A novel continuum-style robot with multilayer compliant modules

Abstract

This paper introduces a novel continuum-style robot that integrates multiple layers of compliant modules. Its essential features lie in that its bending is not based on natural compliance of a continuous backbone element or soft skeletal elements but instead is based on the compliance of each structured planar module. This structure provides several important advantages. First, it demonstrates a large linear bending motion, whilst avoiding joint friction. Second, its contraction and bending motion are decoupled. Third, it possesses ideal back-drivability and a low hysteresis. We further provide an analytical method to study the compliance characteristics of the planar module and derive the statics and kinematics of the robot. The paper provides an overview of experiments validating the design and analysis.

Full text


Abstract— This paper introduces a novel continuum-style
robot that integrates multiple layers of compliant modules. Its
essential features lie in that its bending is not based on natural
compliance of a continuous backbone element or soft skeletal
elements but instead is based on the compliance of each struc-
tured planar module. This structure provides several important
advantages. First, it demonstrates a large linear bending motion,
whilst avoiding joint friction. Second, its contraction and
bending motion are decoupled. Third, it possesses ideal
back-drivability and a low hysteresis. We further provide an
analytical method to study the compliance characteristics of the
planar module and derive the statics and kinematics of the robot.
The paper provides an overview of experiments validating the
design and analysis.
I. INTRODUCTION AND BACKGROUND
Continuum-style robots, including those inspired by bi-
ology, increasingly arouse the attention of researchers due to
the compliance capability and the wide range of motion. In the
last two decades, there have been remarkable developments:
many new designs appeared and various applications in both
medical and industrial fields were demonstrated [1]. The re-
lated scientific problems range from designing and modeling
to low-level control and high-level task execution. Compared
to modular rigid-link robots, continuum-style robots are more
diverse, often resembling animals or animal appendages, such
as snakes, elephant trunks and octopus tentacles [2].
Historically, the first continuum-style robot is generally
accepted to be Anderson and Horn’s tensor arm manipulator
invented in the late 1960s [3] – a tendon-driven spine-like
flexible arm. Subsequently in 1971, Hirose started to propose
creative designs of snake-like robots and appropriate control
systems based on the biomechanical study of snakes [2]. Early
works also include Chirikjian’s pilot research in the 1990s on
establishing the fundamental modeling technique to formulate
the dynamics of hyper-redundant manipulators [4]. The late
1990s and the 2000s saw an increasing trend of miniature
continuum-style robots being moved into robotic surgery with
a view to finding solutions for robot-assisted minimally
invasive surgery with its inherent access problems through
small incisions [5]. Meanwhile, soft robotics as a subset of
continuum-style robotics emerged with the development of
novel soft actuators and sensors [6]. Most recently, Walker [1]
reviewed the state of art of continuous backbone robot
manipulators and analyzed the hardware design principles that
inspired our work.
A continuum robot can be identified with a continuous
backbone structure. However, a hyper-redundant robot [4]
P. Qi, C. Qiu, H. Liu, J. S. Dai, and K. Althoefer are with the Centre for
Robotics Research, Department of Informatics, King’s College London,
WC2R 2LS, UK. (e-mail: peng.qi@kcl.ac.uk)
L. Seneviratne is with Khalifa University, Abu Dhabi, UAE and Emeritus
Professor of Mechatronics, King’s College London, UK.
sometimes also has an external continuous appearance which
is comprised of a segmented backbone with many short rigid
links; hence, the latter types of robots, strictly speaking, do not
represent truly continuum robots but will be termed “contin-
uum-style robots” here. Herein, we summarize the frequently
applied continuum-style robot constructions to date according
to the distinctive backbone architecture, but excluding the
subset of “invertebrate” soft robots. Of these, the early robot
construction is composed of serially connected independent
joints, which pertains to the aforementioned hyper-redundant
manipulator. The designs share the advantages of having a
large number of degrees of freedom (DOFs) and accurate
control, however they suffer from the problems of lighter
payload, joint friction and incompressibility/inextensibility.
Perhaps the most common form of truly continuum robots
is to use a spring backbone [3]. Due to the flexibility of the
spring structure, the shape of a robot can be actuated in a
tendon-driven manner and allows an ideal back-drivability
and a relatively low hysteresis. However, its compression and
the bending deflection are mechanically coupled, leading to a
bending actuation that is partially lost in compression [1].
Another popular design of continuum robots utilizes a laterally
super-elastic, but longitudinally incompressible rod/tube as
the backbone element [7]. A distinctive feature of using an
elastic central backbone is design simplicity. On top of this,
both control and modeling will be straightforward. They con-
sistently can be formulated by beam-mechanics-based models.
It is in this regard that active cannulas [8] also falls into this
category. Despite our classification illustrating the diversity of
designs, there do not exist strict boundaries among various
kinds of continuum-style robots. For example, a spring-based
continuum robot sometimes is integrated with an elastic rod as
the incompressible central backbone to diminish the natural
compliance.
Figure 1. A multi-layer structured continuum-style robot.
In this paper, we propose a design of continuum-style ro-
bot that has multiple layers of compliant planar modules
linked in series (see Fig. 1). Its essential features lie in that the
bending of this continuum-style robot is not based on natural
compliance of a continuous backbone element or soft skeletal
elements but utilizes the compliance of each structured planar
module. The main advantages of using compliant planar
Motor package
End-effector
Modular segment
A Novel Continuum-Style Robot with Multilayer Compliant Modules
Peng Qi, Chen Qiu, Hongbin Liu, Jian S. Dai, Lakmal Seneviratne, Kaspar Althoefer
2014 IEEE/RSJ International Conference on
Intelligent Robots and Systems (IROS 2014)
September 14-18, 2014, Chicago, IL, USA
978-1-4799-6934-0/14/$31.00 ©2014 IEEE 3175

modules are due to their linear output motion and avoiding
friction between joints. We present an analytical method to
study the compliance characteristics of the planar module and
derive the compliance matrix to represent the force-deflection
relationships, thus making the linear motion accurately pre-
dictable. Another advantage of the continuum-style robot (Fig.
1) is owing to the serial connection of the conjoined layers,
thus demonstrating a large linear bending motion, although the
linear-motion approximation of one layer only holds under the
condition of small deflections. Additionally, the structure is
back-drivable – a desirable feature in robotics and improving
safety when operating in close vicinity of humans. This
structure behaves like a helical spring, but its contraction and
bending motion are decoupled, thus reducing the uncontrolled
compression when generating normal deflections. This feature
renders the bending of the robot more controllable. Besides, it
has the capability of maintaining better structural rigidity of
the whole continuum body when compared to a
spring-backbone-based design, and thus convinces with
comparatively low hysteresis.
II. CONCEPTUAL DESIGN OF THE ROBOT
A. Segment Design
Figure 2. Design of double-layer modular segment. (a) Top view;
(b) Side view.
Fig. 2(a) depicts a top view of the compliant planar module.
Howell et al. first constructed similar types of designs and
identified different configurations [9]. Due to its out-of-plane
motion along an axis orthogonal to the parent plane, these
devices are also called “ortho-planar springs” [9]. In Fig. 2(a),
the design is presented in detail: three legs (120° apart) radi-
ally extend away from the central platform and are anchored to
the outer base; each leg has two flexible segments shaped like
a “U” (U-shape design); the intermediate platform is consid-
ered infinitely stiff. In the current design the circular outer
contour has a 29mm diameter and the length of each leg is
8mm. The thickness of the flexible beam elements is 1mm; the
width 1.2mm and both can be varied to change the beam
compliance. Part of the base is cut in order to reduce the mass.
Three tendon channels with a 0.8mm diameter are reserved for
guiding tendons through each layer of modules. They are
positioned on the far edge of the base and along the extension
line of the leg. This compliant layer possesses one DOF to
raise and lower the platform relative to the fixed base and 2
DOFs to allow the platform to freely perform titling motions
around the center, thus 3 DOFs in total. A three-legged design
is chosen for the reason that it is the minimum odd number leg
count, which allows reducing the rotational tendencies of each
leg and increasing the stability of the platform [9]. The radial
structure causes the central platform to undergo large deflec-
tions when a given moment is applied to the center.
Fig. 2(b) depicts the modular segment design for our con-
tinuum-style robot. It integrates two layers of compliant planar
modules facing opposite directions; a prism-like shaft and a
mating female cylinder are respectively fixed on each platform
of the top and the bottom. The polygonal cross-section design
of the axial coupling resists relative rotation between the two
segments and while enabling torque transmission. They are
fitted precisely to connect from segment to segment. Except
for the flexible segments and the two platforms with their
“vertebrae”, any other part of the segment is a part of the frame
extending from the base to the tip of the manipulator; this
frame is idealized to be a rigid body. When fixing the bottom
cylinder, if a load is applied to the prism shaft, the relative
displacement or rotation of two platforms would be double
compared to that of one layer for the same load. The gap be-
tween the two layers currently is 5mm, providing enough
space to keep the outer edges of two legs or two platforms of
the top and bottom layers from colliding. The segmented
modular design allows the length of the continuum-style robot
to cope with various intended, bending scenarios.
B. Continuum-Style Robot Assembly
Figure 3. Partial views of continuum-style robot assembly.
The current continuum-style robot prototype consists of 10
modular segments. Fig. 3 shows partial views of the assembly.
Including a distal plate and a bottom support, the total length is
143mm. The distance between the lower face of one segment
and the upper face of the subsequent segment is 5mm, the
same as the gap between the two layers of one segment. Three
tendons are routed along the aligned segments through the
tendon channels and secured to the distal plate, which leads to
a tendon-driven under-actuated design. The rigid distal plate
can be regarded as an extension of the last platform. By pull-
ing the tendons, the load will be transmitted from the distal
platform to the proximal bottom support, thus generating
compression and steering motions. Moreover, depending on
the intended operations, additional groups of tendons can be
used to increase the mobility and functionality. They are se-
cured to some selected point of column and produce torques to
the lower part.
III. COMPLIANCE OF PLANAR MODULE
From the perspective of mechanical design, the planar
module is a type of hybrid flexure mechanisms [9]. Each
flexible segment in each leg can be treated as a beam flexure.
Each leg is a folded serial chain of two fixed-guided beam
Frame
Prism shaft
Female cylinder
Tendon channel
Platform
Intermediate platform
Leg
Flexible segments
Tendons
Top platform
Segment
Column
(a)
(b)
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flexures. The planar module is formed by connecting the
central platform to the outer base through three legs in parallel.
Thus, we can stepwise derive the compliance matrix for the
entire module with a bottom-up approach.
A. Compliance Matrix Derivation
Figure 4. Coordinate frame transformation. (a) One leg of the design;
(b) A compliant layer.
Fig. 4(a) depicts one leg of the design. The small defor-
mation of each beam is defined as a twist deflection, which in
ray coordinates can be denoted by
S = [ θx θy θz δx δy δz ]T (1)
where the first group of three elements represents the three
rotational deflections about their corresponding axes, whilst
the last three elements reveal the corresponding translational
deflections. A twist deflection S is an element of the Lie al-
gebra se(3) of Lie group SE(3).
And in harmony with this, the loading force is considered
as a general wrench in axis coordinates
W = [ mx my mz fx fy fz ]T (2)
in which the primary part
T
x y z
m m m

m
is the vector
attached with the force amplitude, representing the direction
of the axis of the wrench, whilst the location of the axis of the
wrench is given by the secondary part
T
x y z
f f f

f
. A
wrench is an element of the dual Lie algebra se*(3).
Consider beam 1 of the leg in Fig. 4(a), a local coordinate
frame {x1y1z1} generally can be established at the centroid of
the beam. With the coordinates of both the twist deflection and
the wrench written in the same frame {x1y1z1}, then the com-
pliance matrix of beam 1 can be derived [10] and expressed as
33
112 12
y z z y
l l l l l l
diag GJ EI EI EA EI EI




C
(3)
where the primary part represents torsional compliance and
the secondary part the linear compliance. As shown in Fig. 4,
beam 1 has a rectangular cross-section with the width b and
the thickness h (b>h), as well as a length l, and the area of the
cross-section A is equal to bh. E denotes the elastic module of
the material, and G denotes the shear module of the material
with G=E/(2(1+v)) and v Poisson’s ratio. Iy=b3h/12 and
Iz=bh3/12 are the moments of inertia of the beam at the
cross-section with respect to axis y and axis z, and J is the
torsional moment of inertia.
Equivalent results are also produced in references [10],
[11], [12] and there exists remarkable similarity, however, due
to coordinate frame choices, they are diverse in form.
The compliance characteristics of an individual link or a
whole mechanism system are their intrinsic properties, but
notice that the expression of the compliance matrix may vary
and it depends on the coordinate choice. Once the coordinate
system is defined, it also applies for the references when an-
alyzing the twist deflection of a finite segment.
For (1), (2) and (3), we have the relations between a twist
deflection and a loading wrench summarized below
S = C1W ; W = K1S ; C1 = K1
-1 (4)
where K1 is the stiffness matrix.
Beam 2 is an identical flexible segment to beam 1, thus the
compliance matrix is the same but written in its own local
coordinate frame{x2y2z2}. Two beams in the leg are connected
by an intermediate platform, but it is modeled as a fixed pin
joint with its compliance ignored when we consider the
force-deflection relationship of the leg [9]. At the connecting
edge between the leg and the platform, we established the
global coordinate frame {xl1yl1zl1}. To shift the local
coordinate frame of each beam into the global coordinate
frame {xl1yl1zl1}, an adjoint action of Lie group SE(3) on its Lie
algebra is introduced through a 6×6 matrix representation [13]
g



0R
Ad AR R
(5)
where R is a 3×3 rotation matrix of the coordinate transfor-
mation, and A is a skew-symmetric matrix spanned by trans-
lation vector d.
Then, the coordinates of a twist deflection and a wrench in
the coordinate frame {xl1yl1zl1} are calculated as [10], [12]
S' = Adg S ; W' = Adg
-T W (6)
To obtain the compliance matrix C' in the new coordinate
frame, we deduct it as follows based on (4):
S' = Adg S = Adg (CW) = Adg C Adg
T W' (7)
Thus, we derive that the compliance matrix will be trans-
formed to the new coordinate frame according to the relation
C' = Adg C Adg
T (8)
Similarly, we can derive the stiffness matrix in the new
coordinate frame {xl1yl1zl1} as
K' = Adg
-T
K Adg
-1 (9)
Here, the inverse and the inverse transpose of such adjoint
transformation matrix are given respectively by
T
1
TT
g



0R
Ad -R A R
;
T
g



0
R AR
Ad R
(10)
All deformations are written in the same coordinate frame
{xl1yl1zl1}, then the overall compliance matrix of the leg as a
serial flexure chain is obtained [12] by
   
2T
1
1
i
g i g
lii


C Ad C Ad
, (i=1, 2). (11)
Given a compliance matrix of one leg, its corresponding
stiffness matrix K = C-1 is first calculated. It is noted that all
Leg 1
Leg 2
Leg 3 O
x
yz
Beam 1
Beam 2
l
b
hd
(a)
(b)
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twist deflections and wrenches here must be transformed into
the same coordinate frame, and correspondingly, the stiffness
matrix of each leg will be expressed in such a global coordi-
nate frame. We establish the global coordinate frame {xyz} in
the center of the triangular platform, see Fig. 4(b). The radius
of the plate is labeled by parameter r. The coordinate trans-
formation operation from the connecting edge between the leg
and the platform, i.e. the edge of the disc to the center of disc
follows the aforementioned relation in (9). Further considering
that the overall layer’s stiffness is isotropic [14], it gives the
unified form as
T 2 2T
1 1 1
0  
  K K NK N N K N
(12)
where K1' is the stiffness matrix of leg 1 in the global coor-
dinate frame {xyz}; it is derived by the relation K1'= T-TK1 T-1
based on (9), which indicates a coordinate transformation
from the local coordinate frame at the connecting edge to the
global coordinate frame of the platform center. In the case, T
only possesses the translation action along the x axis. N de-
scribes the rotation action based on the fact that three legs are
symmetrically connected to the platform with an angle120°.
Finally, the compliance matrix of the overall planar mod-
ule layer as a type of hybrid flexure mechanisms is computed
by inverting the stiffness matrix K0,
11
22
33
1
00
44
55
66
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
c
c
c
c
c
c












CK
(13)
Here, the nonzero compliance elements are denoted by the
variables with two subscripts. They are all determined by both
material parameters and geometric parameters of the me-
chanical design of the compliant layer structure.
B. Compliance Analysis and Numerical Example
The compliance matrix in (13) is symmetric positive
definite (SPD), and the diagonal entries represent the
translational and rotational compliance in/about all directions,
respectively. Besides, all diagonal compliance elements of C0
can factor out a factor that coincides with the corresponding
elements of beam’s compliance matrix in (3). By observing
compliance elements of C0, we notice that the x-z planar
motion (x, z, θy) is decoupled from out-of-plane forcing and
vice-versa. On the other hand, the entries outside the main
diagonal are all zero, revealing that the out-of-plane rotation
and translational motion of the platform are decoupled. This
further verifies that the contraction effort and bending motion
of the multi-layer structured continuum-style robot will be
theoretically independent to each other.
In the following, we use two numerical examples to further
reveal the information embodied in the compliance matrix.
The dimensions of the planar module are l= 8mm, b=1.2mm,
h=1mm, d=2mm, r=3.5mm. Aluminum alloy (Young’s mod-
ule E=71GPa and Poisson’s ratio v=0.33) and polyethylene
(E=1.1GPa and v=0.42) are selected as fabrication material for
use in the two examples, respectively, thus deriving each
element of the corresponding numerical compliance matrix as
tabulated in Table 1.
Table 1. Numerical examples of compliance elements.
Compliance element
Aluminum alloy
Polyethylene
c11
1.39×10-1
9.54
c22
4.19×10-2
2.71
c33
1.39×10-1
9.54
c44
9.66×10-7
6.23×10-5
c55
4.82×10-6
3.28×10-4
c66
9.66×10-7
6.23×10-5
By analyzing the numerical results, we can draw the
following conclusions.
1. In the group of rotational compliance elements (c11, c22
and c33), the rotational compliance elements both c11 and c33
about the horizontal x and z axis are more than 3 times larger
than the rotational compliance element c22 about the vertical
axis y, indicating its potential to be used for bending motions
in continuum-style robot, while resisting in-plane rotations.
2. In the group of translational compliance elements (c44,
c55 and c66), the vertical compliance element c55 is about 5
times larger than both the horizontal compliance element c66
along z axis and the horizontal compliance element c44 along x
axis. This result agrees with our intuition and the qualitative
study by Howell et al. [9]. Such translational motion along the
vertical axis of the planar module has been investigated for use
in many applications, such as a pneumatic valve controller for
Flowserve [9] and a force sensor [15].
Overall, c11, c33 and c55 are the major compliance elements.
Thus, reasonably, further analysis can focus on the major
displacements θx, θz and δy that are produced by the loads mx,
mz and fy , respectively.
IV. STATICS ANALYSIS AND KINEMATIC MODELING
First of all, there arise three assumptions. One is that only
flexible beams provide elasticity while all the rest of parts are
considered to be rigid body. Another is that the effect of
gravity is neglected. The third one is that the loads exerted on
the top plane are uniformly distributed to each segment of the
robot.
As pointed out earlier, only the two rotational deflections
θx, θz and the longitudinal displacement δy are the main de-
formation corresponding to the three major compliance ele-
ments c11, c33 and c55. Thus, simplifying:
11
33
55
00
00
00
xx
zz
yy
n c M
n c M
n c F






   

   

   

   


   
(14)
where Mx, Mz and Fy denote the loads on the system as a
whole; n is the number of compliant layers.
In this tendon-driven design, the loads are applied to the
top plane via three non-stretchable tendons. Pre-tightening
force will be applied, thus, activating one or two tendons, can
result in rotational deflection and equally activating three
tendons together leads to longitudinal compression.
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Figure 5. Configuration of two segments assembly 2D bending.
Fig. 5 shows a bending configuration of the planar model
in the xy-plane, where the base of the robot is centered about
the origin and the coordinate system orientation parallel to the
global coordinate frame of the proximal layer. For simplicity,
we only assembled two planar modules, Fig. 5. The bending
of this continuum-style robot is utilizing the local beam de-
flection of each compliant planar module, thus we do the
calculations based on the rotational deflection angle to derive
the length changes of the three tendons. Firstly, we calculate
the length of inner and outer boundaries of the planar model.
2 ; 2
sl
LLL N L N     
(15)
where Ls and Ll denote the length of inner and outer bounda-
ries of the planar model, respectively; L is constant, repre-
senting the initial length of this continuum-style robot; N is
the number of the double layered modular segment, Fig. 2(b);
∆ denotes the spacing changes of segments and ∆=Rsinθ,
where θ is the generalized rotational deflection angle of each
compliant layer and R is the distance from the tendon channel
to the center of the plane.
In the example of Fig. 5, the structure is bending about the
z axis, and the inner boundary corresponds exactly to one of
the tendons on the x-axis. Later, we can obtain the rest of
another two tendon lengths based on spatial model with the
known distances of inner and outer boundaries.
Because the gap between the two layers of a modular
segment is unchanged, we can only consider the spatial con-
figuration of the gap between the two adjacent segments
connected by a column, which is shown in Fig. 6.
Figure 6. 3D bending geometry and cross-section area.
Besides, from the cross-sectional geometry of Fig. 6, the
positional relation between the inner and outer boundaries
and the three tendons can be expressed in terms of the relative
orientation φ between the two adjacent segment surfaces [16].
The orientation φ is the resultant of both θx and θz. We can
calculate the lengths of three tendons based on the angular
relationship, as follows:
 
2
k
s s y
kl
L L L L N


   
, ( 1,2,3).k
(16)
where 2N·δy denotes the total longitudinal compression of this
continuum-style robot; k identifies the tendon.
Referring back to Fig. 5, given the rotational deflection θz
and the segment number N, the tip position of such design on
the xy-plane can be calculated to be
 
 
 
 
sin sin(2 ) sin(2 )
1 cos cos(2 ) cos(2 )
0
y z z z
y z z z
gN
x
y g N
z
   
   
      
        

 
 
 

 

(17)
where g denotes the distance between the lower face of one
segment and the upper face of the subsequent segment. Here,
the equation involves the longitudinal displacement δy for the
case of that the axial compression is generated.
After that, we rotate the planar model about the y-axis
with an angle ω and obtain a spatial model. The derivation of
spatial position coordinates is obtained by rotating the xy
positions about the y-axis. The tip position in space is then
given by multiplying the rotation matrix R (ω) and (17),
yielding
 
 
 
cos sin sin(2 ) sin(2 )
1 cos cos(2 ) cos(2 )
sin sin sin(2 ) sin(2 )
z z z
y z z z
z z z
xN
y g N
zN
   
   
   
     
        
      

 
 
 

 
(18)
The occurrence of the rotation is a synergistic effect of
both rotational deflections 2Nθz about the z-axis and 2Nθx
about the x-axis. It can be derived as
arctan x
z



(19)
We have now found the positions of the continuum-style
robot tip as functions of the three major displacements θx, θz
and δy thus completing the kinematics model. With the cal-
culated tendon lengths, we have derived a model that could be
used to control this continuum-style robot.
V. PROTOTYPE EXPERIMENT
A prototype of the multilayer structured continuum-style
robot was tested; test procedures and results are described in
this section. The double-layered segment is made of acrylo-
nitrile butadiene styrene (ABS) plastic material and is 3D
printed using a rapid prototyping machine (VisiJet® EX200).
Besides, a mini-camera (NanEye Stereo, AWAIBA®) holder
is designed and printed to realize a possible application of the
robot as an example (here: an endoscopic camera). The length
of the assembled prototype is 150mm and its diameter is
29mm. Each tendon is driven by a DC motor (Maxon Motor®)
y
x
o
Tendon
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with a pulley; the employed 128:1 reduction gearhead allows
tendon actuation with a high rotational resolution. Due to the
limited compliance of the fabrication material, the prototype
only serves as a preliminary setup for the investigation of the
performance of hysteresis, back-drivability and bending mo-
tions.
Fig. 7 shows a comparison after and before of the longi-
tudinal contraction, which indicates the back-drivability and
to some extent ensures the safety when interacting with en-
vironments. We can also observe that the tendons’ pulling
force is equally distributed to each of the compliant layers and
results in equal longitudinal displacements.
Figure 7. (a) After and (b) before longitudinal contraction.
Fig. 8(a) shows a 2D bending motion of the robot. The
bending control effort does not generate compressions, which
verifies that its contraction and bending motion are decoupled
in the unique design. In addition, the equally distributed
bending deformations are also presented here; compared with
the sketch in Fig. 5, we can see that the experimental
performance is virtually coinciding with the model. Fig. 8(b)
shows a 3D bending motion of the robot. Some bending
nonlinearity is observable, which we suspect to be because of
the influence of gravity and the nonlinear stress due to
non-homogenous material properties.
Figure 8. Bending deformation of the robot; (a) 2D bending motion;
(b) 3D bending motion.
VI. CONCLUSIONS AND FUTURE WORK
This paper presents the design of a continuum-style robot
with multiple layers of compliant planar modules linked in
series. Firstly, we reviewed frequently applied continu-
um-style robot constructions to date based on the distinctive
backbone architecture. Through our study, we found that our
structure has advantages over other existing traditional con-
tinuum-style robot: a large linear bending motion, avoidance
of joint friction, back-drivability, largely decoupled contrac-
tion and bending motions as well as low hysteresis.
We derived the compliance matrix of the planar module
and provided statics and kinematics descriptions for the
overall robot construction. We built and tested a prototype
and observed its performance. The experimental results veri-
fied some of the characteristics of the robot, such as contrac-
tion, equally distributed longitudinal/bending displacements
and decoupling.
A finite element method (FEM) analysis is being con-
ducted to further confirm the predicted behavior of the pre-
sented continuum-style robot and subsequently a quantitative
empirical validation. In the view of that the compliance
characteristics of the planar module are determined by both
material parameters and geometric parameters of the me-
chanical design, we aim to test different fabrication materials
and other layer configuration, such as side-leg design and
changing the number of flexible segments.
ACKNOWLEDGMENT
The work described in this paper was partially funded by
European Commission's Seventh Framework Programme
under grant agreement 287728 in the framework of EU pro-
ject STIFF-FLOP and the China Scholarship Council.
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132mm
146mm
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