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Exploiting the Morphology of a Shape Memory Spring as the Active Backbone of a Highly Dexterous Tendril Robot (ATBR)

Authors:
Exploiting the Morphology of a Shape Memory Spring as the Active
Backbone of a Highly Dexterous Tendril Robot (ATBR)
Kayode Sonaike* and S.M.Hadi Sadati*, Christos Bergeles, Ian D. Walker
Abstract Tendrils are common stable structures in nature
and are used for sensing, actuation, and geometrical stiffness
modulation. In this paper, for the first time we exploit the helical
geometry of a shape memory alloy (SMA) tendril as a simple to
fabricate highly dexterous robotic continuum tentacle that we
called Active Tendril-Backbone Robot (ATBR). This is achieved
via partial (120 deg) activation of single helix turns resulting
in backbone directional bendings. A 141.5 mm prototype (130
mm when fully compressed) has been fabricated and a simple
theoretical framework is proposed and experimentally validated
for modeling of the tentacle configuration. The manipulator has
five 2-DOF joints capable of reaching bending angles of up to
54.5 deg and angular speed of up to 6.8 deg/s. The dexterity of
the manipulator is showcased empirically in reaching complex
configurations and simple navigation through confined space of
a curving path.
Keywords- Tendril, Continuum manipulator, Dexterous robot,
Shape Memory Alloy, Morphological contribution.
I. INTRODUCTION
Performing complicated tasks such as manipulation in
unpredictable conditions where safe interaction with the en-
vironment is important requires dexterity and compliance. In
such tasks, low actuation energy, high dexterity, reachability,
maneuverability, back drivability and self-adjustability of
continuum mechanisms are shown to be advantageous. Con-
tinuum manipulators are novel robotic archetypes, presenting
a single continuous backbone structure with a compliant
backbone. Interest in these single form robotic manipulators
began as early as the 1960’s [1], in which Anderson and
Horn’s Tensor arm was developed for underwater explo-
ration. Since then, numerous contributions towards contin-
uum manipulator research have been made, facilitated by the
development of soft actuators. The actuation mechanism of
this class of manipulators has been always at the center of
scientific debate. Some of the recent designs are inflatable
tendon driven backbones [2], braided extensile pneumatic
actuators [3], braided hydraulic actuators [4], braided pneu-
matic actuators in a silicon body shell [5], shrinkable design
with antagonistic tendon and pneumatic actuation [6], long
tendon driven tendril [7], bioinspired SMA actuators [8],
and origami structure backbones [9]. The tendon driven
and pneumatically or hydraulically actuated designs suffer
from routing complexities, bulky external power supply and
control units, and limitations in designing highly dexterous
This research was supported by an ERC Starting Grant [714562]. K
Sonaike is with the University of Bristol, Bristol, UK. S.M.H. Sadati and C.
Bergeles are with the Robotics and Vision in Medicine (RViM) Lab, School
of Biomedical Engineering & Imaging Sciences, King’s College London,
London, UK. Ian D. Walker is with the Department of Electrical and Com-
puter Engineering, Clemson University, Clemson, USA. Correspondence:
smh sadati@kcl.ac.uk. *Equal contributions.
a) b) c) d)
e) f)
Fig. 1: Complex shapes resulted from actuating (local heating)
different joints along an ATBR.
systems. Smart materials, artificial muscles, and shape mem-
ory structures on the other hand are usually hard to fabricate.
Recently, a new field of research, so-called ”embodied
intelligence”, ”morphological contribution” or ”morphologi-
cal computation”, has emerged wherein the physical body
morphology is exploited to simplify the perception and
control tasks [10]. In this context, the tendril is one of the
most studied structures in biology and zoology [11] for their
interesting morphological properties such as geometrical
compliance. Bioinspired tendril morphologies are utilized as
robot backbone [7], actuator [8], stiffness controllable inter-
faces [12], [13], [14], and fiber optics based bending sensors
[15], [16] for continuum robots. SMA tendrils (sometimes
known as artificial muscles) are used as single actuation
units[8], [17].
In this paper, for the first time, we utilize the partial
actuation of a single SMA tendril to achieve multiple local
directional bending (Fig. 1). The SMA helix is considered
both as the manipulator backbone and actuator and named
Active Tendril-Backbone Robot (ATBR). Despite the afore-
mentioned means of actuation, an ATBR actuation principle
and fabrication are simple, affordable, and compact. The
actuation process is as simple as connecting a flexible electric
wires to the activation site (120 deg portion of a single helix
turn covered with heat shrink) and one to the tendril base.
The SMA shape change is achieved through local heating
of the covered area by the heat shrink, that we suspect
is due to high current local sparks at the wire connection
points, while the rest of the tendril remains intact due to
insufficient Joule heating effect (increasing temperature of
𝑝c𝑝h<𝑝c
Rear view- Straight
Rear view- Actuated
Side view- Actuated
Actuated
region
(heated)
a) b)
G
V
V
V
Fig. 2: Working principle of a single full turn of a SMA tendril
as an independent 3-DOF joint. The SMA tendril is compressed
when heated. a) Rear and side view of the tendril when one third
(120 deg) of a full turn is activated (heated- in red). A twist along
this section results a reduction in the helix pitch on the opposite
side and hence bending the backbone in the opposite direction. b)
Wiring diagram for different activation scenarios. V- power supply
connection through a relay board and PWM current controller, G-
permanent ground connection red- active (heated) section, blue-
inactive (cold) section.
a metal through passing electrical current). As a result, the
backbone bends due to local change of the tendril pitch. Each
single turn of the tendril can be turned into an independent
3-DOF joint (two side bendings and axial shrinkage) along
the continuum arm forming a highly dexterous continuum
arm. As the proof of concept, a continuum arm is fabricated
with five sets of triple-wires along the tendril. A simple
theoretical framework based on identification of the SMA
tendril properties and Constant Curvature (CC) assumption
is proposed for modeling of the manipulator.
In the rest of this paper, first the the manipulator working
principle and design are discussed in section II. A simple
modeling framework is discussed in section III. Experimental
study and simulation validations are presented in section IV
followed by a short discussion on our future plans. Finally
conclusions are presented in section VI.
II. MAN IPU LATOR WORKING PRINCIPLE & DESIGN
A one-way SMA tendril was used as both the backbone
structure and actuator for the continuum manipulator. The
tendril had 0.9 mm wire diameter, 5.4 mm coil mean diame-
ter and 80 mm length when fully collapsed. The tendril was
extended to 141.5 mm, in which the tendril pitch (p=l/n-
tendril length lto number of turns nratio) is 6.741 mm and
coil mean diameter was reduced to 4.69 mm, and undergone
shrinkage when heated. Fig. 2 shows the ATBR working
principle and actuation wiring diagram. The experimental
setup, control diagram, and modeling framework are pre-
sented in Fig. 3.
A. Local Directional Bending
A uniform change in a tendril pitch results in a uniform
elongation or contraction. On the other hand, local partial
(e.g. one-third of a full turn) modulations through local
heating results in lateral bending of the backbone toward
the opposite direction of the activated section (Fig. 2-a).
Having three equally spaced activation regions of 120 deg
(by connecting three actuation wires), each full turn acts as
a local independent 3-DOF joint (Fig. 2-b). The number of
joints can be as many as the number of turns in the tendril.
B. Local Heating
Control wires (three per joint) were passed through the
center of the helix, turned around the SMA tendril wire at
the connection point, and covered with two layers of heat
shrink to stay in place. A single wire at the tendril base
was connected to the ground pin of the electrical current
control module. Connecting any of the control wires to the
power supply resulted in electrical current between the wire
connection point all the way to the tendril base. We observed
that by fixing the supply current to 1 A, the electrical power
was not enough to heat the entire SMA tendril through Joule
heating. However, this current was enough to observe local
heating in the area around the active wire connection point
that is covered by a heat shrink (see the supplementary media
files). Since the same area around the other inactive wire
connection points was not heated, we suspect that the current
was high enough to form micro-sparks at the connection site.
As a result, local heat is generated and accumulated, due
to heat insulation by the heat shrink cover, causing a local
change in the wire temperature and consequently SMA wire
deformation. This way, for the first time, we programmed
a SMA morphology by design to locally response (in the
form of generating local heat) to a dispersed electrical
signal that propagates throughout the material. The exact
mechanism behind the observed local heating is subject to
further investigation in the future. Five single-turn bending
sections, each with three control wires, were created along
the SMA tendril. A total of 16 wires were used.
C. SMA Tendril Selection
To simplify the controller mechatronic design, the chosen
SMA tendril retained its configurations after the activation.
As a result, the control wires could be activated one at a
time with a single electrical current control unit that was
connected to the wires through a set of timed relay switches.
This limited the manipulator load bearing capacity to an
amount that does not deform the inactive SMA tendril. Hence
this control architecture is better for tasks involving known
limited external load.
Furthermore, the material shape memory response to heat
should be faster than its thermal conductivity. A low response
and highly thermal conductive SMA results in uniform
distribution of heat, and hence deformation, even when it is
locally heated. The load bearing requirement of the inactive
SMA tendril, and the material shape memory response vs.
thermal conductivity limit the available choices for a useful
tendril. Through testing different tendril sizes and material,
we could find a suitable one-way SMA tendril with a fully
collapsed state as its programmed (heated) shape. As a side
effect of such choice, an activated section was collapsed and
could not retain its initially elongated configuration. This
problem can be addressed by introducing a secondary SMA
tendril with elongated programmed shape to elongate back
the tendril after it is collapsed. Alternatively, a compression

Activate section
Inactivate
section

Control
Program
(PC)
Microcontroller
(Arduino Uno)
A PWM Current
Control Unit
(Motor Driver)
Relay Switches
(connect current
controller to a
section at a time)
5 sets of 3 wires activating 120o
of a single SMA helix turn
a) b) c)
Relay board Arduino Uno
& Motor
Shield
SMA Tendril
Wire
contacting
points with
120ooffset
Wires for other
sections closer to tip
Section 1
Section 2
Section 3
Section 4
Section 5
Ground
Fig. 3: ATBR diagrams, (a) Constant Curvature modeling framework, (b) a simple feed-forward control structure that actuate one wire
at a time, (c) experimental setup design.
Tj(κ, l, φ) =
cos(κl) cos(φ)2+ sin(φ)2cos(κl) cos(φ) sin(φ)cos(φ) sin(φ) sin(κl) cos(φ)(cos(φ)(cos(κl)1))
cos(κl) cos(φ) sin(φ)cos(φ) sin(φ) cos(φ)2+ cos(κl) sin(φ)2sin(κl) sin(φ)(sin(φ)(cos(κl)1))
sin(κl) cos(φ)sin(κl) sin(φ) cos(κl) sin(κl)
0 0 0 1
(1)
elastic backbone can be introduced to force a pitch increase
(elongation) in the bent opposing side of the helix when a
section is bent. Activation of this elongated portion results
in the bent to become straight again. We will address these
issues and design considerations in more details in a future
design.
D. Controller Design
A simple control setup was implemented based on an
Arduino Uno micro-controller and an L298P Arduino Motor
Shield to control the supply current. The current control unit
was connected to control wires (denoted by V in Fig. 2-b)
through a 40 V 16-channel relay board one at a time. Pulsed
Width Modulated (PWM) signals were used to supply fixed 1
A electric current (supploed through a current power supply)
to each control wire. Compared to a constant voltage power
supply, providing fixed current resulted in unified energy
transfer to the material regardless of the SMA wire length.
The relay board was used in a normally-open configuration
and controlled in an on/off fashion for a controlled amount
of time (10 s for identification tests and 5 s for reaching com-
plex configurations) using the Arduino Uno micro-controller
board. A control program was developed using Arduino IDE
which commands the relay and motor driver shield through
the IDE standard serial protocol. A complex desired shape
was achieved through sequential activation of the sections
in the right amount of time found based on identification
of the SMA tendril thermal properties. This simple control
structure was possible since the SMA backbone holds its
shape in place after every activation sequence.
III. KINEMATIC MODELING & SIMULATION STUDY
There exist a variety of modeling approaches for the
mechanics of continuum manipulator in the literature, such
as lumped system methods, Constant and Variable Curva-
ture assumptions, reduced-order methods [18], [19]. Among
them, the Constant Curvature (CC) assumption is probably
the more broadly applicable method allowing for closed-
form computation of the manipulator forward and inverse
kinematics [20]. This approach approximates the backbone
-10-50510 y [mm]
0
5
10
15
z [mm]
a)
-10-50510 y [mm]
0
5
10
15 b)
-10-50510
y axis
-5
0
5
10
15 c)
y [mm]
Fig. 4: Work-space (black dots) difference between a manipulator
with one, two, and three independent sections for similar overall
length, maximum curvature, and change in the curve parameters.
as a constant curvature curve with curvature κj, length lj
and bending plane angle φjas the curve parameters. The
manipulator kinematic transformation consists of a transfor-
mation from the actuator space to the configuration (curve)
space (robot specific mapping), followed by a transformation
from the configuration space to Cartesian (task) space (robot
independent mapping). Fig. 3-a presents the CC parameters
used in this study.
The robot independent mapping is presented by a trans-
formation matrix Tm=Tj.Tlfor each individual section,
where Tjis a joint (single helix turn) CC kinematics as in
Eq. 1 [20], Tlis the linear transformation associated with an
inactive straight section of length ll=nlp,nlis the number
of inactive turns in a section. See Table I for the experimental
setup parameters.
The robot specific mapping consists of two steps, a map-
ping from local variation of the tendril pitch pto the length
of three imaginary actuation lines lji, i [1,3] (Fig. 3.a), and
a mapping from ljto the CC parameters. Each imaginary line
lies on a circle with coil mean radius (r= 2.325 mm) on
the opposite side of a set of 120 deg sections. The former
is easily identifiable from the thermal identification of the
tendril as
lji=lj0njpi,(2)
where nj= 1/3is the number of active turns (here one-third
of a full turn is active at a time), lj0=njpis the joint initial
length, and piis the change in the pitch of the ith 120 deg
segment of the joint. An empirical relation for ptwill
21.5
22
22.5
23
23.5
525 45 65
Temp [C]
Time [s]
-50
-40
-30
-20
-10
0
21.5 22 22.5 23 23.5
∆p [mm/turn]
Temp [C]
Laser Target Point
a) b) c) d)
Laser
Thermometer
Manipulator -19
-14
-9
-4
1
525 45 65
∆p [mm/turn]
Time [t]
y = -0.3573x + 6.1078
R2= 0.95085
Fig. 5: Thermal properties identification of the SMA tendril, (a) a laser thermometer pointing at the active coils, (b) change in the pitch
vs. time pt, (c) temperature vs. time Tt, (d) and pitch vs. temperature pTfor different experimental trials (different colors)
with a single tendril turn.
Fig. 6: (a) Single section bending experiment of the manipulator
versus (b) simulation results (actuation time: 10 s).
be identified. The latter mapping is as in [20]
lj=
3
X
i=1
lji, φj= atan 3(lj2+lj32lj1)
3(lj2lj3)!,(3)
κj=
2ql2
j1+l2
j2+l2
j3lj1lj2lj1lj3lj2lj3
r(lj1+lj2+lj3).
Fig. 4 shows the comparison of three tendril manipulators
with same length but one, two, and three independent active
sections but similar overall length, maximum curvature, and
change in the curve parameters. The plots show significant
improvements in the work-space volume and manipulator
manipulability (denser reachable space) as the manipulator
dexterity increases.
The presented modeling framework is the simplest pos-
sible for an ATBR. A more detailed model for constant
curvature bending of a tendril is presented in our previous
work [21].
IV. EXP ERI MEN TAL IDENTIFICATION & VALI DATI ONS
A. SMA Thermal Properties Identification
The tendril pitch variation δp and actuation velocity ver-
sus time tand local temperature Twere experimentally
identified through analyzing video recordings of the tendril
in controlled uniform activation of a full turn of the SMA
tendril. A 30 fps camera, set up to minimize the parallax
error, was used to capture a recording of the backbone
during actuation which is latter analyzed using openCV.
A non-contact laser thermometer, as the easiest way to
measuring the surface temperature, was placed at a distance
close enough to capture the temperature reading and tendril
deformation within the same camera video frame (Fig. 5.a).
The helix pitch angle was determined based on the backbone
displacement measurement.
Fig. 5.b-d shows the identification experiment setup and
result plots for pt,Tt, and p− T relations in
six different trials with similar conditions. The inefficiency
of our temperature measurements technique has resulted in
scattered plots for T tand p− T , while the ptplot
shows an almost linear relation identified as
p= (0.3573C1)t+ (6.1078 + C2)(4)
= (0.3573C1)(tt0C3),
in mm/turn with mean R2= 0.9508, where t0= 17.1s
is the system thermal lag, and Ciare individual correction
coefficients for each joint.
Observing the unreliable measured temperature dependent
relations, we substitute Eq. 2 in Eq. 2 for model and
control the change in the local pitch based on the section
activation time. This is more suited to our simple feed-
forward control architecture where there is no need for a
temperature sensor. We left more accurate identification of
the temperature relations for a further study.
B. Individual Joints’ Correction Coefficients
Fig. 6 shows experiments on simple activation of second
segment of the 4th joint for 10 s. Individual correction coef-
ficients Ciare found for each Joins’ segment by comparing
the experimental and simulation results as in Fig. 6.b. The
identified values are presented in Table I. The manipulator
is capable of reaching a bending angles of up to 54.5 deg
(mean 34 deg) with a angular speed of up to 6.8 deg/s (mean
4.3 deg/s) disregarding the thermal lag (t0&C3).
C. Complex Configurations’ Experiments & Simulations
Six random combinations of the actuation of the ma-
nipulator different joints were tested (approximate values
are listed in Table I) to showcase the dexterity of the
proposed design and to validate our modeling framework.
The simulation results proved accurate in predicting the
overall deformation concodering teh correction coefficients
(Fig. 7). More detailed analysis of the modeling and control
errors is left for a future work. Hysteresis in the material,
f)d)c)b)a) e)
Fig. 7: Complex deformations of the ATBR according to the approximate input values in Table I, in comparison with the numerical
simulations.
variation in the initial configuration of the tendril when
manually extended after each experiment, and variation in the
environment factors such as room temperature and humidity
are the possible causes of such errors.
V. DISCUSSION & FUTURE WORK
As a proof-of-concept design, we have demonstrated the
capabilities of a novel highly dexterous miniature continuum
manipulator by exploiting the helical geometry of a SMA
tendril as the manipulator backbone and actuators. Possible
applications of this design include inspection of confined
spaces in environments with limited variation in temperature
and proper natural cooling, e.g. underwater inspection, in-
spection in cold places such as poles, mountain tops, caves,
and Space. For such applications, usually a small camera
would be attached at the tip of the manipulator as a fixed tip
load to be considered in the SMA tendril selection process.
Alternatively, such a manipulator, with its easy and cheap
to build design and control architecture, can be a good
subject for studying continuum manipulators kinematics,
control, and design. Fig. 8 shows a sample implementation of
navigating in an imaginary narrow port. We plan to conduct
more practical experiments in our future study.
A. Design Limitations
Currently, the presented ATBR needs to extended back
manually to an initial fully extended configuration after
each round of activation. This problem can be tackled by
introducing a compression elastic beam as the manipulator
backbone that preserves an initially elongated shape for the
tendril when no section is activated. In this case, the SMA
tendril should be strong enough to bend the elastic core when
activated but soft enough to follow its shape when inactive.
Alternatively, two way shape memory tendrils with suitable
thermal and mechanical elasticity properties can be used.
Such designs requires constant activation of the joints to
keep a deformed configuration. A simpler solution could
be using two concentric SMA tendrils but with opposing
programmed shapes. Such tendrils should be fully compliant
to the opposing tendril movement when inactive but stiff
enough to move the opposing tendril when active. Thermal
insulation between the tendrils and extra wires to control
both of them should be considered.
TABLE I: Setup parameters and approximate activation time for
six random control input combinations as in Fig. 7. The 1st module
is the closes to the base.
Trial Labela b c d e f
Sec. nlSeg. C1C3Approx. Activation Time [s]
1 0.465 -15.1 0 0 25 0 0 20
1 4 2 0.795 -15.1 0 15 0 0 10 0
3 1.252 -16.1 0 0 0 0 0 0
1 1.697 -16.1 0 0 10 5 5 5
2 2 2 1.68 -14.1 0 5 0 0 0 0
3 2.008 -16.1 5 0 0 0 0 0
1 2.027 -15.1 0 0 5 5 10 0
3 3 2 2.383 -14.1 5 0 0 0 10 10
3 1.201 -14.1 0 0 0 0 0 10
1 2.254 -15.1 5 0 10 10 0 0
4 3 2 2.357 -15.1 0 0 0 0 0 0
3 2.89 -15.1 0 5 0 0 0 10
1 2.868 -14.1 5 0 0 5 0 0
5 2 2 2.504 -14.1 0 0 0 0 0 5
3 3.095 -15.1 0 0 0 0 0 0
We rely on natural air convection in room temperature for
our tests. A proper cooling mechanism is needed to achieve
fast enough reactivation cycles depending on the application,
e.g. this may not be a problem for underwater or application
in very cold places.
The same control architecture as in Section II-D can
be used if two opposing tendrils are used as explained
above. However, the use of a passive inner backbone or
a double-way SMA tendril would require maintaining a
joint temperature constant for maintaining any configuration.
This requires a closed-loop temperature controller relying on
implementation of temperature sensors which is an issue due
to space limitations, wiring complexity, and commercially
available sensor sizes. Such control structure requires more
than one current control unit or very fast switching of the
relay board to maintain the sections temperature in a very
slow PWM fashion.
B. Future Work
In further research, we will address the limitations with
the design and control architecture. On the design front, we
will investigate the possible usage of two opposing one-way
SMA tendrils. A more thorough theoretical study based on
differential geometry of the tendril and the variable curvature
kinematics of the backbone will assist with investigating the
effect of payload on the proposed manipulator. The SMA
behavior is subject to hysteresis properties of the material
and the environmental changes in temperature and humidity.
A detailed model of the material properties and behavior
1) 2) 3) 4)
Fig. 8: Sequences of a sample navigation task in an imaginary
confined pathway. The pathways imaginary walls are drawn on a
paper to prevent any interaction with the manipulator that may
result in passive deformation of the backbone. The manipulator
base moves upward while the backbone sections are activated
sequentially to comply with the curved pathway.
will assist taking these effect into consideration or suggesting
an automated tuning mechanism in the form of an adaptive
control architecture. Detailed error analyses are required
regarding different aspects of this research, e.g. validation
of the theoretical framework, payload bearing capability of
the device, motion repeatability, accuracy of the control
architecture, temperature estimation, etc. The addition of
these features would allow for increased functionality of the
proposed manipulator.
VI. CONCLUSION
We have presented a proof-of-concept design for a novel,
easy to build and affordable continuum manipulator named
Active Tendril-Backbone Robot (ATBR). We utilized the
morphology of a SMA helix tendril, as both the manipulator
backbone and actuator, and local heating in response to gen-
eral dispersed electrical current throughout the material via
structural design. Each full turn of the helical backbone can
act as a 3-DOF joint by local activation of one-third of the
full turn. Our miniature manipulator is 4.69 mm in diameter,
elongated to 141.5 mm length, lightweight, and features five
bending sections capable of reaching approximate bending
angles of up to 54.5 deg and angular speeds of up to 6.8
deg/s. A simple modeling framework based on the Constant
Curvature assumption is proposed and successfully verified
through simulations and experimental study. The presented
manipulator is unique in design with minimal fabrication
efforts, yet demonstrates noteworthy potential for inspection
tasks in environments with proper natural cooling and for
educational purposes.
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