of 0.08 m

in length were placed on a universal tensile testing machine

(Instron 5944, Instron Corp., High Wycombe, United

Kingdom). A quasi-static tensile experiment was conducted

using the sensor samples with themachine. The sensors were

loaded and unloaded in the axial direction to a maximum

strain of 50% of their initial length. Three cord samples were

tested to ensure repeatability of the results. The straining

process of the sensors was repeated for 100 cycles at a speed

of 60 mm/min to test linearity and hysteresis of the sensor.

344 P. H. Nguyen et al.

123

A voltage divider was used across the sensors’ ends to

measure the change in voltage while their lengths were

varied. In Fig. 3, we show the characteristic behavior of

this stretch sensor and it is noted that all three cord samples

demonstrated similar characteristic behaviors. This off-the-

shelf stretch sensor demonstrates fairly linear response up

to a strain of 40%, however, some minimal hysteresis is

seen during the loading and unloading cycles.

The sensor samples were also subjected to tensile loading

until failure and observed that the material had plastically

deformed at a strain of 70% and fractured at a strain of 140%

approximately. From the sensor characterization experiments,

itwas concluded that the sensor had a fairly linear (R2 = 0.91)

strain range when tested within the desired strain limits of our

applicationwhichwas less than 30%strain. Therefore, a linear

fit was applied to the sensor for this working range.

To ascertain reliable operation of the sensor under the

linear regimen, pressurization tests that result in bending

motions of the 3CAwere performed such that both the desired

bending angles and the strain on the integrated sensors could

bemeasured. From the sensor measurements, it was observed

that the maximum 3CA bending strain is achieved at a pres-

sure of 0.172 MPa that is well under 30%, thus making this

sensor suitable for this application. Though the sensor shows

some hysteresis, prior work on hysteresis compensation has

been demonstrated in prior work (Chinimilli et al. 2016) has

been omitted in this paper for future work.

4 Modeling of the 3CA

To determine the relation between the strain in the actuator

and the end effector position, a linear regression model was

generated relating the strain in each of the stretch sensor

and the coordinates of the end effector. This model was

considered to be accurate with an R2 value of 0.83 hence

proving that the pressure, strain and the end effector

position were interrelated with a relatively accurate fit. It

was also ensured that unique end effector positions were

obtained for unique combination of pressure values of the

chambers of the 3CA.

x

y

z

24

35 ¼

k11 k12 k13k21 k22 k23k31 k32 k33

24

35 �

S1S2S3

24

35 ð1Þ

In Eq. (1), x, y and z are the end effector positions

corresponding to strains S1, S2, and S3 for the three

chambers. The coefficient matrix k is a 3 9 3 matrix

consisting constant coefficients.

To correlate the strain of each of the chambers of the

actuator with the respective pressure, the assumption of the

linear relation between pressure and strain was made via a

general model created using a linear regression method and

the input dependent model.

S1S2S3

24

35 ¼

A11 A12 A13

A21 A22 A23

A31 A32 A33

24

35 �

P1

P2

P3

24

35 ð2Þ

In Eq. (2), S is the strain vector of order 3 9 1, A, the

linear regression matrix of order 3 9 3 and P, a 3 9 1

vector of the pressure values. For the linear regression

model, each coefficient in matrix A is a scalar providing a

linear combination of pressure and strain and hence opti-

mized for 9 parameters.

In case of the input dependent model, A is a 3 9 3

matrix with each term expressed as a combination of the

three input pressures provided to each of the chambers of

the actuator, hence the name. It is as expressed in Eq. (3).

S1

S2

S3

264

375¼

a0þa1p1þa2p2þa3p3 � � � c0þc1p1þc2p2þc3p3

..

. . .. ..

.

g0þg1p1þg2p2þg3p3 � � � i0þ i1p1þ i2p2þ i3p3

2664

3775 �

P1

P2

P3

264

375

ð3Þ

where each of the terms of the coefficient matrix A is

expressed as a linear combination of the pressures and P1,

P2, and P3 are the pressures in chambers 1, 2, and 3

respectively. Therefore, a total of thirty-six constants were

obtained for the nine coefficients of the matrix A. Here, a

quadratic relation is applied as the strain is computed as a

function of pressure to as compared to the linear regression

model which utilizes a linear relation. Therefore, the strain

of each of the chambers of the 3CA can be estimated using

the model provided that the internal pressure of each of the

chambers is given in both the models. To improve the

accuracy of the input dependent model, the 36 parameters

were optimized using a least-squares cost function,

Fig. 3 Obtained data showing the off-the-shelf stretch sensor output

when subjected to cyclical strain

Design and control of a 3-chambered fiber reinforced soft actuator with off-the-shelf… 345

123

JðhÞ ¼X3i¼1

Si �X3j¼1

AijPj

" #2

ð4Þ

where J(h) is the cost function that is optimized to find the

36 parameters, h. Si, Aij, and Pj is the corresponding strain,

coefficient, and pressure of respective chamber.

To model the strain in the actuator with respect to the

corresponding chamber pressures, the actuator was pres-

surized at 5 different intervals (0, 0.0345, 0.0689, 0.1034,

0.1378 and 0.1724 MPa), alternating in sequence, between

the three chambers. Figure 4 depicts the pressurization pat-

tern for all the chambers of 3CA used to collect the end

effector position data required for modeling. This pattern

was used in order to cover the entire workspace around the

actuator. From this pattern, a combination of 216 unique

positions, based on the position of the actuator’s end effector

and also stretch sensor readings, were obtained using a

motion capture system (OptiTrack Trio V120, Natural Point

Inc., Corvallis, OR) and a data acquisition system.

To obtain the points in space traceable by the actuator

using the motion capture system, reflective passive markers

were placed at various locations of the actuator. Three

markers at the base provide a ground reference plane, three

at the end cap of the actuator and one at the end effector

position. The cameras of the system were oriented in a way

that all marker points were visible during the calibration

phase. For calibration, the system would detect the markers

present at the base and set them as the ground plane of the

actuator. The motion of the other four markers would then

be compared with the ground plane to get the points swept

by the top marker.

The obtained 216 positions in space were plotted in 3D

space to form a point cloud. Figure 5 depicts the point

cloud obtained and the articulation capability of the 3CA.

Based on the point cloud coordinates a model was created

to find the correlation between pressure and strain values of

the stretch sensor. The desired pressure for each chamber

was provided as the input to the model and the strain

corresponding to the pressure was obtained as the output.

A new input dependent model was then generated uti-

lizing the data from the point cloud. The reasoning behind

the generation of the new input dependent model was to

reduce the dependence on approximation using the linear

regression based, general model. Tracking error of the new

input dependent model and the general model was com-

pared in simulation, the results are shown in Fig. 6. The

errors when utilizing the input dependent model were

estimated to be smaller than the general model by a root

mean square (RMS) value of 0.02 V.

4.1 3CA control

To control the position of the end effector of the actuator in

space, a low-level controller was designed to guide the

motion of the 3CA using the strain (S) values. In Sect. 4,

the reachable points and the range of motion of the actuator

were modelled with respect to the pressure (P) and stretch

sensor values (S). In our experiments, we designed and

tested two models with the controller as discussed in

Sect. 4. The controller was designed to minimize the error

signal, which is the difference between the reference strain

value we set and the feedback strain value of the stretch

sensors generated from the model (M). Strain (S) was

chosen the control variable keeping in mind, the interaction

of the 3 chambers of the actuator during pressurization. We

have observed that having only pressure control would not

be entirely reliable because the interaction of the three

chambers while inflating can cause one chamber to squeeze

the other thus possibly altering the internal pressure of the

adjacent chambers. The system’s feedback control loop

(Fig. 7), shows the ability of the controller to use pressure

information to control the values of the stretch sensors and

Fig. 4 Pressurization sequence of: a chamber 1; b chamber 2; c chamber 3 of the 3CA. All individual chamber pressurizations occur under the

same time domain following an incremental pressure pattern

346 P. H. Nguyen et al.

123

in turn position the end effector of the actuator to its

desired location in space.

The control loop used an experimental setup with the

use of six valves (VQ110U-5M, SMC Corporation of

America, Noblesville, IN), three pressure sensors (ASD-

XAVX100PGAA5, Honeywell International Inc., Morris

Plains, NJ), and the three stretch sensors. Three valves

were placed in series in each of the chambers of the

actuator to eliminate venting of air pressure during opening

and closing of a single valve during pressurization or

depressurization respectively.

The set points of the controller are Sd measured in strain

(%) i.e. the desired target values of the actuator to reach.

An error (ev) is generated by comparing the set points to the

continually updated stretch sensor positions S. This error is

compensated by a proportional controller with a coefficient

Kp and the controller’s output, P, is used to pressurize/

depressurize the desired chamber, which then updates the

sensor positions (S1, S2, S3) by using a general model.

The proportional gain constant, Kp, was chosen based on

the strain over pressure data collected and the model of the

system. The Kp value was determined by feeding real-time

pressure and strainvaluesof the 3CA into themodel toobtain a

roughproportional gain constant byapplyinga proportionality

relation. This gain constant was then utilized in the controller

and then further tuned experimentally by trial and error

method in order to optimize the performance of the 3CA. This

process was repeated for both the input dependent and general

models. Both simulations and real time experiments were

conducted to compare the performance of both models.

5 Simulation

The controller’s feedback control loop performance with the

general model was evaluated in a two-part test. Both parts used

a step-response validation process. The first experiment was

with a single-step response and the second experiment used a

multi-step response. The step-response of the three stretch

sensor values, using the strain in the stretch sensor were plotted

against time (Fig. 8). The controller’s feedback control loop

performance with the input dependent model was also evalu-

ated and compared to the one with the general model. This

comparisonwas done using step-response simulations utilizing

single (Fig. 9). The simulated single step response for all three

chambers for the general model and the input dependentmodel

are as shown in Figs. 8 and 9 respectively.

Fig. 5 Point cloud map of the end effector location of the 3CA (left) as captured using the motion capture system (right)

Fig. 6 Simulated performance of input dependent model and linear

regression (general) model over multiple sample indexes

Fig. 7 Controller block diagram with strain values feedback

Design and control of a 3-chambered fiber reinforced soft actuator with off-the-shelf… 347

123

6 Results and discussion

From the simulations shown in Figs. 8 and 9, it was observed

that the errors had been minimized when using the input

dependent model based controller as compared to the general

model based controller. TheKp values selected using the both

the models, in simulation, were utilized for real-time experi-

ments with the strain sensor feedback. Multi-step response

experimentswere performed as shown in Figs. 10 and 11. The

error variation in the input dependent model based controller

in real time experiments is lower, as also verified by a root

mean square (RMS) error of 0.6% over 1.8% of the general

model. The controller response is not as smooth as expected

primarily due to the fact that the valves used for the system are

limited by a slow response time during actuation, hence

causing the actuator to oscillate around the reference signals,

as observed from Figs. 8, 9, 10, and 11.

A differential term in the controller is not added since

the models presented in this paper are quasi-static and not

dynamic. The simulated results of chamber two demon-

strated significantly more signal fluctuation compared to

the other two chambers using the same model. We

hypothesize that amongst the 216 points collected for the

modeling of the end effector position of the actuator, not

enough data pertaining to chamber two were gathered

(Sect. 4 and Fig. 4), leading to a less accurate model

description. This could have also been caused by the par-

ticular pressurization sequence of the actuator during the

data collection for modeling, which might have caused

inaccurate results pertaining to chamber 2. Another possi-

ble reason that could have affected the model behavior of

chamber two could have resulted from inconsistencies in

the sensor readings while building the model.

The values for Kp were chosen using the information that

was provided from simulation using the input dependent and

the general models. As observed from Figs. 8, 9, 10, and 11,

the controller response for the twomodels differ significantly

as the input dependent model was able to provide a better Kp

selection compared to the general model.

The Kp values that were tested during the simulated

responses of both models were then used in the step response

experiments of the 3CA. The experimental results for the

multi-step response using the input-dependent model is

shown in Fig. 12. To eliminate jittering of the system due to

constant error correction, a stabilization function was added.

This stabilization function was introduced to lock the actu-

ator end effector position within a small deadzone. Utilizing

the stabilization function the 3CA system is able to close off

the fluidic valveswhen the desired strain value is reached and

eliminate unwanted jittering motion. This is done by

Fig. 8 Simulated step response for each of the 3 chambers of the 3CA with a normalized setpoint with Kp obtained from the general model

Fig. 9 Simulated step response for each of the 3 chambers of the 3CA with a normalized setpoint with Kp obtained from the input dependent

model

348 P. H. Nguyen et al.

123

continually comparing the amplitude of the desired reference

valuewith the current strain reading.When the strain reading

is detected to bewithin the deadzone around the reference for

over a short period of time, the pressure values are held at that

set point until there is a new desired set point.

7 Conclusions and future work

A new design of a 3CA pneumatic actuator with integrated

stretch sensors was developed via a multi-step fabrication

process capable of generating complex 3-D movements,

utilizing simple control inputs, at a low-cost, independent

of material properties and geometrical parameters. The end

effector positions of the actuator were pre-mapped using a

motion capture system while recording the associated

strain values at every instant. The range of motion of the

system was visualized and the relationship between the

pressure, stretch sensor, and the position of the end effector

of the actuator were evaluated and modelled. An analytical

approach to predict the actuator performance with explicit

relationships between the set strain values, the pressure

output from the controller, and the model generated strain

values was used. The model estimated the stretch sensor

values, which represented the position end effector of the

actuator in space, based only on the supplied air pressure.

A feedback control loop with two different models, a

general and an input-dependent model, were implemented

to demonstrate the ease of actuator controllability. The

effectiveness of the position controller was demonstrated

using single and multiple step functions. The valve con-

troller of the feedback control loop successfully tracked

the reference signals for both models presented in this

work. The general model tracked a single-step signal with

a small time delay, but had a lot of valve switching in

comparison to the controller that used the input-dependent

model, which was more stable and showed higher

accuracy.

Jerky motion leading to unstable states of the end

effector position of the 3CA was also observed. This was

because of the constant error correction of the controller

having a delay due to inherent nature of the selected valves

having a low operational bandwidth. The undesired motion

can be reduced employing higher quality valves that offer

faster switching modes. Moving forward, the dynamic

behavior of the 3CA will be explored leading to more

effective models and efficient system behavior.

Fig. 11 Experimental feedback control loop performance for multi-

step response using a Kp value indicated by the input dependent

model

Fig. 12 Experimental feedback control loop performance for multi-

step response using a Kp value indicated by the input dependent

model with a stabilization function

Fig. 10 Experimental feedback control loop performance for multi-

step response using a Kp value indicated by the general model

Design and control of a 3-chambered fiber reinforced soft actuator with off-the-shelf… 349

123

Although inexpensive, durable, and readily available,

the stretch sensor did not necessarily provide always

repeatable values when in operation and present non-linear

behavior post 50% strain. To further use these sensors, a

hysteresis compensator would have to be implemented in

order to improve the strain readings of the sensors, each of

the chambers. Therefore, new methods and filtering algo-

rithms will be explored for more accurately sensing the

strain in the chambers.

Lastly, the stretch sensor positions and corresponding

error could be utilized to relate the elongation of each of

the chambers with the bending angle of the actuator. With

the bending angles known, a model that translates a desired

azimuth and elevation (Firouzeh et al. 2015) to the stretch

sensor strain can be generated. In the future, multiple 3CAs

will be stacked together, each actuator acting as a single

joint, to create a highly articulate soft-robotic arm that will

be able to safely interact with humans and the environment.

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Pham Huy Nguyen received

the B.S.E in Mechatronics (First

Class Honors) from the Asian

Institute of Technology in

Bangkok, Thailand in 2013 and

the M.Sc. degree in robotics

from the EMARO (European

Masters in Advanced Robotics)

Program in 2015. He is cur-

rently a Graduate Research

Assistant with the Ira A. Fulton

Schools of Engineering at Ari-

zona State University, USA,

with the Bio-Inspired Mecha-

tronics Lab. His research inter-

est includes the fields of bio-inspired, soft, and wearable robotics.

Saivimal Sridar received his

B.Tech in mechanical engi-

neering from SASTRA Univer-

sity, Thanjavur, India in 2014

and a M.S. in Robotics Engi-

neering from Worcester

Polytechnic Institute in 2016.

He is currently a Graduate

Research Assistant at the

Polytechnic School, the Ira.

A. Fulton Schools of Engineer-

ing, Arizona State University,

USA pursuing a Ph.D. at the

Bio-inspired Mechatronics lab.

His research interests include

soft robotics, wearable robotics, and bio-mechatronic systems.

Wenlong Zhang is currently an

Assistant Professor in the

Polytechnic School at the Ira

A. Fulton Schools of Engi-

neering, Arizona State

University. He received his

B.Eng. degree in control sci-

ence and engineering from

Harbin Institute of Technol-

ogy, and M.S. in mechanical

engineering, M.A. in statistics,

and Ph.D. in mechanical engi-

neering all from University of

California, Berkeley. His

research interests lie in the

design, modeling, and control of cyber-physical systems, with

applications to healthcare, robotics, and manufacturing. He

received several honors and awards, including Berkeley Fellow-

ship for Graduate Study from UC Berkeley, Best Paper Award in

the 2013 IEEE Real-time System Symposium, and Semi-Plenary

Paper Award Finalist in the 2012 ASME Dynamic Systems and

Control Conference.

Panagiotis Polygerinos re-

ceived the B.Eng. degree (top of

his class) in mechanical engi-

neering from the Technological

Educational Institute of Crete,

Heraklion, Greece in 2006, the

M.Sc. (with distinction) degree in

Mechatronics and Ph.D. in

mechanical engineering/medical

robotics from King’s College

London, London, U.K., in 2007

and 2011, respectively. From

2012 until 2015, he was a post-

doctoral fellow of technology

development with the Harvard

Biodesign Lab and the Wyss Institute for Biologically Inspired Engi-

neering at Harvard University. He is currently an Assistant Professor

with the Ira A. Fulton Schools of Engineering at Arizona State

University, USA, and director of the Bio-Inspired Mechatronics Lab. His

research interests focus on the realization of tasks that are essential to the

design, implementation and integration of novel soft robotic systems and

mechatronic devices.

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123