carterpillar sinusoidal oscillator

Research Article
Analysis and Implementation of Multiple Bionic Motion
Patterns for Caterpillar Robot Driven by Sinusoidal Oscillator
Yanhe Zhu, Xiaolu Wang, Jizhuang Fan, Sajid Iqbal, Dongyang Bie, and Jie Zhao
State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150000, China
Correspondence should be addressed to Jizhuang Fan; [e-mail]
Received  February ; Accepted  April ; Published  May 
Academic Editor: Yong Tao
Copyright ©  Yanhe Zhu et al. is is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Articulated caterpillar robot has various locomotion patterns—which make it adaptable to dierent tasks. Generally, the researchers
have realized undulatory (transverse wave) and simple rolling locomotion. But many motion patterns are still unexplored. In this
paper, peristaltic locomotion and various additional rolling patterns are achieved by employing sinusoidal oscillator with xed
phase dierence as the joint controller. e usefulness of the proposed method is veried using simulation and experiment. e
design parameters for dierent locomotion patterns have been calculated that they can be replicated in similar robots immediately.
1. Introduction
e Almighty God created many chain-type creatures such as
caterpillar, snake, and earthworm. By utilizing their inherent
special structure, they can adapt to various environments
through multiple locomotion patterns [,]. For instance, a
caterpillar can move in transverse-wave motion to run fast or
peristaltic motion to sneak through a narrow hole.
e robotics community has been trying to make arti-
facts to exploit the movement mechanism of these versatile
animals. Many specially designed caterpillar robots have
been realized. Besides, the modular self-recongurable robot
(MSRR) composed of many building blocks can be used to
construct diverse types of robots, including caterpillar robot.
Several architectural groups are classied according to the
geometrical arrangement of MSRR units: chain-type, lattice-
type, and hybrid-type [,]. Chain-type and hybrid-type
robot ts for application of coordinated locomotion.
Transverse-wave locomotion is realized on many articu-
lated chain-type caterpillar robots, as in [–]. In these stud-
ies, dierent kinds of transverse-wave forms are employed,
including sine-based wave. But peristaltic motion is not real-
ized on articulated caterpillar robots. Only robots utilizing
special material like SMA (shape memory alloy) or special
structure that mimic the stretch characteristics of caterpillar
and earthworm [–] realize this motion pattern. Besides,
many implemented rolling motions based on chain-type
robot are hand-planned [] and lack generality.
Transverse-wave and peristaltic motion can adapt to
dierent environments, but to the best of our knowledge
no researcher has yet achieved both two motion patterns in
articulated chain-type robot. In this paper, simple sinusoidal
oscillator with xed phase dierence is employed as the
joint controller for achieving transverse-wave and peristaltic
motion. Additionally, multipattern rolling motion like ellipse,
triangle, and other polygon rolling is planned using the same
controller. Figure illustrates some motion patterns suggested
in this paper. Motion patterns from top down are transverse-
wave motion similar to caterpillar and millipede; peristaltic
motion like earthworm; and various rolling patterns beyond
the capability of animals like armadillo.
is paper is organized as follows: Section introduces
the caterpillar robot model and its simple controller. Section 
presents the details of unied planning method for many
bionic motion patterns. e experimental results are shared
in Section . Discussion and future work are presented in
Section . Finally Section concludes the paper.
2. Caterpillar Robot and Simulator
2.1. Caterpillar Robot. Caterpillar robot, also known as
“worm-robot” or “snake-robot,” is an articulated chain-type
Hindawi Publishing Corporation
Advances in Mechanical Engineering
Volume 2014, Article ID 259463, 12 pages
http://dx.doi.org/10.1155/2014/259463

Advances in Mechanical Engineering
F : Multipattern locomotion examples.
12 in
X
Y
P00
P10
J10
J00
Z
i+1 n−1
······
··· ···
F : Kinematics model of UBot module and topology of composed caterpillar robot.
robot. Its joint axes are perpendicular to its motion direction
and parallel to ground. Our investigated caterpillar robot is
composed of UBot modules [,], which are hybrid-type
MSRR. Figure shows kinematics model of UBot module
and caterpillar robot. Each UBot module has two rotary
degrees of freedom. Each joint can rotate ranging from −∘
to ∘.Forcaterpillarrobot,eachmoduleusesonlyone
joint perpendicular to body line from head to tail. It can be
recognized as a planar linkage mechanism for analyzing its
kinematics.
2.2. Controller. Sine-based controller, model-based con-
troller, and CPG (central pattern generation) are oen
employed to generate rhythmic locomotion for robots.
Model-based controller relies on careful analysis and is oen
piecewise function to keep motion shape. Corresponding
model should be carefully designed for certain motion
patterns. Examples like triangular wave and trapezoidal
wavecanbeseenin[,]. CPG-based controller is very
useful for smoothing gaits transition which depends on
communication between modules. If just using CPG-signal
without communication coordination, we do not see any
advantage in controlling modular robot compared with sine-
based controller.
Sine-based controller is easy to implement and can mimic
lots of rhythmic motion patterns. In this paper, sine-based
controller with certain phase-lag is used on each module; see
(). Oset, amplitude, and phase dierence are the same for
all the modules. us only three design parameters need to
be designed: Oset, ,and. Consider
𝑖()=Oset +∗sin +∗ ,
Oset ∈−90
∘,90∘,

Advances in Mechanical Engineering 
Parameters
set panel
F : UBotsim—D dynamics simulator.
∈0,90
∘−|Oset|,
 ∈ [0,],
()
where is module ID and ID increases from head to tail.
Oset is oscillatory center of joint angle. is signal amplitude
relative to Oset.  is the phase dierence (or phase-
lag) between adjacent modules. us joint signals are the
same with an identical phase dierence. A variety of novel
motionpatternscanbeachievedbymanipulatingthethree
parameters.
2.3. UBotsim Simulator. To quickly verify the eectiveness
of the proposed strategy, a dynamics simulator is required.
Many leading MSRR researchers have developed their own
simulator to customize the analysis and evaluation. A newly
developed D dynamics simulator UBotsim is used to test
the method. It is based on PhysX engine and OGRE (object
oriented graphics rendering engine). Figure shows a screen-
shot of UBotsim. A parameter panel is designed to tune
planning parameters, which is strictly related to the joint
controller ().
3. Planning of Multiple Bionic
Motion Patterns
3.1. Wave Patterns. In wave motions patterns, drive signal
vibrates at the joint osetwhich is always set as ∘.
3.1.1. Undulatory Motion Like Transverse Wave. In this pat-
tern,robotshapelookslikeasinecurveduringmotion
procedure(asshowninFigures(a),(b),and(c)). e
phase dierence is determined by the number of modules
in a complete waveform. Suppose there are modules in a
waveform(herecountmodulesonheadandtailofacomplete
waveformas;belowisthesame);theequationcanbe
achieved as  = 2/(−1).Inotherwords,determines
thenumberofmodulesinasine-waveform.Ifis identical,
the greater the amplitude is, the higher the waveform height
will be.
Figure (d) shows module has displacements both in
horizontal and vertical directions. When right grounding
module is replaced by another module, the robot moves a
distance of .ereare−1replacement processes in a
period of time . Consequently, when is the same, the
higher the waveform is, the faster the robot runs. Here the
robot speed can be written as  V= ((−1)∗ )/. Generally
the greater the amplitude is, the higher the speed is.
e waveform resembles a sine curve if is big. But
considering the geometry and load capacity of actual module,
thereshouldbelessthantenmodulesinacompletewaveform
(it varies for dierent robot). To make the replacement of
grounding modules successful, there should be more than
four modules in a full waveform.
According to the above analysis, motion planning
method for caterpillar robot in sine-waveform can be set as
𝑖()=Oset +∗sin +∗ ,
Oset =0
∘,
∈0,90
∘,
 = 2
−1,≥4.
()
Two types of sine-wave locomotion when takes
dierent values are discussed below.
Caterpillar-Like Locomotion. is locomotion has obvious
arches. To simulate a caterpillar, there should be certain
number of modules in a full-waveform. In this pattern,
the emergence of crest and trough is inevitable. Figure 
illustrates the simulation screenshot that a caterpillar robot
composed of  modules moves in transverse wave. e
shape of the robot looks like the caterpillar. e parameters
are set as =30
∘and  = /4(=9).
Millipede-Like Locomotion. If =4( = 2/3), the
number of modules in a complete waveform is fewest. In
this situation, waveform does not resemble the sine curve.
e number of grounding modules is at its maximum. Robot
movement looks like a millipede. As it is unable to shape
ahigharch,amplitudecan be set to the maximum to
increase motion speed. Figure is a simulation screenshot of
millipede-like locomotion when =90
∘.
As the amplitude increases, waveform height will also
increase.ismayleadtocollisionbetweenmodules.An
instance for =80
∘canbeseeninFigure.Aquestionis
whatthebiggestvalueofis for specic .Innumerical
simulation of kinematics, if any distance between module
centers at time is less than the threshold 1.414∗Module-
Length, corresponding is recognized as the biggest ampli-
tude for corresponding . is condition guarantees that
collision would not happen throughout motion procedure.
To make the motion process stable, the ratio between
wave-height and wave-length should be small, as shown
in Figure . If the ratio is too small, robot locomotion is not
ecient and robot moves slowly. Combining stability and
speed, amplitudes located in
0.2 ≤ ratio =
≤ 0.6 ()
are set as preferred amplitudes scope.

Advances in Mechanical Engineering
1t=t
0
𝜃(𝜙)
−A
A
𝜙
𝜆
Δ𝜙
(a)
2t=t
0+T/12
𝜃(𝜙)
−A
A
Δ𝜙
𝜙
𝜆
(b)
𝜃(𝜙)
Δ𝜙
−A
A
3t=t
0+T/6
𝜙
𝜆
(c)
Motion
direction
s
3
1
2
(d)
F : Locomotion mechanism of caterpillar robot in sine-waveform.
F : Caterpillar-like locomotion of -module robot.
F : Millipede-like locomotion of -module robot.
e biggest and preferred amplitudes are calculated using
numerical simulation. is is implemented in MATLAB as
follows. Firstly, set the metrics of corresponding biggest and
preferred amplitudes. en set coordinates of module ID
as (, ) and compute each module’s coordinate in time
Distance between
module centers
F : Collision example.
(∈[0,]). According to the coordinates information,
we can calculate whether corresponding amplitude fullls
the metrics condition. Here evaluated amplitude values are
integers from ∘to ∘for the sake of reducing computation
time.

Advances in Mechanical Engineering 
h
𝜆
F : Waveform parameters.
Figure illustrates the results; red line is the biggest
amplitude. Other lines represent biggest amplitude when
ratio is less than a specic number. Combining the design
formula (), this can be a reference graph for planning sine-
wave locomotion for series of caterpillar robot.
3.1.2. Peristaltic Motion Like Longitudinal Wave. If  = ,
the robot just expands and contracts its body because joint
angles of adjacent modules are opposite. e robot expands
its body when all joint angles are ∘and contracts its body
when all joints are at amplitude (±). But the whole body
cannot move.
If 2/3 <  < , segment of adjacent modules
can also expand and contract because adjacent module
angles are approximately opposite. Meanwhile there are
both expanding and contracting segments across the whole
body. As time passes, expanding segment and contracting
segment swap states to make robot move like a longitudinal
wave.
Figure  shows joint angle and robot shape states at
two time instants when  = 11/12,=90
∘.When
=
0,theneighborhoodsegmentofjointangleequalto
∘(blue area) is in expanding state, and center distance of
adjacent modules projected in motion direction is large and
shapesthesparsepartoflongitudinalwave.eareaofjoint
angle equal to −∘(red area) is in contracting state, center
distance of adjacent modules projected in motion direction
is small, and this segment shapes dense part of longitudinal
wave. When =
0+ /4, joint of ∘rotates to ∘and joint
−∘to ∘; expanding and contracting states switch. Dense
part is useful for support robot and sparse part for transfer
modules. is is a little analogous to the peristaltic motion of
earthworm.
e module whose joint angle is at ± is the center
ofdensepartandthemodulewhosejointangleisat
∘
is the center of sparse part. In a period of ,amodule
can be the center of dense and sparse part twice. Modules
between adjacent dense (or sparse) centers create a complete
longitudinal waveform. e phase dierence of two adjacent
4 5 6 7 8 9 10
20
30
40
50
60
70
80
90
Number of modules in a complete wave
Amplitude (deg)
Biggest amplitude
Ratio ≤ 0.6
Ratio ≤ 0.5
Ratio ≤ 0.4
Ratio ≤ 0.3
Ratio ≤ 0.2
F : Amplitude design reference in sine-waveform motion.
dense (or sparse) centers is .Supposetherearemodules in
a complete waveform. is is accumulated by −1controller
deviation of  from ;thatis,( − 1) ∗ ( − ) = .
Consequently, peristaltic motion design formula is achieved
as
𝑖()=Oset +∗sin +∗ ,
Oset =0
∘,
∈0,90
∘,
 = − 
−1,>4.
()
e larger the amplitude is, the denser the contracting
part will be. Owing to the wave height is small, amplitude 
couldhaveabiggervaluewithoutconcerningaboutmodule
collision. To make a robot move in complete waveform, 
should be less than the robot module number. When is
larger than , the longitudinal eect becomes apparent.
Earthworm-Like Locomotion. An earthworm can move for-
ward by stretching its special body structure, as shown in
Figure (a) []. Using above method, this type of locomotion
can be simulated in articulated chain-type robot, as shown in
Figure (b). e simulation screenshots are a half-motion
when =90
∘and  = 11/12. It can be seen that the robot
moves by alternately exchanging dense part and sparse part
just like the earthworm.
3.2. Closed-Loop Rolling. Technical artifacts can surpass
locomotion abilities of natural creatures; for example, a
caterpillar robot can roll in a loop. e caterpillar robot
composed of UBot MSRR modules can form a loop by
connecting head and tail module. More than ve modules
are needed to make a loop suitable for motion. In a rolling
loop, the sum of exterior angles must be ∘.Figure
illustrates the exterior angles of a polygon. Joint angle shapes
the exterior angle.