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13 Figures# Modeling of Soft Fiber-Reinforced Bending Actuators

Abstract

Soft fluidic actuators consisting of elastomeric matrices with embedded flexible materials are of particular interest to the robotics community because they are affordable and can be easily customized to a given application. However, the significant potential of such actuators is currently limited as their design has typically been based on intuition. In this paper, the principle of operation of these actuators is comprehensively analyzed and described through experimentally validated quasi-static analytical and finite-element method models for bending in free space and force generation when in contact with an object. This study provides a set of systematic design rules to help the robotics community create soft actuators by understanding how these vary their outputs as a function of input pressure for a number of geometrical parameters. Additionally, the proposed analytical model is implemented in a controller demonstrating its ability to convert pressure information to bending angle in real time. Such an understanding of soft multimaterial actuators will allow future design concepts to be rapidly iterated and their performance predicted, thus enabling new and innovative applications that produce more complex motions to be explored.

Figures

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IEEE TRANSACTIONS ON ROBOTICS 1

Modeling of Soft Fiber-Reinforced

Bending Actuators

Panagiotis Polygerinos, Member, IEEE, Zheng Wang, Member, IEEE, Johannes T. B. Overvelde, Kevin C. Galloway,

Robert J. Wood, Katia Bertoldi, and Conor J. Walsh, Member, IEEE

Abstract—Soft ﬂuidic actuators consisting of elastomeric ma-

trices with embedded ﬂexible materials are of particular interest

to the robotics community because they are affordable and can

be easily customized to a given application. However, the signiﬁ-

cant potential of such actuators is currently limited as their design

has typically been based on intuition. In this paper, the principle

of operation of these actuators is comprehensively analyzed and

described through experimentally validated quasi-static analytical

and ﬁnite-element method models for bending in free space and

force generation when in contact with an object. This study pro-

vides a set of systematic design rules to help the robotics community

create soft actuators by understanding how these vary their out-

puts as a function of input pressure for a number of geometrical

parameters. Additionally, the proposed analytical model is imple-

mented in a controller demonstrating its ability to convert pressure

information to bending angle in real time. Such an understanding

of soft multimaterial actuators will allow future design concepts

to be rapidly iterated and their performance predicted, thus en-

abling new and innovative applications that produce more complex

motions to be explored.

Index Terms—Bending, ﬁber reinforced, ﬂuidic actuator, mod-

eling, soft robot.

I. INTRODUCTION

SOFT robotics is a rapidly growing research ﬁeld that com-

bines robotics and materials chemistry, with the ability to

preprogram complex motions into ﬂexible elastomeric materials

(Young’s modulus ∼102−106Pa) [1]–[4]. These soft systems

are engineered using low-cost fabrication techniques, provide

adaptable morphology in response to environmental changes,

and are ideally suited for gripping and manipulating delicate

objects [2]–[7].

Manuscript received March 26, 2014; revised February 1, 2015; accepted

April 23, 2015. This paper was recommended for publication by Associate

Editor S. Hirai and Editor B. J. Nelson upon evaluation of the reviewers’ com-

ments. This work was supported in part by the National Science Foundation

under Grant #1317744 and Grant #IIS-1226075, by DARPA Award W911NF-

11-1-0094, and by the Wyss Institute and the School of Engineering and Applied

Sciences, Harvard University.

P. Polygerinos, R. J. Wood, and C. J. Walsh are with the School of Ap-

plied Sciences and Engineering and Wyss Institute, Harvard University, Cam-

bridge, MA 02138 USA (e-mail: polygerinos@seas.harvard.edu; rjwood@seas.

harvard.edu; walsh@seas.harvard.edu).

Z. Wang is with the Department of Mechanical Engineering, The University

of Hong Kong, Hong Kong (e-mail: zwangski@hku.hk).

J. T. B. Overvelde and K. Bertoldi are with the School of Applied Sci-

ences and Engineering and Kavli Institute for Bionano Science and Tech-

nology, Harvard University, Cambridge, MA 02138 USA (e-mail: overvelde@

seas.harvard.edu; bertoldi@seas.harvard.edu).

K. C. Galloway is with Wyss Institute, Harvard University, Cambridge, MA

02138 USA (e-mail: kevin.galloway@wyss.harvard.edu).

Color versions of one or more of the ﬁgures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TRO.2015.2428504

Soft actuators are commonly constructed as monolithic struc-

tures from compliant materials such as electroactive polymers

[8]–[10], shape memory alloys [11], [12], elastomers [2], hydro-

gels [13], [14], or composites that undergo a solid-state phase

transition [15]. Their actuation can be achieved by a variety

of stimuli, including electrical charges [9]–[12], chemical reac-

tions [16], [17], and pressurized ﬂuids [2], [3], [7], [15]–[22]. In

particular, pneumatic and hydraulic powered soft actuators are

promising candidates for robotics applications because of their

lightweight, high power-to-weight ratio, low material cost, and

ease of fabrication with emerging digital fabrication techniques

[15]–[19], [23]. Upon pressurization, embedded chambers in

the soft actuator expand in the directions associated with low

stiffness and give rise to bending [2], twisting [24], and extend-

ing/contracting motions [25]. Furthermore, these actuators can

be integrated into the structure of soft robotic systems both as

actuators and structural elements [2], [3], [5], [7], [18], [25],

[26]. For a more comprehensive view on the soft robotic liter-

ature, the authors refer to review works of Majidi [1], Trivedi

et al. [27], and Kim et al. [28].

While empirical approaches have highlighted the exciting

potential of soft actuators, the lack of robust models for soft

multimaterial ﬂuidic actuators is greatly limiting their potential.

Predicting a soft actuator’s performance (e.g., deformation and

force output in response to a pressurized ﬂuid) prior to manu-

facture is nontrivial due to the nonlinear response and complex

geometry. One class of soft actuators that has received signiﬁ-

cant research attention in recent years are soft bending actuators,

but limited modeling work has been conducted. To make these

actuators widely applicable, a systematic understanding of the

relationship between actuator geometry and its performance is

required.

In this study, soft actuators are considered that are activated

by pressurized air and are constructed from a combination of

elastomeric (hyperelastic silicones) and inextensible materials

(fabrics and ﬁbers), i.e., soft ﬁber-reinforced bending actuators

(see Fig. 1) [8], [29]–[31]. Compared with existing geometri-

cally complex soft bending actuator designs with bellows [2],

[3], [18], [24], the widely used soft ﬁber-reinforced bending ac-

tuators have a much simpler tubular geometry that offers ease

of manufacture, and where ﬁbers can be arranged along their

length to enable nontrivial deformation modes. In addition, a

strain-limiting layer added to one side enables bending. To get

deeper insight into the response of the system and be able to ef-

ﬁciently design application-speciﬁc soft actuators, quasi-static

analytical and ﬁnite-element method (FEM) models are devel-

oped. Compared with previous FEM models, the proposed 3-D

models capture the contact interaction information between the

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2IEEE TRANSACTIONS ON ROBOTICS

Fig. 1. (a) Soft ﬁber-reinforced bending actuator in the unpressurized state

and a closeup view of the ﬁber reinforcements (ﬁber winding). (b) Same actuator

in the pressurized state.

straining elastomer material and the nonstraining ﬁber rein-

forcements. This enables to capture in a realistic manner the

behavior of the bending actuators while providing details about

stress concentration points and the generated strains. In addi-

tion, a series of experimental tests are conducted to validate

the models. In particular, 1) the bending of the actuator in free

space and 2) the force applied by the actuator at its proximal

tip when in contact with an object are measured. Furthermore,

the developed analytical model is used in feedback control loop

experiments to demonstrate its ability to perform real-time con-

version of the supplied air pressure signal into bending angle

information.

II. ACTUATOR FABRICATION

The widely used design of the soft ﬁber-reinforced bending

actuator is in this study fabricated following a new multistep

molding process developed by the authors that ensures faster

production times and more robust and repeatable actuator out-

comes. This fabrication technique is comprised of four parts:

1) a hemicircle elastomeric air chamber (including the caps at

the distal and proximal ends); 2) circumferential ﬁber windings

that run along the length of the chamber; 3) an inextensible

base layer; and 4) a soft coating material (sheath) that encapsu-

lates the entire system [31]. The circumferential reinforcement

provided by the ﬁbers limits radial expansion and promotes

linear extension, while the strain limiting layer at the base re-

stricts linear extension on one face of the actuator. Therefore, as

the actuator is pressurized, part of it expands while the strain-

limited portion restrains any linear expansion along one surface

(see Fig. 1), producing a bending motion. More details about

the described fabrication method can also be found at the soft-

roboticstoolkit.com website [38] The Soft Robotics Toolkit is a

collection of shared resources to support the design, fabrication,

modeling, characterization, and control of soft robotic devices.

To offer complete control over every aspect of the assembled

actuator including geometry, material properties, and pattern of

ﬁber reinforcements, a multistep molding approach was used.

The molds for the actuator were 3-D printed with an Objet

Connex 500 printer. The ﬁrst rubber layer (Elastosil M4601

A/B Wacker Chemie AG, Germany) [see Fig. 2(a)]used a half

round steel rod to deﬁne the interior hollow portion of the ac-

tuator. Woven ﬁberglass (S2-6522, USComposites, FL, USA)

was glued to the ﬂat face to serve as the strain limiting layer

[see Fig. 2(b)]. After molding the ﬁrst rubber layer, ﬁber rein-

forcements were added to the surface [see Fig. 2(c)]. A single

Kevlar ﬁber (0.38-mm diameter) was wound in a double helix

pattern around the length of the actuator body. Raised features

in the mold were transferred to the actuator surface to deﬁne

the ﬁber path for consistency of ﬁber placement. Fiber rein-

forcements were further secured by placing the entire assembly

into another mold to encapsulate the actuator body in a 1.0-mm-

thick silicone layer (Ecoﬂex-0030 silicone, Smooth-on Inc., PA,

USA) [see Fig. 2(d)]. The actuator body was then removed from

the mold and the half round steel rod [see Fig. 2(e)]. The ﬁrst

open end was capped by placing it into a small cup of uncured

silicone. Once this end cured, a vented screw was fed through

the 15-mm-thick silicone cap to form the mechanical connec-

tion for the pneumatic tubes (see Fig. 2(e), top right). The other

open end was capped in a similar manner (see Fig. 2(e), lower

right).

III. ACTUATOR MODELING

In rigid-bodied robots, there are well-deﬁned models to char-

acterize the motion of mechanical linkages and the force they

can produce. In this study, both detailed FEM models and

computationally inexpensive analytical models of a soft ﬁber-

reinforced bending actuator were pursued to analyze the behav-

ior of the actuator and obtain a relationship between the input

air pressure and the bending angle, as well as the relationship

between the input air and the output force.

A. Analysis of Actuator Cross-Sectional Shapes

The actuator design can be tuned by varying a number of

geometrical parameters including the wall thickness of the air

chamber, the length of the actuator, the diameter of the hemicir-

cle chamber shape, and the ﬁber winding pitch and orientation

(see Fig. 3). Changing any of these parameters will result in

different performance. Furthermore, the shape of the cross sec-

tion can also signiﬁcantly affect the response of the system as

the magnitude of the area determines the force generated by the

pressure acting on it and it will also inﬂuence the stress distri-

bution in the elastic material as it resists expansion. In the past,

rectangular (RT), circular (FC), and hemicircular (HC) shapes

have been used in soft actuator designs without explicitly com-

paring their efﬁciencies [8], [29], [32]. In this study, these three

cross-sectional shapes were compared to identify the most ef-

fective shape for a soft bending actuator based on which requires

the least pressure to bend to the same angle while preserving its

original cross-sectional shape.

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POLYGERINOS et al.: MODELING OF SOFT FIBER-REINFORCED BENDING ACTUATORS 3

Fig. 2. Schematic outlining some stages of the soft ﬁber-reinforced bending actuator fabrication process. (a) First molding step using a 3-D printed part.

(b) Strain limiting layer (woven ﬁberglass) is attached to the ﬂat face of the actuator. (c) Thread (Kevlar ﬁber) is then wound along the entire length of the actuator.

(d) Second molding step: the entire actuator is encapsulated in a layer of silicone to anchor all ﬁber reinforcements. (e) In the ﬁnal step, the half-round steel rod is

removed and both ends of the actuator are capped allowing one end to have a port for the inﬂow/outﬂow of air.

Fig. 3. Soft ﬁber-reinforced bending actuator showing numbered and labeled the geometrical parameters and design variables that can affect its behavior.

Materials A, B, C, and D represent the material properties of the actuator body, sheath, ﬁber reinforcements, and base inextensible layer, respectively.

The dimensions for each shape were obtained [see Fig. 4(a)]

using the same cross-sectional area of a2, and vis the ratio

between rectangular edges. Assuming an actuator wall thick-

ness of t=a/4, with an input air pressure of Pin, the bending

torques(Ma)of internal air pressure against the distal cap of the

actuator geometry were calculated as

MRT

a=0.5

va3Pin (1)

MHC

a=0.34a3Pin (2)

MFC

a=0.72a3Pin.(3)

A larger Mavalue indicated that a particular shape could gen-

erate a larger bending torque for the same input pressure.

To create actuator bending, the torque Mamust overcome the

internal bending moments, which are also functions of the actua-

tor geometry. To quantify and compare this effect, the ratio of the

actuator internal bending moment and the pressure-generated

bending torque Mais denoted as the bending resistance, and the

bending resistance for all three cross-sectional shapes is shown

in Fig. 4(b) for a bending angle ranged from 0°to 360°.A

lower vertical axis value indicates an actuator that is theoret-

ically easier to bend, and therefore, the RT shape was found

less suitable since it required the highest amount of pressure to

reach the same bending angle. On the other hand, the HC was

found easier to bend. Additionally, the RT shape was assumed

with a ratio (v)of 1.47, such that it could generate a bending

torque Maequal to that of the HC shape when the same amount

of pressure Pin was provided. As a result, both the RT and FC

shapes demonstrated similar bending resistance. Based on the

above, the HC shape was chosen for this study.

B. Analytical Modeling

An analytical model was developed that captures the explicit

relationship between input pressure, bending angle, and output

force by taking into consideration both the hyperelastic material

property of silicone rubber and the geometry of the actuator.

The variables in the model were actual actuator dimensions and

material properties that could be either measured or obtained

from calibrations.

4IEEE TRANSACTIONS ON ROBOTICS

Fig. 4. (a) Cross-sectional views of a rectangular (RT), hemicircle (HC), and

full circle (FC) actuator shape with equal cross-sectional area and with a strain

limiting layer attached at their bottom face. (b) Efﬁciency comparison (bending

resistance) of the different actuator shapes. A lower bending resistance indicates

that an actuator is easier to bend with less pressure.

1) Material Model: The soft ﬁber-reinforced bending actua-

tors were fabricated using silicone rubber. This was modeled as

an incompressible Neo–Hookean (NH) material [33] so that the

strain energy is given by

W=μ

2(I1−3) (4)

where I1is the ﬁrst invariant of the three (axial, circumferential

and radial) principal stretch ratios λ1,λ2,and λ3as

I1=λ2

1+λ2

2+λ2

3(5)

and μis the initial shear modulus of the material. The principal

nominal stresses sicould then be obtained as a function of W,

λi, and the Lagrange multiplier pas

si=∂W

∂λi−p

λi

.(6)

2) Model for Bending Angle in Free Space: A geometrical

model of the soft ﬁber-reinforced bending actuator that relates

the input air pressure and the bending angle in free space is

derived fully accounting for large deformations. It was assumed

that when compressed air (P1>P

atm) is supplied to the air

chamber, the top wall will extend while the bottom layer will be

constrained by the inextensible layer, thus causing the actuator

to bend toward the bottom layer with a radius Rand angle θ(see

Fig. 5). Here, the ﬁber-reinforced mechanism was considered to

be a hard constraint to the actuator. Although the actuator has

a multilayered structure, for the sake of simplicity, it was mod-

eled as a homogeneous incompressible NH material [33] with

effective initial shear modulus ¯μ. The dynamics associated with

pressurization were neglected in the model, and it was assumed

that the actuator always has a uniform bending curvature.

Here, the principal stretch λ1along the axial direction of

the actuator was denoted. Furthermore, due to the ﬁber rein-

forcement constraint, the strain in the circumferential direc-

tion was negligible so that λ2=1. Finally, considering the

incompressibility of the material, λ1λ2λ3=1, it was obtained

Fig. 5. (Top left) Side view of the soft ﬁber-reinforced bending actuator in

a bending state. Closeup view: view of the actuator distal tip showing the

generated moments. Lower center: Cross-sectional view of the actuator.

that

λ1=λ,λ2=1,λ3=1

λ.(7)

Next, a vanishing stress was assumed in radial direction

through the thickness of the actuator (i.e., s3=0), and by com-

bining (6) with (4) and (5) as

s1=∂W

∂λ1−P

λ1

=¯μλ−1

λ3(8)

s2=∂W

∂λ2−P

λ2

=¯μ1−1

λ2(9)

s3=¯μλ3−P

λ3

=0 (10)

p=¯μλ2

3=¯μ

λ2.(11)

Within the range of stretches considered in this application

(1≤λ<1.5), the circumferential stress s2was signiﬁcantly

smaller than s1(i.e., s2<s

1/2). Therefore, s1was considered

to be the only nonvanishing principal stress and hereafter de-

noted as s.

The internal stretch of the actuator materials resulted in an

opposing bending moment. Therefore, at each bending conﬁgu-

ration, a torque equilibrium was reached around the fulcrum O,

as it is shown in Fig. 5, that can be obtained from

Ma=Mθ(12)

where Mais the bending torque of internal air pressure against

the distal cap of the actuator, and Mθis the combined moment

of the stresses stand sbon the top and bottom layers. Using the

hemicircular geometry with radius athe distal actuator cap was

a, Macan be calculated as

Ma=2(P1−Patm)π

2

0

(asin ϑ+b)a2cos2ϑdϑ

=4a3+3πa2b

6(P1−Patm).(13)

POLYGERINOS et al.: MODELING OF SOFT FIBER-REINFORCED BENDING ACTUATORS 5

Moreover, combining the effect of the stresses acting on the

top and bottom layers, the bending moment is

Mθ=b

0

sβ·2(a+t)Lβdβ

+2

t

0π

2

0

sτ,φ (a+τ)2sin φ+b(a+τ)Ldφ

dτ.

(14)

Furthermore, by introducing the local coordinate β, the lon-

gitudinal stretch and strain in the bottom layer can be calculated

as (see Fig. 5)

λβ=R+β

R=L/θ +β

L/θ =βθ

L+1 (15)

sβ=¯μλβ−1

λ3

β.(16)

Similarly, for the top layer with the coordinate τ(see Fig. 5):

λτ,φ =R+b+sinφ(a+τ)

R(17)

sτ,φ =¯μλτ,φ −1

λ3

τ,φ .(18)

By substitution of (13) and (14) into (12), a relationship be-

tween the input air pressure Pin and the bending angle θin free

space can be obtained

Pin =6Mθ(θ)

4a3+3πa2b(19)

where Pin =P1−Patm,aand bare the air chamber radius and

bottom thickness of the actuator, respectively, and Mθ(θ)was

given in (14). Substituting (15)–(18) into (14) to eliminate sand

λ, it is possible to show that Mθis a function of ¯μ, a, b, t, andθ.

However, the integral in (14) could not be computed analytically,

and therefore (14), and hence (19), had to be solved numerically.

The material property coefﬁcient ¯μcan be obtained through

calibration tests.

3) Model for Bending Torque/Force: An expression for the

actuator force can be derived by extending the analytical model

previously developed for bending angle. In this analysis, the

actuator was assumed to be constrained at a zero bending angle

(i.e., constrained in a ﬂat conﬁguration) such that no internal

bending moments (Mθ) were generated under pressurization.

Therefore, the torque equilibrium at the fulcrum Oof Fig. 5

becomes

Mf=FL

f=Ma=κPin (20)

where Fis the contact force between the actuator distal cap

and the environment, Lfis the distal cap length, Mfis the

external bending torque generated by the contact force around

O, combining (20) with (13), and κis a function of the actuator

geometry given by

κ=4a3+3πa2b

6.(21)

This equation describes the pressure–force relationship under

an isometric process (constant bending angle). Although (20) is

only applicable for a speciﬁc bending angle (i.e., zero degrees),

it does provide insight into the relationship between actuator

geometry and bending force. It also follows that under isotonic

conditions (constant pressure), the force output will decrease as

bending angle increases, because larger bending moments are

required to bend the actuator to the desired angle. Hence, the

bending force described in (20) can be deﬁned as the maximum

force output for a particular input pressure.

C. Finite-Element Method Modeling

The analytical model quickly generates insights into the re-

sponse of an actuator to pressurized air for a particular geometry.

However, it cannot capture certain aspects of the soft actuator

behavior such as the interaction of internal layers of differ-

ent materials. FEM models, on the other hand, provide a more

realistic description of the nonlinear response of the system, al-

though at a higher computational cost. An additional advantage

of FEM is that the deformation (and stress) in soft actuators can

be readily visualized, leading to a better understanding of the

inﬂuence of local strain on global actuator performance. Prior

work on FEM modeling soft elastomeric actuators with ﬁber

reinforcements has demonstrated the shape due to bending [7],

[34], but minimal work has been done to validate these models

experimentally or used to characterize the actuator stiffness and

force-generating capabilities [35], [36].

Prior to simulations, elastomeric samples of the individual

materials used to fabricate the actuator were tested accord-

ing to ASTM D638 (Type IV) at a rate of 500 mm/min for

uniaxial tensile strength, and compression samples were com-

pressed at a rate of 500 mm/min to obtain accurate material

properties. A hyperelastic incompressible Yeoh material model

[37], with strain energy U=2

i=1 Ci(Ii−3), was used to

capture the nonlinear material behavior of both the Elastosil

and the Ecoﬂex materials. In particular, the material coefﬁ-

cients were C1=0.11MPa,C

2=0.02MPa for the Elastosil

and C1=0.012662MPa and C2=0MPafor the Ecoﬂex. It is

noted that the initial shear modulus was ¯μ=2C1.

To model the behavior of the actuators, 3-D FEM models

were constructed and analyzed with ABAQUS/Standard (Simu-

lia, Dassault Systemes). Simpliﬁcations in the model were kept

to a minimum in order to closely match the experimental setup.

The inlet for pressurized air was not taken into account in the

model as the pressure was applied to all the internal walls of

the chamber. All the components of the actuator were modeled

using solid tetrahedral quadratic hybrid elements (Abaqus ele-

ment type C3D10H). For the thin ﬁber windings, quadratic beam

elements were used (Abaqus element type B32), which were

connected to the Elastosil by tie constraints. The material of the

ﬁber winding was modeled as linear elastic (Young’s modulus of

E=31,076MPa and a Poisson’s ratio of v=0.36). The num-

ber of nodes and elements used in the models are summarized

in Table I.

As expected, the modeled beam elements introduced some

bending support, while the ﬁber windings provided no bending

6IEEE TRANSACTIONS ON ROBOTICS

TAB LE I

NUMBER OF NODES AND ELEMENTS FOR THE SOFT ACTUATOR FEM MODELS

Radius

(mm)

Length

(mm)

Wall Thickness

(mm)

Number of

Nodes

Number of

Elements (B32,

C3D10H)

6.0 100 2.0 71 309 44 465

6.0 130 2.0 95 061 59 108

6.0 160 2.0 118 708 73 614

8.0 100 2.0 98 113 62 301

8.0 130 2.0 128 787 81 219

8.0 160 1.0 90 449 55 141

8.0 160 2.0 160 711 101 097

8.0 160 3.0 185 274 118 557

10.0 160 2.0 192 650 121 106

12.0 160 2.0 208 921 131 646

stiffness. To decrease the modeled stiffness from the beam ele-

ments, the radius of the beam elements was reduced by a factor

of 2. This radius reduction resulted in an insigniﬁcant change

in tensile strength of the wire as it remained signiﬁcantly stiffer

than the elastomer. It is also noted that although the physical

ﬁber windings did not have any compressive stiffness, the beam

elements of the FEM model added some. However, the inﬂu-

ence of this effect on the simulation result can be neglected,

since all the beams were under tension. Furthermore, for sake

of computational efﬁciency and to increase the convergence of

the simulation, the bottom layer of the actuator, consisting of an

inextensible layer, was modeled as an elastomer (Yeoh material

with Ccombined =7.9MPa). The stiffness of the combined layer

remained sufﬁcient to function as an inextensible layer. Finally,

to model loading of the actuator, an internal pressure was applied

to the surface of the chamber. The deformation of the actuator

obtained with the proposed FEM model is illustrated in Fig. 6.

Similarly, the previously developed FEM model was also used

to conduct a force analysis. In this force model, the proximal

cap was completely ﬁxed, and the bending deformation of the

actuator was also constrained. The force was then determined

by summing the reaction forces at the nodes on the edge of the

distal cap.

IV. TESTING OF SOFT FIBER-REINFORCED

BENDING ACTUATORS

A. Experimental Platform

An experimental platform was developed (see Fig. 7) to val-

idate the analytical and FEM models. This platform permitted

fast and easy characterization and incorporated multiple sens-

ing modalities [31], [36]. Within the platform, the soft actuator

proximal cap with the air inlet was clamped in a rigid ﬁxture,

emulating the boundary constraints deﬁned with the modeling

approaches. The distal cap of the actuator was free to bend in

the vertical plane. It is noted that a horizontal bending would

be less favorable since gravitational forces could bring the ac-

tuator out of plane. A high-deﬁnition camera (DSLR, Rebel

T2i, Canon Inc., NY, USA), was used to monitor the actuator

from the side so that the bending trajectory of its distal cap (tip)

could be recorded. The camera was aligned with a checkered

background. This technique allowed lens distortion issues to be

Fig. 6. Three-dimensional FEM model result for the actuator at unpressurized

and pressurized state at 196 kPa. (Top) FEM modeled ﬁber reinforcements,

inextensible layer in an unpressurized state. The arrows indicate their location

at the soft actuator. (Lower left) The bending angle shape at 360°of the FEM

modeled soft actuator in a cross-sectional view demonstrating the air chamber

and the ﬁber reinforcements. (Lower right) Bending angle shape at 360°of the

FEM modeled soft actuator in a strain contour view that highlights the maximum

principal strain locations and ﬁber reinforcements.

Fig. 7. Evaluation platform with all the associated equipment for monitor-

ing and control of the soft actuator. The evaluation platform is described in

[31], [36].

addressed and measurement accuracy to be enhanced. A metric

ruler was also placed on the rigid ﬁxture, next to the actuator,

to provide a correlation between number of pixels in the pic-

ture frames and the actual length. Postprocessing of the video

frames was performed with freely available software (Kinovea

0.8.15), where the xand ycoordinates of the actuator tip trajec-

tory were tracked and bending angle was calculated. A six-axis

force/torque sensor (Nano17, ATI Industrial Automation, NC,

USA) was used to measure the force generating capability. A

short post was mounted on the force sensor and brought in

contact with the tip of the actuator. The actuator top surface

was placed in contact with a rigid ﬁxture to minimize nonlinear

POLYGERINOS et al.: MODELING OF SOFT FIBER-REINFORCED BENDING ACTUATORS 7

effects due to bending. The pressure inside the actuator was

gradually increased, while the force exerted by the actuator’s

tip was recorded. The experiments for each version of the soft

ﬁber-reinforced bending actuators were performed three times

to assess accuracy and repeatability.

B. Calibration Process

Five trials were conducted, and a one-step least-squares es-

timation procedure of ¯μ, was obtained using experimentally

measured input pressure and bending angles. In each trial, the

same actuator was pressurized to bend in free space. Although

the estimated ¯μvalue was expected to be actuator speciﬁc, in

reality, the difference was not signiﬁcant among different ac-

tuator samples. The estimated ¯μvalue was 0.314 MPa for an

actuator with (a, b, t, L)=(8,2,2,160) mm. The same ¯μvalue

was used in all subsequent studies with good results.

V. VALIDATION AND EXPERIMENTAL RESULTS

A. Evaluation of Analytical and Finite-Element Method Model

To demonstrate the value of the proposed analytical and FEM

models, several physical parameters of the actuator (i.e., length,

radius, and wall thickness) were varied to evaluate their inﬂu-

ence on bending angle at 90°, 180°, and 360°(i.e., full circle)

(see Fig. 8). A baseline set of geometrical parameters (160.0-

mm length, 2.0-mm wall thickness, and 8.0-mm radius) was

chosen as a starting point for the soft actuator where the max-

imum bending angle (i.e., 360°) could be reached at around

200 kPa (∼30 PSI). These dimensions were chosen as such

an actuator would be suitable for wearable robotic applications

[35]. An additional six variations of this parameter set were

used (e.g., the actuator length was varied while diameter and

wall thickness kept constant) to demonstrate the inﬂuence of

actuator geometry, as presented in Fig. 8. The results from this

evaluation presented some deviations in the absolute pressure

values. This was mainly due to the assumption in the analytical

model that the bottom layer of the actuator remained ﬂat during

pressurization. In contrast, this radial bulging was captured by

the FEM models resulting in the actuator cases of radius and

wall thickness, which were cross section dependent, to deviate

more. Nonetheless, both models were found to provide similar

trends for all parameter variations. Speciﬁcally, the results of

Fig. 8(b) showed that for an increase in the length, higher air

pressure was required to achieve full 360°bending. Similarly,

a decrease in radius required higher air pressures for actuation

[see Fig. 8(a)]. Finally, it was shown that as the wall thickness

increased, air pressure also had to increase to achieve a given

bending angle [see Fig. 8(c)].

B. Bending Angle Experiments

The bending trajectories of the baseline actuator compared

with the analytical and the FEM models are illustrated in Fig. 9.

A good match between the theoretical and experimental data

can be observed from the plot (maximum displacement error of

3.7%), demonstrating the validity and accuracy of the models. In

addition, the pressure locations are shown for 0°and 360°bend-

ing in Fig. 9. These pressure angle-related locations presented

Fig. 8. Analytical and FEM modeling results for the soft ﬁber-reinforced

bending actuator in free space at: 90°, 180°, and 360°. (a) Pressure versus

actuator radius, for radius analytical values ranging from 6.0 to 12.0 mm and

FEM speciﬁc values of 6.0, 8.0, 10.0, and 12.0 mm. (b) Pressure versus actuator

length, for analytical length values ranging from 80.0 to 180.0 mm and FEM

speciﬁc values of 100.0, 130.0, and 160.0 mm. (c) Pressure versus wall thickness,

for analytical wall thickness ranging from 1.0 to 3.0 mm and FEM speciﬁc values

of 1.0, 2.0, and 3.0 mm.

only small discrepancies in pressure values due to some initial

prebending (i.e., at 0 kPa) and gravitational inﬂuences in the

fabricated actuator with a maximum pressure error of 10.9%.

Experimental data were collected with the six variations of

actuator designs as described in the previous section. Each ac-

tuator was pressurized ﬁve times in order to bend in free space,

and the supplied pressure along with the corresponding bending

angle was measured using the experimental setup of Section IV-

A. The contractions occurred at a slow pressure rate of 0.2 Hz in

order to avoid any dynamic oscillations. Rates slow as these can

still be considered sufﬁcient in some robotic applications where

speed of actuation is not of paramount importance. Examples

can be in soft rehabilitation devices where range of motion is

more important than speed [36]. The averaged measured pres-

sures were used with the analytical and FEM models to calculate

actuator bending angles. In Fig. 10, these results are compared

with the measured angles from the experiments. The ﬁndings

demonstrate that both models capture the overall trend of the

actuators. The discrepancies showed by the analytical model

were potentially a product of linearization of the NH model

at large deformations, radial bulging effects at the base layer,

and expansion of the elastomer. This nonlinear effect was more

apparent in shorter actuators due to the increased pressure, mak-

ing the bulging more profound. Finally, the experimental results

8IEEE TRANSACTIONS ON ROBOTICS

Fig. 9. Soft ﬁber-reinforced bending actuator tip trajectory for bending angle

from 0°to 360°. The experimental results are presented along with the analytical

and FEM model predictions. Images of the FEM modeled and physical actua-

tor at different bending angles are overlaid and superimposed with the graph,

respectively. The 0.0 kPa and maximum pressure locations are also shown for

FEM, experimental, and analytical results.

presented a repeatable nonlinear pattern (s-type curves, Fig. 10).

This was possibly due to gravitational forces that acted on the

actuators (i.e., in all stages of their bending, the center of gravity

of the actuators was changing compared with the path followed

by the actuator distal end).

C. Force Experiments

Soft actuators are capable of exerting forces either at their

tip or at the interaction points along their body as they con-

form around an object. As shown in Fig. 11(a), the top layer

of the actuator was constrained to minimize nonlinear effects

(i.e., the tendency of the actuator to bend when pressurized) and

to concentrate the force at the distal cap. This way, the max-

imum force that could be generated by the actuator at its tip

was measured when the distal cap was brought in contact with

the force/torque sensor. The experimental results obtained from

examining three actuators (two with same radius of 8.0 mm

but different lengths of 160.0 and 130.0 mm to assess the in-

ﬂuence of length on force, and one with 6.0-mm diameter and

160.0-mm length to assess inﬂuence of radius on force) were

compared with the corresponding analytical and FEM models.

The results (see Fig. 11) demonstrated the ability of both models

in predicting force exertion from the tip of the actuator for this

conﬁguration. In particular, the analytical model demonstrated

a maximum force error of 4.3% and the FEM model 10.3%.

In addition, it was shown that the actuator length has small in-

ﬂuence on force generation, whereas changes in radius have a

more signiﬁcant role. In particular, because the κcoefﬁcient of

(21) is a function of the actuator radius (a), a decrease in radius

leads to signiﬁcant loss of ability to deliver high forces.

Fig. 10. Input actuator pressure against bending angle results that were ob-

tained from the analytical model, FEM model and experimental data for a

bending angle ranging from 0°to 360°. (a) Soft ﬁber-reinforced bending actua-

tor length 160.0 mm, (b) 130.0 mm, and (c) 100.0 mm, with radius of 8.0 mm

and wall thickness of 2.0 mm. (d) Soft ﬁber-reinforced bending actuator length

160.0 mm, (e) 130.0 mm, and (f) 100.0 mm, with radius of 6.0 mm and wall

thickness of 2.0 mm.

VI. SOFT FIBER-REINFORCED BENDING ACTUATOR CONTROL

A feedback control loop with an angle ﬁlter, as shown in

Fig. 12, was implemented to demonstrate the ability of the an-

alytical model of (19) to use pressure information to estimate

bending angle in real time. The control loop was built using the

experimental platform of Section IV-A, with a pressure regula-

tor, two pneumatic valves—inlet/outlet (X-valves, Parker Han-

niﬁn Corp., OH, USA)—and a pressure sensor (BSP001, Balluff

Inc., KY, USA). The two valves were connected to the soft ac-

tuator where the inlet was in line with the pressure regulator and

the outlet with the air exhaust. Between the two valves, the air

pressure Paof the actuator was measured. Utilizing (19) and the

measured input air pressure information Pa, the angle ﬁlter of

the feedback loop was able to estimate the actuator bending an-

gle θa. According to the error angle signal θe(i.e., desired angle

signal θdminus the bending angle θaof the actuator), the valve

controller Cvwith a sampling rate of 100 Hz was used to drive

the valves. In particular, positive angle θevalues indicated that

the soft actuator was not bent enough and thus enabled the valve

controller to open the inlet and close the outlet valve, and vice

versa. A deadzone was also introduced at the valve controller

to reduce undesired frequent switching of the valves. The dead-

zone created boundaries around the angle signal θethat allowed

POLYGERINOS et al.: MODELING OF SOFT FIBER-REINFORCED BENDING ACTUATORS 9

Fig. 11. Force responses measured at the distal tip of the actuators using

the analytical model, FEM model, and experimental data (a) while the top

layer of the actuator was constrained. (b) Force responses for an actuator with:

160.0-mm length, 8.0-mm radius, and 2.0-mm wall thickness. (c) Force re-

sponses for an actuator with: 130.0-mm length, 8.0-mm radius, and 2.0-mm

wall thickness. (d) Force responses for an actuator with: 160.0-mm length,

6.0-mm radius, and 2.0-mm wall thickness.

Fig. 12. Feedback control loop scheme with the analytical model embedded

into the angle ﬁlter to calculate actuator bending angle from measured air

pressure.

the state of the valves to remain unchanged until the input was

changed adequately. This was expressed as

θDDZ =±θd

k+θc(22)

where k=50and θc=0.07 rad were parameters empirically

selected to minimize oscillations. A larger θDDZ value made the

valve controller more tolerant to signal noise, but also less agile

to changes of θdand hence reduced its tracking performance,

and vice versa.

The feedback control loop was tested in a step response ex-

periment and a sinusoidal tracking experiment. For both signal

forms, the time delay for the system to track the desired an-

gle signal θdand the unintended switching of the valves were

evaluated. In the step response test, as shown in Fig. 13(a), the

actuator angle was able to follow the reference signal with an

average convergence time of 91 ms and with an undesired valve

switching of 0.85% of the total time. It is noted that the exhaust

of the outlet valve was directly connected to the environment

Fig. 13. Feedback control loop performance. (a) Step response of the actual

signal (θa) and reference signal (θd), the angle error (θe) is shown with the

deadzone. (b) Sinusoidal tracking performance with a reference signal (θd)of

0.2 Hz.

resulting in slower discharging speed (124 ms). In the sinusoidal

experiment of Fig. 13(b), the actuator bending angle was suc-

cessful in tracking a θdangle signal of 0.2 Hz with a tracking

delay of 60 ms and an undesired valve switching of 0.5% of the

total time.

VII. CONCLUSION

Soft ﬂuidic actuators can generate complex 3-D outputs at a

very low mechanical cost with simple control inputs. To date,

the development of such actuators has largely been an empirical

process. In order to enable the robotics research community to

deterministically design new soft robotic systems and provide

information on their performance prior to their manufacture, ac-

curate and experimentally validated quasi-static computational

(FEM) and analytical models were developed for a speciﬁc class

of soft actuators, the soft ﬁber-reinforced bending actuator.

The FEM models provide the ability to simulate the function

of the actuators and highlight local stress/strain concentrations

such as where the ﬁbers interacted with the elastomer. Alter-

natively, the simpliﬁed analytical approach provided a means

of predicting actuator performance with explicit relationships

between input pressure, actuator bending angle, and output

force. The ﬁndings from the modeling work were also eval-

uated through experimental characterizations, which provided a

better understanding of the individual parameters that affect the

10 IEEE TRANSACTIONS ON ROBOTICS

TAB LE I I

COMPARISON BETWEEN DIFFERENT DESIGN PARAMETERS OF THE

SOFT FIBER-REINFORCED BENDING ACTUATOR

Increase in: Required pressure at

360°(i)

Force generated at 0°and

constant pressure (ii)

Radius ↓↑

Length ↓−

Wall Thickness ↑n/a

↑: higher ↓:lower−: insigniﬁcant n/a: not available

(i) Required pressure to reach 360°bending angle. (ii) Force generation at the

proximal cap for a constant pressure at 0°bending angle.

performance of these soft actuators (see qualitative parameter

summary in Table II). Furthermore, a feedback control loop was

created to demonstrate the ease of actuator controllability. In this

case study, the analytical model for bending in free space was

utilized to create an angle ﬁlter and estimate the bending angle

of the soft actuator based only on the supplied air pressure. The

valve controller of the feedback control loop was successful in

tracking step and sinusoidal angle signals.

In the future, the dynamic behavior of the ﬁber-reinforced

bending actuators will be investigated, and the methods for sim-

ulating, fabricating, and controlling other types of soft multima-

terial ﬂuidic actuators will be extended. Variations of the ﬁber

winding pitch and ﬁber orientation will also be investigated to

study the inﬂuence of these parameters on actuator performance,

speciﬁcally, the types of motions that can be achieved with a

single pressure control input.

APPENDIX

This analysis is to compare the bending torques (Ma)of

internal air pressure against the distal cap of each actuator ge-

ometry. The ﬁrst factor to consider is the cross-sectional area.

For the same input pressure, the pressure-generated force on

each actuator tip will be the same if each actuator has the same

cross-sectional area. For this, if the area of each actuator is as-

sumed to be a2, the width and height of the RT shape and the

radii of the HC and FC shape are hence

wRT =va, hRT =a/v, rHC =0.80a, rFT =0.56a

where vis the coefﬁcient determining the height/width ratio of

the rectangular shape.

Next, assuming the wall thicknesses of the actuators are t=

a/4, the bending torques of each actuator shape around the

bottom layer can be calculated as follows.

For RT shape:

The force generated by input pressure on each horizontal line

of the actuator tip with distance αfrom the bottom layer is

fRT =vaPindα. (A1)

Hence, the torque becomes

MRT

a=a

v

0

fRT (α+t)=1+0.5v

2va3Pin (A2)

For HC shape:

The force generated by input pressure on each horizontal line

of the actuator tip with distance αfrom the bottom layer is

fHC =2rHC cos θPindα (A3)

where θ=asin α

rHC ; hence, α=rHCsinθ.

Therefore, the torque becomes

MHC

a=rHC

0

fHC α+a

4=2

3Pinr3

HC +πPinr2

HCa

8.

(A4)

Substituting rHC =0.80a,

MHC

a=2

3Pin (0.8a)3+πPin (0.8a)2a

8=0.59a3Pin.(A5)

For FC shape:

The force generated by input pressure on each horizontal line

of the actuator tip with distance αfrom the bottom layer is

fFC =2rFC sin φPindα (A6)

where φ=acos rFC −α

rFC ; hence, α=rFC(1 −cos φ).

The torque then becomes

MFC

a=2rFC

0

fFC α+a

4

=2rFCPin 2rFC

0

sin φα+a

4dα. (A7)

Solving the above integration and substituting rFT =0.56a

gives

MFC

a=πr2

FC rFC +a

4Pin =0.80a3Pin.(A8)

Equations (A2), (A5), and (A8) are the corresponding bending

torques provided by the RT, HC, and FC shapes by supplied

pressure on their tips, respectively. In particular, the coefﬁcient

vin (A2) is to be determined. In order to compare with the HC

shape, vis chosen to give the RT shape the same Maas the HC

shape with the same input pressure Pin, such that

MRT

a=1+0.5v

2va3Pin =MHC

a=0.59a3Pin.(A9)

Therefore, the value of coefﬁcient vcan be calculated as

v=1.46.(A10)

Hence, the RT shape with v=1.46 has a cross-sectional

width of 1.46aand a height of a/1.46 = 0.68a. Compared with

the corresponding HC shape with a cross-sectional width of

2∗0.8a=1.6aand height of 0.8a, the RT shape is notably

narrower and shorter, while having both the same cross-sectional

area and the same bending torque as the HC shape.

The pressure-induced bending torques in (A2), (A5), and

(A8) alone do not fully describe the actuator characteristics dur-

ing bending. Another important aspect is the internal material

stretch moment occurring with the bending motion as a resis-

tance. To quantify this, a model of the actuator internal stretch is

required. Here, a similar approach is taken in comparison with

POLYGERINOS et al.: MODELING OF SOFT FIBER-REINFORCED BENDING ACTUATORS 11

the modeling procedure presented in this paper, where the hy-

perelastic material behavior is modeled by the NH model, and

only the axial direction principal stretch ratio λ1is considered

(see Section III-B1). Therefore the different geometries of three

actuator shapes could be considered separately, using the same

variable notation as in Fig. 5 of Section III-B2.

For RT shape:

With actuator length L, bending angle θ, and overall actuator

curve radius R(as shown in Fig. 5)

λ=d+R

R=θd

L+1 (A.11)

where dis the distance between the point where λis deﬁned

to the actuator bottom. Therefore, the internal stretch moment

combining the top, bottom, and side actuator walls becomes

MRT

θ=2t+a/v

t+a/v

va ·L·d·μλ−λ−3·dd

+t

0

va ·L·d·μλ−λ−3·dd

+22t+a/v

0

t·μλ−λ−3·L·d·dd. (A12)

For HC shape, the result from (14) can be used (with a=

rHC and b=t):

MHC

θ=t

0

sβ·2(rHC +t)Lβdβ

+2t

0π

2

0

sτ,φ (rHC +τ)2sin φ

+t(rHC +τ)) Ldφ)dτ. (A13)

where sβand sτ,φ are deﬁned as in (15) and (18), respectively.

For FC shape:

The axial principal stretch λis

λ=t+R+rFC −(rFC +c)cosφ

R

=t+rFC −(rFC +c)cosφ

Lθ+1 (A14)

where cis the radial distance between the point where λis

deﬁned to the actuator inner surface. Therefore, the internal

stretch moment of the actuator wall becomes

MFC

θ=2

π

0

μλ−λ−3t

0

((rFC +t)(rFC +c)

−(rFC +c)2cos φLdφdc. (A15)

Numerically solving the integrals in (A12), (A13), and (A15),

the internal stretch moments could be obtained for all three

actuator shapes. Consequently, the bending resistance, as shown

in Fig. 4(b), is deﬁned as the ratio of the internal stretch moment

over the supplied bending torque:

Bending Resistance = Mθ

Ma

.(A16)

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fabrication

Panagiotis Polygerinos (M’11) received the B.Eng.

degree in mechanical engineering from Technologi-

cal Educational Institute of Crete, Heraklion, Greece,

in 2006, and the M.Sc. (with distinction) degree in

mechatronics and the Ph.D. degree in mechanical en-

gineering/medical robotics from King’s College Lon-

don, London, U.K., in 2007 and 2011, respectively.

He is a Technology Development Fellow with

Wyss Institute and the School of Engineering and

Applied Sciences, Harvard University, Cambridge,

MA, USA, where he specializes in soft robotic sys-

tems that ﬁnd application in wearables, medical, and rehabilitation areas.

Zheng Wang (M’10) received the B.Sc. degree (with

merit) from Tsinghua University, Beijing, China; the

M.Sc. degree (with distinction) from Imperial Col-

lege London, London, U.K.; and the Ph.D. degree

(with merit) from Technische Universit¨

at M¨

unchen,

M¨

unchen, Germany.

He was a Postdoctoral Research Fellow with

Nanyang Technological University, Singapore, be-

tween 2010 and 2013 and a Postdoctoral Fellow with

the School of Engineering and Applied Sciences and

Wyss Institute of Bioinspired Engineering, Harvard

University, between 2013 and 2014. Since July 2014, he has been an Assistant

Professor with the Department of Mechanical Engineering, University of Hong

Kong, Hong Kong. His research interest include haptics human–robot interac-

tion, teleoperation, cable-driven mechanisms, and soft robotics.

Johannes T. B. Overvelde received the B.Sc. and

M.Sc. degrees (both with distinction) in mechani-

cal engineering from Delft University of Technol-

ogy, Delft, The Netherlands, in 2012. He is currently

working toward the Ph.D. degree in applied mathe-

matics with Katia Bertoldi’s Group, School of En-

gineering and Applied Sciences, Harvard University,

Cambridge, MA, USA.

His research interests include the ﬁeld of structural

optimization and computational mechanics.

Kevin C. Galloway received the B.S.E. and Ph.D.

degrees in mechanical engineering from University

of Pennsylvania, Philadelphia, PA, USA.

He is a Research Engineer with the Advanced

Technology Team, Wyss Institute, Harvard Univer-

sity, Cambridge, MA, USA. His research interests

are in applying knowledge of materials and prototyp-

ing techniques toward the development of bioinspired

robots and medical devices.

Robert J. Wood received the Master’s and Ph.D.

degrees in electrical engineering from University of

California, Berkeley, CA, USA, in 2001 and 2004,

respectively.

He is an Associate Professor with the School of

Engineering and Applied Sciences and the Wyss In-

stitute for Biologically Inspired Engineering, Harvard

University, Cambridge, MA, USA. His research in-

terests include the areas of microrobotics and bioin-

spired robotics.

Katia Bertoldi received the Master’s degrees from

University of Trento, Trento, Italy, in 2002, and from

Chalmers University of Technology, G¨

oteborg, Swe-

den, in 2003, majoring in structural engineering me-

chanics, and the Ph.D. degree in mechanics of materi-

als and structures from University of Trento in 2006.

She then joined the group of Mary Boyce, Mas-

sachusetts Institute of Technology, Cambridge, MA,

USA, as a Postdoctoral Researcher. In 2008, she

moved to University of Twente, Twente, The Nether-

lands, where she was an Assistant Professor with the

faculty of Engineering Technology. In January 2010, she joined the School of

Engineering and Applied Sciences, Harvard University, Cambridge, as an As-

sociate Professor of applied mechanics and established a group studying the

mechanics of materials and structures.

Conor J. Walsh (M’12) received the B.A.I. and B.A.

degrees in mechanical and manufacturing engineer-

ing from Trinity College Dublin, Dublin, Ireland, in

2003, and the M.S. and Ph.D. degrees in mechanical

engineering from Massachusetts Institute of Tech-

nology, Cambridge, MA, USA, in 2006 and 2010, re-

spectively, with a minor in entrepreneurship through

the Sloan School of Management and also a Certiﬁ-

cate in Medical Science through the Harvard–MIT

Division of Health Sciences and Technology.

He is an Assistant Professor with the Harvard

School of Engineering and Applied Sciences and a Core Faculty Member with

Wyss Institute for Biologically Inspired Engineering, Harvard University, Cam-

bridge. He is the Founder of the Harvard Biodesign Laboratory, which brings

together researchers from the engineering, industrial design, apparel, clinical,

and business communities to develop new technologies and translate them to

industrial partners. His research focuses on new approaches to the design, man-

ufacture, and control of soft wearable robotic devices for augmenting and restor-

ing human performance, and evaluating them through biomechanical and phys-

iological studies.

Project

Leveraging printed-circuit-inspired manufacturing processes and origami to develop high-quality, multi-modal sensors for biomedical applications.

Conference Paper

Established design and fabrication guidelines exist for achieving a variety of motions with soft actuators such as bending, contraction, extension, and twisting. These guidelines typically involve multi-step molding of composite materials (elastomers, paper, fiber, etc.) along with specially designed geometry. In this paper we present the design and fabrication of a robust, fiber-reinforced... [Show full abstract]

Article

Soft bending actuators are inherently compliant, compact, and lightweight. They are preferable candidates over rigid actuators for robotic applications ranging from physical human interaction to delicate object manipulation. However, characterizing and predicting their behaviors are challenging due to the material nonlinearities and the complex motions they can produce. This paper investigates... [Show full abstract]

Article

Soft robots actuated by inflation of a pneumatic network (a “pneu-net”) of small channels in elastomeric materials are appealing for producing sophisticated motions with simple controls. Although current designs of pneu-nets achieve motion with large amplitudes, they do so relatively slowly (over seconds). This paper describes a new design for pneu-nets that reduces the amount of gas needed... [Show full abstract]

Article

Soft robotics is a fast-emerging interdisciplinary field combining mechatronics, control, material science and biomimetics. With their unique inherent compliance feature, soft robots have advantages over rigid-bodied robots for operations in unstructured environments. On the other hand, most soft robots reported to date are laboratory prototypes rather than end products. To fill this gap, they... [Show full abstract]