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

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.
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 *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
Rear view- Straight
Rear view- Actuated
Side view- Actuated
a) b)
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.
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
(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
SMA Tendril
points with
Wires for other
sections closer to tip
Section 1
Section 2
Section 3
Section 4
Section 5
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
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
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.
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]
z [mm]
-10-50510 y [mm]
15 b)
y axis
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
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
525 45 65
Temp [C]
Time [s]
21.5 22 22.5 23 23.5
∆p [mm/turn]
Temp [C]
Laser Target Point
a) b) c) d)
Manipulator -19
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]
lji, φj= atan 3(lj2+lj32lj1)
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].
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
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.
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.
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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[21] S. Sadati, et al., “A Geometry Deformation Model for Braided Con-
tinuum Manipulators,” Front. Robot. AI, vol. 4, 2017.
... This is a modular closed-chain rolling robot with compliant SMA wires which has the perfect terrain adaptability and maneuverability. An active Tendril-Backbone Robot (ATBR) was built [43] as the manipulator backbone and actuator which utilized the SMA helix. Fuzzy logic control is implemented to control the displacement by currents for underwater robots in [44]. ...
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This paper mainly focuses on various types of robots driven or actuated by shape memory alloy (SMA) element in the last decade which has created the potential functionality of SMA in robotics technology, that is classified and discussed. The wide spectrum of increasing use of SMA in the development of robotic systems is due to the increase in the knowledge of handling its functional characteristics such as large actuating force, shape memory effect, and super-elasticity features. These inherent characteristics of SMA can make robotic systems small, flexible, and soft with multi-functions to exhibit different types of moving mechanisms. This article comprehensively investigates three subsections on soft and flexible robots, driving or activating mechanisms, and artificial muscles. Each section provides an insight into literature arranged in chronological order and each piece of literature will be presented with details on its configuration, control, and application.
... Progress in plant and especially tendrilinspired soft robotics has enhanced the derivation of functionalities adapted from the plant behavior that will have significant effect on environmental applications, such as remote exploration, monitoring agriculture, fixture for vegetation or crop handling, biomedical applications, and many more [4], [6]- [10]. Several robots and actuators have already been developed that mimic the tendril-like coiling behavior [7]- [9], [11]- [15] by using combination of an interaction between materials and structural arrangement. This approach in soft robots is usually realized in two ways: (i) using flexible and complaint systems A plant tendril-like soft robot that grasps and anchors by exploiting its material arrangement including pneumatics [16], [17], hydraulics [18], and tendondriven systems [19]; (ii) using smart materials and stimuli responsive actuation like magnetic [20], light [21], [22], heat [23], [24], humidity [25], [26] and osmosis [12]. ...
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Some climbing plants use tendrils as efficient strategies to anchor and support their weights while they move in unstructured environments. In this letter, we mimic the essential functions of tendrils that wrap around the support in a soft state by a spiral winding (coiling) and then lignify or stiffen to strengthen the attachment. We implement a simple hierarchical pre-programmed functionality at the material level using off-the-shelf materials and easy fabrication methods to achieve coiling and stiffening and incorporate an electrical control. The resulting robots hence consist of a bilayer of silicone elastomers that encapsulate a thermoplastic core and a heating element. The bilayer that spontaneously forms a helically coiled configuration in its equilibrium state is controlled by a solid-to-liquid phase transition of the thermoplastic core upon resistive heating.Integrating these mechanisms into a single structure allows mimicking the basic tendril functions. Our realization is a straight forward assembly with electrical control that offers the perspective to be a building block for soft robots that require controllable attachment solutions such as growing artifacts and devices that operate in unstructured environments, e.g.,operating in vegetation.
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A reliable, accurate, and yet simple dynamic model is important to analyze, design and control hybrid rigid-continuum robots. Such models should be fast, as simple as possible and user-friendly to be widely accepted by the ever-growing robotics research community. In this study, we introduce two new modeling methods for continuum manipulators: a general reduced-order model (ROM) and a discretized model with absolute states and Euler-Bernoulli beam segments (EBA). Additionally, a new formulation is presented for a recently introduced discretized model based on Euler- Bernoulli beam segments and relative states (EBR). We implement these models to a Matlab software package, named T M T Dyn, to develop a modeling tool for hybrid rigid-continuum systems. The package features a new High-Level Language (HLL) text-based interface, a CAD-file import module, automatic formation of the system Equation of Motion (EOM) for different modeling and control tasks, implementing Matlab C-mex functionality for improved performance, and modules for static and linear modal analysis of a hybrid system. The underlying theory and software package are validated for modeling experimental results for (i) dynamics of a continuum appendage, and (ii) general deformation of a fabric sleeve worn by a rigid link pendulum. A comparison shows higher simulation accuracy (8-14% normalized error) and numerical robustness of the ROM model for a system with small number of states, and computational efficiency of the EBA model with near real-time performances that makes it suitable for large systems. The challenges and necessary modules to further automate the design and analysis of hybrid systems with a large number of states are briefly discussed in the end.
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We present a 3D-printable thermoactive scale jamming interface as a new way to control a continuum manipulator dexterity by taking inspiration from the helical arrangement of fish scales. A highly articulated helical interface is 3D-printed with thermoactive functionally graded joints using a conventional 3D printing device that utilizes UV curable acrylic plastic and hydroxylated wax as the primary and supporting material. The joint compliance is controlled by regulating wax temperature in phase transition. Empirical feed-forward control relations are identified through comprehensive study of the wax melting profile and actuation scenarios for different shaft designs to achieve desirable repeatability and response time. A decentralized control approach is employed by relating the mathematical terms of the Cosserat beam method to their morphological counterparts in which the manipulator local anisotropic stiffness is controlled based on the local stress and strain information. As a result, a minimalistic central controller is designed in which the joints' thermo-mechanical states are observed using a morphological observer, an external fully monitored replica of the observed system with the same inputs. Preliminary results for passive shape adaptation, geometrical disturbance rejection and task space anisotropic stiffness control are reported by integrating the interface on a continuum manipulator.
Conference Paper
Full-text available
We present a 3D-printable thermoactive scale jamming interface as a new way to control a continuum manipulator dexterity by taking inspiration from the helical arrangement of fish scales. A highly articulated helical interface is 3D-printed with thermoactive functionally graded joints using a conventional 3D printing device that utilizes UV curable acrylic plastic and hydroxylated wax as the primary and supporting material. The joint compliance is controlled by regulating wax temperature in phase transition. Empirical feed-forward control relations are identified through comprehensive study of the wax melting profile and actuation scenarios for different shaft designs to achieve desirable repeatability and response time. A decentralized control approach is employed by relating the mathematical terms of the Cosserat beam method to their morphological counterparts in which the manipulator local anisotropic stiffness is controlled based on the local stress and strain information. As a result, a minimalistic central controller is designed in which the joints' thermo-mechanical states are observed using a morphological observer, an external fully monitored replica of the observed system with the same inputs. Preliminary results for passive shape adaptation, geometrical disturbance rejection and task space anisotropic stiffness control are reported by integrating the interface on a continuum manipulator.
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Continuum manipulators have gained significant attention in the robotic community due to their high dexterity, deformability, and reachability. Modeling of such manipulators has been shown to be very complex and challenging. Despite many research attempts, a general and comprehensive modeling method is yet to be established. In this paper, for the first time, we introduce the bending effect in the model of a braided extensile pneumatic actuator with both stiff and bendable threads. Then, the effect of the manipulator cross-section deformation on the constant curvature and variable curvature models is investigated using simple analytical results from a novel geometry deformation method and is compared to experimental results. We achieve 38% mean reference error simulation accuracy using our constant curvature model for a braided continuum manipulator in presence of body load and 10% using our variable curvature model in presence of extensive external loads. With proper model assumptions and taking to account the cross-section deformation, a 7–13% increase in the simulation mean error accuracy is achieved compared to a fixed cross-section model. The presented models can be used for the exact modeling and design optimization of compound continuum manipulators by providing an analytical tool for the sensitivity analysis of the manipulator performance. Our main aim is the application in minimal invasive manipulation with limited workspaces and manipulators with regional tunable stiffness in their cross section.
Conference Paper
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Investigations on control and optimization of continuum manipulators have resulted in a number of kinematic and dynamic modeling approaches each having their own advantages and limitations in various applications. In this paper, a comparative study of five main methods in the literature for kinematic, static and dynamic modeling of continuum manipulators is presented in a unified mathematical framework. The five widely used methods of Lumped system dynamic model, Constant curvature, two-step modified constant curvature, variable curvature Cosserat rod and beam theory approach, and series solution identification are reviewed here with derivation details in order to clarify their methodological differences. A comparison between computer simulations and experimental results using a STIFF-FLOP continuum manipulator is presented to study the advantages of each modeling method.
Conference Paper
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Continuum and soft robotics showed many applications in medicine from surgery to health care where their compliant nature is advantageous in minimal invasive interaction with organs. Stiffness control is necessary for challenges with soft robots such as minimalistic actuation, less invasive interaction, and precise control and sensing. This paper presents an idea of scale jamming inspired by fish and snake scales to control the stiffness of continuum manipulators by controlling the Coulomb friction force between rigid scales. A low stiffness spring is used as the backbone for a set of round curved scales to maintain an initial helix formation while two thin fishing steel wires are used to control the friction force by tensioning. The effectiveness of the design is showed for simple elongation and bending through mathematical modelling, experiments and in comparison to similar research. The model is tested to control the bending stiffness of a STIFF-FLOP continuum manipulator module designed for surgery.
A foldable arm is one of the practical applications of folding. It can help mobile robots and unmanned aerial vehicles (UAVs) overcome access issues by allowing them to reach into confined spaces. The origami-inspired design enables a foldable structure to be lightweight, compact, and scalable while maintaining its kinematic behavior. However, the lack of structural stiffness has been a major limitation in the practical use of origami-inspired designs. Resolving this obstacle without losing the inherent advantages of origami is a challenge. We propose a solution by implementing a simple stiffening mechanism that uses an origami principle of perpendicular folding. The simplicity of the stiffening mechanism enables an actuation system to drive shape and stiffness changes with only a single electric motor. Our results show that this design was effective for a foldable arm and allowed a UAV to perform a variety of tasks in a confined space.
Deep intracranial tumor removal can be achieved if the neurosurgical robot has sufficient flexibility and stability. Toward achieving this goal, we have developed a spring-based continuum robot, namely a minimally invasive neurosurgical intracranial robot (MINIR-II) with novel tendon routing and tunable stiffness for use in a magnetic resonance imaging (MRI) environment. The robot consists of a pair of springs in parallel, i.e., an inner interconnected spring that promotes flexibility with decoupled segment motion and an outer spring that maintains its smooth curved shape during its interaction with the tissue. We propose a shape memory alloy (SMA) spring backbone that provides local stiffness control and a tendon routing configuration that enables independent segment locking. In this paper, we also present a detailed local stiffness analysis of the SMA backbone and model the relationship between the resistive force at the robot tip and the tension in the tendon. We also demonstrate through experiments, the validity of our local stiffness model of the SMA backbone and the correlation between the tendon tension and the resistive force. We also performed MRI compatibility studies of the three-segment MINIR-II robot by attaching it to a robotic platform that consists of SMA spring actuators with integrated water cooling modules.
Due to their small size and flexibility, fiber Bragg grating (FBG) sensors have been integrated into needle-sized continuum robots for shape estimation and force measurement. The challenge in extending previous shape and force sensing technologies to pre-curved continuum robots, such as concentric-tube robots, is that torsion information is essential for accurate shape estimation, and the force-strain relationship is nonlinear. In this letter, a novel helically wrapped FBG sensor design and corresponding force-curvature-strain model are developed to provide simultaneous curvature, torsion, and force measurement. To validate this design and modeling technique, two sensorized Nitinol tubes were fabricated and tested in an experimental setup. The results showed that accurate and sensitive curvature, torsion, and force measurements can be obtained at a 100 Hz sampling rate.