Directional Adhesive Structures for Controlled Climbing on Smooth Vertical Surfaces

Abstract

Recent biological research suggests that reliable, agile climbing on smooth vertical surfaces requires controllable adhesion. In nature, geckos control adhesion by properly loading the compliant adhesive structures on their toes. These strongly anisotropic dry adhesive structures produce large frictional and adhesive forces when subjected to certain force/motion trajectories. Smooth detachment is obtained by simply reversing these trajectories. Each toe's hierarchical structure facilitates intimate conformation to the climbing surface resulting in a balanced stress distribution across the entire adhesive area. By controlling the internal forces among feet, the gecko can achieve the loading conditions necessary to generate the desired amount of adhesion. The same principles have been applied to the design and manufacture of feet for a climbing robot. The manufacturing process of these directional polymer stalks is detailed along with test results comparing them to conventional adhesives

Full text

Directional AdhesiveStructures for Controlled Climbing
on Smooth Vertical Surfaces
Daniel Santos, Sangbae Kim, MatthewSpenko, Aaron Parness, Mark Cutkosky
Center for Design Research
Stanford University
Stanford, CA 94305-2232, USA
contact: dsantos@stanford.edu
Abstract—Recent biological research suggests that reliable,
agile climbing on smooth vertical surfaces requirescontrol-
lable adhesion. In nature, geckos control adhesion by prop-
erly loading the compliant adhesivestructures ontheir toes.
These strongly anisotropic dry adhesivestructures produce
large frictional and adhesiveforces when subjected to certain
force/motion trajectories. Smooth detachmentis obtained by
simply reversing these trajectories. Each toe’shierarchical
structurefacilitates intimate conformation to the climbing
surface resulting in abalanced stress distribution across the
entireadhesivearea. By controlling the internal forces among
feet, the gecko can achievethe loading conditions necessary to
generate the desired amount of adhesion. The same principles
havebeen applied to the design and manufactureof feet fora
climbing robot. The manufacturing process of these Directional
Polymer Stalks is detailed along with test results comparing
them to conventional adhesives.
I.INTROD UCTIO N
As mobile robots extend their range of traversable terrain,
interest in mobility on vertical surfaces has increased. Pre-
vious methods of climbing include using suction [18], [19],
magnets [5], [29], and avortex[28] to adhere to avariety
of smooth, flat, vertical surfaces. Although these solutions
havehad some success on non-smooth surfaces, in general,
the variety of climbable surfaces is limited. Taking cues
from climbing insects, researchers havedesigned robots that
employlarge numbers of small (∼10µmtip radius) spines
that cling to surface asperities [1], [22]. This approach works
well for surfaces such as concrete or brick but cannot be used
for smooth surfaces likeglass.
Recently,robots havebeen demonstrated that use adhe-
sives for climbing. Early approaches used pressure-sensitive
adhesives (PSAs) to climb smooth surfaces [9], [26], while
more recent approaches used elastomeric pads [8], [27].
PSAs tend to foul quickly,which prevents repeated use,
and also require relatively high energy for attachment and
detachment. Elastomer pads are less prone to fouling, but
generate lower levels of adhesion.
In an effort to create an adhesivethat does not foul over
time, there has been research on “dry” or “self-cleaning”
adhesives that utilize stiffmaterials in combination with
microstructured geometries to conform to surfaces. Fig. I
shows arange ofadhesivesolutions ordered in terms of
feature size and effectivemodulus. Amaterial is considered
tackywhen the effectivemodulus is less than 100kPa[2],
Urethane
(bulk)
Fat PMMA Rubber Epoxy
Carbon
nanotubes
102105107109
Young’s Modulus (Pa)
β−keratin gecko
setal array
1012
1mm 100um 1um 10nm
10um
tacky nontacky
100um
Shape sensitivity LowHigh
DPS
(Directional
polymer stalks) β−keratin
(bulk)
Feature Size
PSA
Fig. 1. Shape sensitivity of different structures and modulus of elasticity of
various materials. Microstructured geometries can lower the overall stiffness
of bulk materials so that theybecome tacky.This principle allows geckos
to use β-keratin for their adhesivestructures.
[7]. Since adhesion is primarily aresult of van der Waals
forces, which decrease as 1/d3where dis the distance
between the materials, it is crucial to conform to the surface
over all relevant length scales.
Dry adhesives, such as the geckohierarchyof microstruc-
tures consisting of lamellae, setae, and spatulae, conform to
the surface despite having bulk material stiffnesses that are
relatively high (approximately 2GPafor β-keratin) [2]. The
hierarchical geometry lowers the effectivestiffness to make
the system function like a tackymaterial.
Synthetic dry adhesives havebeen under development
for several years. Examples include arrays of vertically
oriented multiwall carbon nanotubes [31], [32] and polymer
fibers [11], [15], [20], [25]. These adhesives employstiff,
hydrophobic materials and therefore havethe potential tobe
self-cleaning. In anumber of cases, useful levels of adhesion
havebeen obtained, but only with careful surface preparation
and high preloads. As the performance of these synthetic
arrays improves, their effectivestiffnesses could approach
the 100kPa“tack criterion”.
Adifferent approach usesstructured arrays of moderately
soft elastomeric materials with abulk stiffness less than
2007 IEEE International Conference on
Robotics and Automation
Roma, Italy, 10-14 April 2007
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3MPa.Because these materials are softer to begin with,
theyconform to surfaces using feature sizes on the order of
100µm.One example is amicrostructured elastomeric tape
[8], [21]. Because the material is notvery stiff, it attracts dirt.
However,in contrast to PSAs, it can be cleaned and reused.
The microstructured adhesivepatches described in Section
III, termed Directional Polymer Stalks (DPS), also employ
an elastomer but are designed to exhibit adhesiononly when
loaded in aparticular direction.
In addition to stiffness, feature size and shape of the struc-
ture is important in creating adhesion. Asdiscussed in [10],
[11], [16], [30], the available adhesiveforce is afunction
of the shape and loading of the micro-structured elements.
The importance of optimizing tip shape increases as feature
size increases. For extremely small elements such as carbon
nanotubes, the distal geometry is relatively unimportant,
but for larger features (O(100µm))tip geometry drastically
affects adhesion. At these sizes, the optimal tip geometry,
where stress is uniformly distributed along the contact area,
has atheoretical pulloffforce of more than 50-100 times [10]
that of apoor tip geometry.In Section III we describe the
processes wehavedeveloped to obtain desired shapes at the
smallest sizes our current manufacturing procedures allow,
and in Section IV we present experimental results obtained
with these shapes.
II.ANISOTROPICVERSUSISOTROPICAD HESIO N
At present, no synthetic solution has replicated the adhe-
sion properties of geckofeet. However the main obstacle
to robust climbing is not moreadhesion but controllable
adhesion. Stickytape is sufficiently adhesivefor alight-
weight climbing robot, but its adhesiveforces are difficult
to control. Geckos control theiradhesion with anisotropic
microstructures, consisting of arrays of setal stalks with spat-
ular tips. Instead of applying high normal preloads, geckos
increase theirmaximum adhesion by increasing tangential
force, pulling from the distal toward the proximal ends of
their toes [3]. In conjunction with their hierarchical struc-
tures, this provides geckos with acoefficient of adhesion,
µ′=Fa/Fp,between 8and 16 [2] depending on conditions,
where Fais the maximum normal pulloffforce and Fpis
the maximum normal preload force.
A. Description of Contact Models
The frictional-adhesionmodel (Fig. 2) is used to describe
the geckoadhesion system [3]. When pulling along the adhe-
sivedirection (B, positivetangential), the maximum adhesive
force is directly proportional to the applied tangential force:
−FN≤FTtan α∗(1)
where FNis the normal force, FTis the tangential force
(positivewhen pulling from distal to proximal), and α∗is the
angle of abest fit line for test data obtained with individual
setae, setal arrays, and geckotoes [3]. When pulling against
the adhesivedirection (A), the behavior is described by
Coulomb friction. An upper limit is placed on the maximum
−100 0 100 200 300
−200
−150
−100
−50
0
50
100
150
Tangential Force (%Body Weight)
Normal Force (%Body Weight)
Frictional−Adhesion
JKR
A
B
C
Fig. 2. Comparison of frictional-adhesion and JKR contact models. Both
models havebeen scaled to allowa50g geckoor robot to cling to an
inverted surface. Parameters and overlayed data for the anisotropic frictional-
adhesion model are from [3] for geckosetae, setal arrays, and toes. The
isotropic JKR model is based on parameters in [21], [23].
tangential force in the adhesivedirection (C), which is a
function of limb and materialstrength.
Fig. 2also compares frictional-adhesion and the Johnson-
Kendall-Roberts (JKR) model [12], [13], an isotropic adhe-
sion model based on spherical elastic asperities in contact
with aflat substrate. This model predicts that maximum
adhesion occurs at zero tangential force. Increasing tangential
force decreases the contact area, thereby decreasing the
overall adhesion. For positivevalues of normal force FT∝
FN
2/3[24]. The models havebeen scaled to givecomparable
values of adhesion and tangential force limits, and the curves
represent the maximum normal and tangential force at which
acontact will fail.
The anisotropic model shows howmaximum adhesion can
be controlled simply by modulating the tangential force at the
contact. Its intersection with the origin allows for contact ter-
mination with negligible forces, whereas the isotropic model,
which does not intersect the origin, predicts large force
discontinuities at contact termination. This feature makes the
anisotropic model better-suited for vertical climbing than the
isotropic model. If the anisotropyis aligned properly,then
gravity passively loads the contact to increase adhesion.
B. Implications for control ofcontact forces
In general, both anisotropic and isotropic adhesives may
provide adhesion comparable to the body weight of agecko
or arobot; however,the models lead to different approaches
for controlling contact forces during climbing. Asimplified
planar model of aclimbing geckoor robot (Fig. 3) is used
for studying the implications of different contact models.
Work in dexterous manipulation [14] is adapted to study the
static stability of the model on inclined surfaces. There are
four unknowns and three equilibrium constraints, leaving one
degree of freedom: the balance of tangential force between
the front (FT1)and rear (FT2)foot (i.e. the internal force),
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q
y
z
FT2 FN2
FT1 FN1
mg
Fig. 3. 2-Dimensional model of ageckowith twofeet in contact with aflat
inclined plane. Foot-substrate interactions are modeled as point contacts.
Anisotropic Adhesive
Isotropic Adhesive
Fig. 4. Schematic of optimal tangential forces for isotropic and anisotropic
adhesion at different inclinations. Arrowdirections and magnitudes shown
in proportion to optimal tangential forces (dot represents zero tangential
force).
FInt =FT1−FT2.The maximum tangential force for each
foot is limited by the contact model.
The stability of the system can be used to determine
howbest to distribute contact forces between thefeet. The
stability margin is the minimum distance, in force-space, over
all feet, that anyfoot is from violating the contact constraints.
It defines the maximum perturbation force that the system
can withstand without failure of anyfoot contacts.
Let Fi=[FTi,FNi]be the contact force at the ith foot.
The contact model can be defined by aparametric convex
curveR(x, y),with points F=[FT,FN]lying inside the
curvebeing stable contacts. The distance any particular foot
is from violating acontact constraint is then:
di=min
x,y (||Fi−R(x, y)||).(2)
For amodel with two feet in contact with the surface, the
overall stability margin becomes d=min(d1,d2),where d1
represents the front foot and d2represents the rear foot.
The 2-D model’sextra degree of freedom canbe used to
maximize the stability margin. This produces different force
control strategies using the anisotropic or isotropic models at
different surface inclines (Fig. 4). On avertical surface the
front foot must generate adhesion. The anisotropic model
predicts the front foot should bear more of the gravity load,
since increasing tangential force increases available adhesion.
The isotropic model predicts the opposite, namely that the
rear foot should bear more of the gravity load, because
tangential forces on the front foot decrease its available
adhesion. On an inverted surface, the isotropic model predicts
zero tangential forces for maximum stability since gravity
is pulling along the normal. Alternatively,the anisotropic
model cannot generate adhesion without tangential forces
and this model must rotate the rear foot and pull inward to
Fig. 5. Stickybot experimental climbing robot for testing directional
adhesives. Each limb has twotrajectory degrees of freedom (fore-aft and
in-out of the wall) and one toe-peeling degree of freedom. The entire robot
weighs 370 grams.
generate tangential forces that will produce enough adhesion
for stability.Interestingly,the anisotropic model predicts that
reversing the rear foot and pulling inward is also optimal on
level ground, which would increase the maximum pertur-
bation force that could be withstood. Thepredictions of the
anisotropic model qualitatively match observations of geckos
running on walls and ceilings and reorienting their feet as
theyclimb in different directions [4].
III.DESIGN A ND MA NU FACTURING O FAN ISOTROPIC
AD HESIVEPAD S
The utility of anisotropic adhesion has been demonstrated
on anewexperimental robot, Stickybot (Fig. 5). Details of
Stickybot design and control are covered in acompanion
paper [17]. In this section we explain the DPS manufacturing
process, and in the nextsection we present test results
comparing the DPS to isotropic stalks of equivalent size and
density.
The anisotropic stalks used on the bottom of Stickybot’s
feet are fabricated from apolyurethane (InnovativePolymers,
IE-20 AH Polyurethane, Shore-20A hardness, E≈300kPa).
Custom miniature tooling was used to create amold from
which the DPS were fabricated (Fig. 6). After aprocess
of trial and error,ageometry was found that produced
reasonable results for climbing. The stalks are cylindrical and
tilted with respect to the backing. The upper stalk is cropped
at an oblique angle thatcreates asharp tip. The cylinders
are 380µmin diameter and approximately 1.0mm long from
base to tip. Cylinder axes are inclined 20◦and slanted tips
are inclined 45◦,bothwith respect to the vertical. The shape
of the stalks is defined by the intersections of slanted circular
holes with narrow Vee-shaped grooves.First, the grooves are
cut into the mold using acustom 45◦degree slitting saw.This
angle dictates the angleof the tip. Slanted circular holes are
then drilled into the grooves such that the opening resides
entirely on the 45◦face.
Asilicone (TAP Plastics, Silicone RTV Fast Cure Mold-
Making Compound) form-fitting capis molded from the
Vee grooves before holes are created. Liquid polymer is
poured into the mold and capillary action fills the holes. The
form-fitting cap is pressed down into the grooves, forcing
excess polymer out the sides (Fig. 6). An SEMphoto of
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Filling liquid
Polymer
Assembly
with top mold
Normal
Releasing
Lateral
Tangential
Fig. 6. Molding process used to fabricate anisotropic patches. Mold is
manufactured out of hard wax and then filled with liquid urethane polymer.
Acap eliminates contact with air and creates final tip geometry.
Unloaded
Loaded
45r
rr
r20r
rr
r
380um
Fig. 7. 380µmφanisotropic stalks oriented at 20◦with stalk faces oriented
at 45◦,both with respect to normal.
the stalks created using this process isshown in Fig. 7. The
process yields asharp, thin tip (10 −30µmthickness). When
the stalksfirst contact asurface, this tip adheres and the
tangential force required to engage the remaining area of the
DPS face is very low.Fig. 7shows the geometry of the stalks
in both the unloaded and loaded states.
IV.ADH ESION TESTSA ND RESULTS
Specimens of the anisotropic material were tested under
avariety of tangential and normal loading conditions to
characterize their adhesiveproperties. For comparison, an
array of isotropic cylinders (vertical cylinders of the same
diameter with flat tops) made from the same polymer was
also tested.
Both the anisotropic and isotropic patches were approxi-
mately elliptical in shape with atotal area of 3.5−4cm2,
corresponding to one toe of Stickybot. The anisotropic
specimens contained ∼500 individual stalks while isotropic
specimens contained ∼250 stalks. Specimens were prepared
by washing with soap and water and then blowing dry with
compressed air.Theywere mounted using thin double-sided
tape to aflat aluminum backing.
The specimens and aluminum backing were fixed on a
two-axis linear positioning stage (VelmexMAXY4009W2-
S4) driven under servocontrol at 1kHz.Specimens were
brought into contact with astationary glass plate affixed to a
0 45 90 135 180
−1
0
1
2
3
4
Pulloff Angle (degrees)
Pulloff Force (mN/stalk)
Isotropic
Anisotropic
Fig. 8. Adhesion forces as afunction of pulloffangle for anisotropic
(700µmpreload) and isotropic (150µmpreload) patches. For anisotropic
patches, adhesion is maximum at shallowpulloffangles in the adhesive
direction and drops steadily as the angle becomes normal to the surface,
becoming negligible at shallowangles in the non-adhesivedirection.
6-axis force/torque sensor (ATI Gamma Transducer). The po-
sitioning stage is astiff, screwdriven device with atrajectory
accuracyof approximately ±20µmwhile in motion at speeds
of 1mm/s.The sensor resolution is approximately 25mN
and 0.5mNm for forces and torques, respectively.Force and
torque data were sampled at 1kHz and filtered at 10Hz using
a3rd −orderButterworth filter.
Following aprocedure used to measure geckosetal array
adhesion forces [3], synthetic patches were moved along a
controlled trajectory in the normal and tangential directions
while measuring resulting forces. Specimens were brought
into contact with the glass substrate and preloaded to a
specified depthin the normal axis. The approach angle for the
anisotropic patches was 45◦,moving with the stalk angle (i.e.
loading the stalks in the preferred direction for adhesion), and
for the isotropic patch was 90◦,along the normal direction.
The patches were then pulled away from the glass substrate at
departure angles between 15◦(mostly parallel to the surface,
with the angle of the anisotropic stalks) and 165◦(mostly
parallel to the surface, against the angle of the anisotropic
stalks). Velocity was maintained at 1mm/s,which provided
afavorable tradeoffbetween avoiding dynamic forces and
minimizing viscoelastic effects.
Fig. 8illustrates the performance of the stalks as afunction
of pulloffangle. The anisotropic patches produce maximum
adhesion when loaded in the positivetangential direction, as
arobot would load them when clinging to avertical wall.
At angles less than 30◦,the maximum adhesion force is
approximately 2.3mN/stalk (1.2N for the entire patch), and
the corresponding value of µ′was approximately 4.5. Pulling
offin the normal direction generates adhesion of about 2/3
the peak value, and whenpulling offagainst the angle of
the stalks the adhesion drops to less than 10% the peak
value. The work required to load an unload and adhesive
material (Work of Adhesion) has also been used as ameasure
of adhesion performance [6]. At apreload of 700µm,the
maximum work loop is approximately 5.2J/m2at a15◦
pulloffangle and the minimum work loop is 0.3J/m2at
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˞
*
-4-2 0 2 4
-3
-2
-1
0
1
2
Isotropic
Tangential Force (mN/stalk)
Normal Force (mN/stalk)
100µm preload depth
150µm preload depth
300µm preload depth
-2 0 2 4 6
-3
-2
-1
0
1
2
Anisotropic
Tangential Force (mN/stalk)
500µm preload depth
600µm preload depth
700µm preload depth
Fig. 9. Experimental limit curves for isotropic and anisotropic patches at different preload depths. Data points correspond to maximum forces at pulloff.
Three series havebeen plotted to showthe dependence of limit curves on the preload.
a120◦pulloffangle. For the isotropic patch, maximum
adhesion is obtained when pulling offin the purely normal
direction, dropping to zero for pulloffangles slightly over
45◦with respect to the normal. The isotropic patch has a
maximum adhesiveforce nearly as high as the anisotropic
patches, but requires ahigher preload force, resulting in aµ′
of approximately 0.5.
The anisotropic patches were also tested on machined
granite todetermine howsurface roughness affects adhesion.
The surface roughness (Ra)of glass is typically less than
10nm and the surface roughness of the graniteis about
10µm.At apreload depth of 700µm,maximum adhesion
force on polished graniteis 1.0mN/stalk (0.5N for the
entire patch) resulting in an approximately 60% decrease in
adhesion force compared to glass.
Fig. 9summarizes the results for the maximum tangential
and normal forces of the different patches over arange
of preload depths and pulloffangles. The results can be
compared directly with the models in Fig. 2. As expected, the
isotropic specimen shows abehavior similar to that predicted
by the JKR model: The limit curveis symmetric about the
vertical axis. Maximum adhesion is obtained when pulling
in the purely normal direction. Under positivenormal forces
Coulomb friction is observed.
The anisotropic patches behavesimilarly to geckosetae.
Fitting aline to the data for positivevalues of tangential
force results in an α∗≈35◦(compared to approximately
30◦for the gecko[3]). When loaded against their preferred
direction (FT<0)theyexhibit amoderate coefficient of
friction; between these two modes, the data intersects the
origin. Thus, likethe geckosetae, the synthetic patches can
easily be detached by controlling internal forces toreduce
the tangential force at the contact. However,unlikethe gecko
setae, the synthetic stalks start to lose adhesion at high levels
of tangential force, at which point the contact faces of the
stalks start to slip.
Fig. 9also shows that forces for isotropic and anisotropic
patches scale with increasing preload. For the isotropic
patches, maximum adhesion is obtained when the specimen
00.5 11.5 22.5 33.5 4
-1.5
-1
-0.5
0
Typical Isotropic Force Profile
Normal Force (N)
00.5 11.5 22.5 33.5 4
-1
-0.5
0
Typical Anisotropic Force Profile
Time (s)
Normal Force (N)
A
BC
D
A
BCD
Fig. 10. Comparison of normal force profiles of anisotropic and isotropic
patches on aclimbing robot. Point Aon the curves refers to the preloading
phase of the cycle. Point Bhighlights when the foot is in the adhesive
regime during astroke. Points Cand Dare when the foot is unloaded and
detached, causing large normal forces in the case of the isotropic patch.
is preloaded to ∼300µmafter initial contact, resulting in
anormal preload of ∼14.3mN/stalk.For the anisotropic
patches, a700µmpreload depth provided maximum adhe-
sion, which corresponds to apreload of ∼0.5mN/stalk.
Larger preloads resulted in no further significant increase
in adhesion; smaller preloadsproduced less adhesion.
Given the foregoing results, anisotropic and isotropic
specimens can be expected to produce rather different effects
when used on arobot. Fig. 10 showstypical force plots for
anisotropic and isotropic toepatches on the Stickybot robot.
The data for three successive cycles are plotted to show
overall variability.In each case, the robot cycled asingle
legthrough an attach/load/detach cycle on the same 6-axis
force sensor in the previous tests nowmounted into avertical
wall. The other three limbs remained attached to the wall
throughout the experiment. In this test, the isotropic patches
consisted of vertical cylinders with athin upper membrane
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bridging the gaps between the cylinders, which increased
the contact area. In each case, legtrajectories were tuned
empirically to provide best results for either the isotropic or
anisotropic patches.
As the plots show,the isotropic patches required alarger
normal force (A) to produce comparable amounts of com-
bined tangential force and adhesion for climbing (B). The
unloading step for the anisotropic patches (C, D) is accom-
plished rapidly and results in negligible detachment force as
the legis removed. In contrast, the isotropic patch requires a
longer peeling phase (C) and produces alarge pulloffforce
(D) as the legis withdrawn. This large detachment force was
the main limitation of the isotropic patches, producing large
disturbances that frequently caused the other feet to slip.
V.CON CLUSION SAN D FUTUREWORK
This paper describes the design and manufacture of novel
adhesives and presents experimental evidence that empha-
sizes theimportance of controllable, directional adhesion for
aclimbing robot. Amodel of geckoadhesion is presented
and compared to acommonly used isotropic model from the
literature, the JKR model. It is shown that the anisotropic
nature ofthe frictional-adhesion model, combined with the
fact that at zero tangential force there is zero adhesive
force, allows arobot to smoothly load and unload afoot.
Current work entails scaling down the size of the anisotropic
stalks in order to utilize harder materialsand climb rougher
surfaces. This will allowfor feet that are easier to clean,
yet still conform and adhere well to surfaces. Future work
includes using analytical or numerical methods to understand
howthe patch geometry will affect adhesion performance
on different surfaces and extending our understanding of
anisotropic adhesion to 3D. This may better predict and
explain the behavior of geckos and guide the design and
control of climbing robots.
ACKN OWLE DG MENT
Wethank Kellar Autumn and hisstudents for discussions
on anisotropic adhesion and testing procedure. This work
was supported through the DARPABioDynotics Program,
the Intelligence Community Postdoctoral FellowProgram,
and the Stanford-NIH Biotechnology Training Grant.
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