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Single actuator wave-like robot (SAW): Design, modeling, and experiments



In this paper, we present a single actuator wave-like robot, a novel bioinspired robot which can move forward or backward by producing a continuously advancing wave. The robot has a unique minimalistic mechanical design and produces an advancing sine wave, with a large amplitude, using only a single motor but with no internal straight spine. Over horizontal surfaces, the robot does not slide relative to the surface and its direction of locomotion is determined by the direction of rotation of the motor. We developed a kinematic model of the robot that accounts for the two-dimensional mechanics of motion and yields the speed of the links relative to the motor. Based on the optimization of the kinematic model, and accounting for the mechanical constraints, we have designed and built multiple versions of the robot with different sizes and experimentally tested them (see movie). The experimental results were within a few percentages of the expectations. The larger version attained a top speed of 57 cm s(-1) over a horizontal surface and is capable of climbing vertically when placed between two walls. By optimizing the parameters, we succeeded in making the robot travel by 13% faster than its own wave speed.
Abstract— In this paper, we present a single actuator
wave-like robot (SAW), a novel robot which can move
forward or backward by producing a continuously
advancing wave. The robot has a unique minimalistic
mechanical design and produces an advancing sine wave,
with a large amplitude, using only a single motor but with
no internal straight spine. The direction of locomotion is
determined by the direction of rotation of the motor. A
kinematic model of the robot is developed that accounts
for the two-dimensional mechanics of motion and yields
the speed of the links relative to the motor. Based on the
optimization of the kinematic model, and accounting for
the mechanical constraints, we have designed and built
multiple versions of the robot with different sizes and
experimentally tested them (see movie). The experimental
results were within a few percentages of the expectations.
The larger version attained a top speed of 23 cm/s over a
horizontal surface and is capable of climbing vertically
when placed between two walls. By optimizing the
parameters, we succeeded in making the robot travel by
13% faster than its own wave speed.
In the last decades, multiple studies have analyzed the
locomotion of crawling robots inside tubes for maintenance
purposes and in biological vessels for medical applications.
In many of those applications, the robots must overcome
rough terrain characterized by anisotropic properties, high
flexibility, varying dimensions, and low friction coefficients
[1]-[4]. A key element in the design of small crawling robot
is a minimalist approach, i.e. small number of motors and
controllers, which allows for miniaturization. Two main
locomotion patterns have been investigated: worm-like
locomotion [5]-[26] and undulating locomotion which
resembles a continuously advancing wave [27]-[43]. Worm-
like robots advance by changing the distance between their
links [5]-[26]. There are two types of worm-like robots;
inchworm-like robots and earthworm-like robots. Inchworm-
like robots [5]-[16] are generally made of two cells
(sometimes three3 as in [15]) fitted with clamps to increase
or decrease the friction forces by changing the normal forces
or the coefficients of friction. Earthworm-like robots [17]-
[24] are made of a larger number of cells, often four or more.
Multiple mechanisms of locomotion were developed using
magnet coils [19], shape memory alloys [17], an external
electromagnetic field [20],[21] and inflatable cells [23].
The Authors are with the Mechanical Engineering Department of Ben
Gurion University P.O. Box 653 Be’er Sheva 8855630 Israel (e-mail:
This research was partially supported by the Helmsley Charitable Trust
through the Agricultural, Biological and Cognitive Robotics Initiative of
Ben-Gurion University of the Negev.
Using the inflatable cells approach, Glozman et al. [24]
applied one actuator and a single air/water source to drive an
inflatable worm made of multiple elastic cells inside the
intestines of a swine. Novel designs of inchworm-like and
earthworm-like robots actuated by a single motor were
developed by Zarrouk et al. [25],[26]. This minimalist design
allowed us to reduce the size, weight, energy consumption,
and to increase the reliability of the robot.
Fig. . The novel single actuator wave like robot (SAW). The robots have a
spine that constrains the links to move around it, producing an advancing
wave like motion (see movie .(
Wave-like locomotion was successfully produced by hyper
redundant snake robots [27]-[34] only (even though,
kinematically speaking a single actuator is required). The
first documented attempt to produce wave like locomotion
dates back to the 1920s by artist Pyotr (Petr) Miturich [41]
who suggested a design comprising an assembly of gears.
But nearly 30 years later the problem remained unsolved.
Taylor et al. (1951-1952) [36],[37][36], who investigated
the locomotion of wave-like and spiral-like locomotion in
low Reynolds environment, expressed his inability to
develop a mechanism that will allow to produce those
motions in order to experimentally validate his analysis.
More recently, some progress was reported by producing
cyclic motion with a small number of actuators which to a
certain extent resembles a wave but is actually a rigid straight
spine Error: Reference source not found-[41]. Other attempts
included producing a wave by vibrating a rod [42],[43], but
this method results in relatively small amplitudes whose size
is a function of the damping.
In this paper, we present the first single actuator wave-like
robot (SAW) which can produce a nearly perfect sinusoidal
advancing wave-like motion (Fig. ). In Section II, we
describe the kinematics of the wave locomotion. In Section
III, we present our novel design for the wave-like robot and
model its kinematics in Section IV. The kinematical model
Single Actuator Wave-Like Robot (SAW): Design, Modeling, and
David Zarrouk, Moshe Mann, Amotz Hess
was used to optimize the design of the robot. Finally,
experiments performed with the robots which we built are
presented in Section V.
In this section, we show that the projection of a rotating
helix forms an advancing sine wave.
A. Traveling wave
The simplest model of traveling wave is an advancing sine
wave, or harmonic wave. Its mathematical presentation is
( ) ( )
, siny x t A kx wt
= −
where x is the space coordinate, t is the time, y is the height
of the wave at point x and time t, and A is the amplitude. The
angular velocity w of the wave is related to the frequency by
and the wave length L of the traveling wave is related to the
wave number by
The travelling speed of the wave is thus
V f L k
= × =
B. Mathematical model of helix and its projection.
A helical curve with its axis in the x direction is described
parametrically by
( )
( )
x a
y A a
z A a
= ×
where L is the length of the pitch and A is the radius of the
helix and a is the independent paramter. The two
dimensional projection of the helix on the X-Y plane ( z = 0)
yields the following sine function:
( )
sin sin
x a
y A a A L
= ×
 
= =  ÷
 
A 3D helix whose axis is parallel to the x direction and its 2D
projection on the X-Y plane are presented in Fig. . Its
projection is a sine wave, as seen from Eq. )(
Fig. . A helix and its projection on the X-Y plane. The projection of the helix
is a sine wave, where the amplitude is the radius of the pitch .
C. Rotating helix and comparison to traveling wave.
When the helix rotates around its axis (the x axis) at a
constant angular frequency w (counterclockwise) the
parametric equations of the helix (Eq. ()) are multiplied by
the rotation matrix around the x axis:
( )
( )
( ) ( ) ( )
( ) ( ) ( )
( )
( )
( )
, 1 0 0 2
, 0 cos sin sin
, 0 sin cos cos
x a t
y a t wt wt A a
z a t wt wt A a
A a wt
A a wt
 
 
   
 
=  
   
 
   
 
 
 
 
= −
 
 
 
 
Inserting a = 2π/L*x into y demonstrates that the projection
of the rotating helix is an advancing sine wave given by:
In the previous section, we showed that the projection of a
rotating helix is an advancing sine wave. Our robot design,
which uses a single motor to produce an advancing wave,
follows the same concept. The robot is composed of four
main parts: the motor house, the motor, the helix, and the
series of links (Fig. ). The motor is attached to the motor
housing from one side and to the helix from the other side.
The links are attached to the motor house. As the motor
rotates the helix, the links cancel the rotation along the axis
of the helix and maintain the vertical motion. In this way, the
links act as a 2D projection of the helix of the robot.
The helix of the larger version is nearly 25 cm long and is
composed of two windings and a short extension to reduce its
diameter. Its external diameter is 5.2 cm and its radius is A =
2.1 cm. The links, presented in Fig. , are 7 cm wide 1.83 cm
high (r = 0.9 cm), and the distance between the joints of two
links is 1.2 cm (Llink = 1.2 cm). The smaller version is nearly
scaled down by a factor of nearly 2:1 and the smallest is
scaled down by a factor of 3:1. The helix and the links are
3D printed. The robot is fitted with a 6 Volt, 12 mm motor
with 300:1 gear ratio. Based on its catalog specifications, the
motors and gearbox produce a torque of 2.9 Kg-cm at 45
rpm. It is noted that in most of the experiments (except when
specified otherwise), we used a single ~4V lithium–ion
battery which is substantially lower than its nominal input (6
-9 Volts). The total weight of the larger robot including one
battery is 188 grams, whereas the smaller one weighed only
47 grams only.
Fig. . The different parts of the robot. The robot has a housing for the motor.
The helix is attached to the motor and rotates relative to the housing. The
links are attached to the housing and do not undergo roll rotation.
In this section, we model the kinematics of the links and
calculate their speed relative to the head of the robot (motor
housing) as a function of its frequency of locomotion f, the
wave length Lwave, the amplitude of the wave A, the length of
the link Llink, and its height r. If the links do not slide over the
surface, (as we experimentally found in section 5 - Fig. ), the
speed of the robot will be equal to the speed of the tips of the
links, along the axis direction. We define the advance ratio
(AR) as the speed of the robot Vrobot divided by the speed of
the travelling wave relative to the motor base Vwave:
wave wave
= =
where Vrobot is the speed of the robot, Lwave is the length of the
wave, and Lcycle is the net advance per cycle (one rotation of
the helix)
robot cycle
V f L
Fig. . The The geometry of the link. The two main parameters are the link
length Llink, the distance between two adjacent joint, r is the height of the link
and wtip is the width of the tip.
A. Kinematics of the links
As the wave advances, the links move both horizontally
and vertically. As the wave advances by Δx, the link will
rotate by Δα (see Fig. ).
( )
( )
( )
( )
( )
atan cos atan sin
x x
dA kx kA k x
 
∆ = =
 ÷
 
Due to the rotation, the tip of the link will move by a distance
( )
sinX r
∆ =
If the speed of the wave is Vwave, the time required by the
wave to advance by a distance of Δx is
t x V = ∆
Therefore the expected speed of the link is
Inserting Eqs. ()-() into Eq. () we obtain the speed of the tip
of the link
( )
( )
( )
sin tan sin
link wave
r a kA k x
− ∆
If we assume small angles
( )
( )
2 2
k x k x
a Ak x Ak x
≈ ∆
∆ ≈
And finally, by inserting Eq. () into Eq. (), one obtains the
speed of the tips of the links as a function of the height r,
amplitude A, wave length Lwave, and wave speed Vwave.
link wave wave
V rAk V rA V
 
=  ÷
 
Alternatively, the speed of the wave can be calculated as a
function of the actuation frequency:
( )
link wave
V rAk V r f
≈ =
Therefore the speed of the link is proportional to the ratio of
the amplitude divided by the wave length, to the height of the
links and to the actuation frequency. In theory, it would be
advantageous to increase A/Lwave and r to increase the speed.
However, increasing those values results in collision between
the tips of neighboring links. This collision is most likely to
occur when two links are symmetrically oriented towards
each-others such as links i-1 and i in Fig. case A. Assuming
zero width of the tips of the links, collision will occur when
/ 2
= ∆
 ÷
 
Inserting the value of Δα into from Eq. () into (), it is possible
to obtain the condition of collision as a function of the size of
the links and the wave parameters.
kA k
 
 
 ÷
   ÷
 ÷
 ÷  
= −  ÷
 ÷  ÷
 
 ÷  
 ÷ +
÷ ÷
   ÷
 ÷
 ÷
 
 
 
Fig. . The rotation of the links during the adavnce of the wave. “A” marks
the beignning of the touchdown of link i and retraction of link i-1. In “B”,
the wave has advanced by Δx and link i is at the lowest point of the wave.
“C”, which occurs after the wave advances by a further Δx, marks the end of
the touching of link “i” and the beginning of the engagement of i+1.
A. Kinematics of the links
We assume that the links slide along the advancing wave
(rotating helix) while the first link is attached to the motor
housing. The number of links is determined by the length of
the wave Ltot divided by the length of the links.
( )
L N y x dx
 
 
= +
 ÷
 ÷
 ÷
 
 
where N is the number of waves in the sine function (N = 2 in
our robot). Equation Chapter 1 Section 1To calculate the
positions of all the links of the robot, we sequentially solve
for the location of the endpoint of each link along the sine
wave. That is, we start with the location of the joint i of link
[xi yi] and solve for the x coordinate of the link’s endpoint
[xi+1 yi+1] by assuming that it is fastened to the sine wave
using the equation:
( ) ( )
2 2 2
1 1
sin( ) y
i i link
i i
x x A kx t L
+ +
+ − − =
where Llink is the length of each link. Solving Eq. () returns
the position of the end point xi+1 of link i. The endpoint of
link “i” serves as the start point of link “i+1”, and so on until
the last link’s location is solved for. The location of each
link’s start point and end point provides complete
information of the link’s orientation, and is used to calculate
the location of the links’ tip [x_tipi y_tipi]:
1 1
1 1
_ 0
_ 0
0 0 0 0 1
i i i i i i
i i i i i i
x tip x x x x x
y tip y y y y y r
+ +
+ +
− −
 
 
= + + − ×
 
 
 
The position of the links when the motor housing is fixed
was simulated using MATLAB (2013) program. Equations
() and () were solved at a rate of 500 times per cycle (results
and optimization are summarized in Fig. and in Ttable I).
The velocity is obtained by deriving the position as a
function of the time. In the simulation, we also accounted for
the width of the tip of the link, since in practice, the width
must be a few millimeters (in the simulation, we used wtip =
0.05 Lwave).
A two dimensional side projection of the simulated robot
is shown in Fig. . The robot consists of 25 rigid links
connected through revolute joints formed into a sine wave of
two spatial cycles. We focus here on the motion of link 5. As
link 5 approaches the lower bottom of the wave, it moves
slightly horizontally and rotates clockwise. Both of these
motions add up to move the bottom tip to the left, and
therefore the robot would move to the right.
Fig. . The simulation of the robot. The “motor housing” is rigidly fixed. As
the wave adavances from left to rightright to left, the lower tips of the links
which will be in contact with the surface move slightly towards the left and
rotate clockwise.
B. Expected robot advancement speed
The simulation allowed us to visually gain insights into
the motion of the links and optimize the design of the robot.
If no sliding occurs, the speed of the robot will be equal (but
to the opposite direction) to the horizontal speed of the links
contacting the surface. Therefore, the simulation calculates
the position of the different links at all times and detects
which of the links is the lowest, i.e. expected to be in contact
with the ground. Averaging the speed of the lowest tips yields
the expected speed of the robot.
In Fig. , we present the advance ratio as a function of the
amplitude for 3 different values of links heights (r/Lwave).
Since practically speaking, the tips of the links have a width
wtip, we determine the maximum value of the amplitude
which results in the collision marked with *. By assuming
that the width of the tips is 5% of the wave length, we found
that the maximum AR is limited to nearly 0.7 in all three
cases because of the collisions between the tips of
neighboring links. See our the Aappendix on how we
managed to overcome this limitation.
Fig. . The advance ratio as a function of the amplitude for three different
heights. The asterix (*) marks the limit for which two neighboring links will
collide with each others.
In Section IV, we calculated the speed of the links as a
function of the different robot parameters such as the length
of the wave, the distance between the links, and their width.
In this section, we will experimentally measure the speed of
our 3D printed robot and compare it to the results of the
simulation. The position of the robot is measured using a 12
cameras Optitrack setup with a frequency of 120 Hz. The
accuracy of the system is nearly 0.1mm. We designed a
special link for holding the reflective marker at the lower tip
of the link (Fig. ). The special link has a side attachment for
the marker in which the center of the marker is on the axis of
the contact line with the surface. Using this link, the marker
remained on the side of the surface and would not interfere
with the experiment. The speed is determined by deriving the
position as a function of the time.
Fig. . A special link was manufactured to hold the reflective marker. The
center of the reflective is along the axis of the tip of the link.
A. Speed of the links
In our first experiment, we determined the trajectory of the
lower tip of one of the links (using the special link) when the
robot motor house was rigidly fixed. The trajectory and the
orientation of the tip of 8 cycles are presented in Fig. . The
motion is very cyclic with very little difference between one
cycle to and another. During a cycle, the tip moves vertically
by nearly 4 cm. This result is slightly less than expected (2*A
= 4.2 cm) and probably due to slight spacing between the
links and the helix. The horizontal motion is nearly 2 cm.
However, the motion of the link from the onset of contact
until disconnecting from the surface is nearly 1 cm.
Fig. . The motion of the bottom tip of the link during 8 cycles when the
robot is not moving. The arrow show the direction of motion.
In the second experiment, the robot was free to advance
and the position of the links was measured using the
Optitrack setup. We performed the experiments over
plywood and over aluminum which has a lower COF with
the links (nearly 0.3 whereas the COF over plywood is nearly
0.4).The results of the trajectory and the speed along the x
axis are presented in Fig. (over aluminum surface). The
trajectory shows that the link touches the surfaces at a single
contact point. Therefore the link is not sliding over the
surface and its relative speed to the surface is zero. Sliding
didn’t occur also when the robot was run at higher speeds.
Fig. . (Top) The position of the lowest tip of a link during horizontal
locomotion over alumium surface. The single point contact at each cycle
proves that no slide between the links and the surface. (Bottom) The
horizontal speed of the links.
Table 1, summarizes the results of multiple experiments that
we performed by the smaller and bigger versions of our
robots. The data is the average of at least 12 cycles. The
results were compared to the simulations and found to be
within a few percentage of each-others. The larger and
smaller versions performed nearly similarly for two different
amplitude to wave length ratios. Following the predictions of
the simulation, we designed special links with large height
that allowed the robot to advance by 13% faster than the
speed of the wave (AR = 1.13). We note here that a short
survey that we made with multiple roboticists found that they
all believed it is impossible to advance faster than the speed
of the wave!
Table I. The advance ratio as a function of the slope.
Lwave A/Lwave r/Lwave Aver. AR STD ΔAR/Lcycle
[cm] [cm] [cm] Lcycle/Lwave AR
Large SAW
10.4 0.2 0.088 0.71 1.7% 2%
10 0.1 0.092 0.33 1.7% 5%
10.4 0.2 0.168 1.13 4.3% 2%
Small SAW
5 0.2 0.092 0.76 7.7% 8%
5 0.1 0.092 0.38 4.4% 8%
B. High speeds
We performed two more experiments to reach higher
speeds with the robot. In the first experiment, we used the
same set up, but we powered the robot with two Lithium-ion
batteries in series producing 8 Volts instead of a single
battery. The robot reached a speed of 10.4 cm/s. In the
second experiment, we attached three batteries in series (12
Volts) and used a 1:100 gear ratio (instead of 1:300). In this
configuration, the robot crawled at 23 cm/s. It is noted that
even at high speed no sliding was observed between the
robot and the surface.
C. Crawling over slopes and vertically between walls
We also the tested ability of the robot to climb by placing
the robot between two layers of polyurethane foam whose
COF with the links of the robot is nearly 0.4. The robot was
powered by two Litium ion battery (as it was not able to
move using a single one) and climbed at a speed of 8.2 cm/s.
The experiment is presented in Fig. . Note that in this
experiment, the two walls must be precisely distanced from
each other (up to a few millimeters of accuracy) in order to
achieve enough normal force for climbing, but without
overly pressing on the robot as it will stall.
Fig. . The robot climbing vertically between two walls. Using 8V input,
the robot reached a speed of 8.2 cm/s.
In this article, we developed a novel robot which generates
an advancing wave, that is nearly identical to a sine wave, by
rotating a helix that moves the links. The robot design is
simple, lightweight, cheap, and requires only a single motor
only to produce the wave. The direction of wave propagation
is determined by the sign of the voltage being applied to the
motor. We developed two prototypes:. tThe larger one with a
wave length of 10 cm thTand weighs only 188 gramsand a
1:2 smaller version weighing 47 grams. Both prototypes
proved to be highly reliable (considering that they are 3D
printed prototypes). During all of our experiments,
practically almost no maintenance was required.
We studied the kinematics of the links and developed a
simple model that explains how the motion is produced. The
model also predicts the approximated speed of the lower tips
of the links as a function of the wave length and amplitude
and size of the links. We also developed a simulation which
calculates the speed and visually presents the locomotion and
detects where collisions between the links will occur. The
simulation allowed us to visually comprehend the locomotion
mechanics and optimize the robot. We introduced the
advance ratio (AR) as the speed of the robot divided by the
speed of the wave. We found that in general, the AR is
smaller than 1, but by increasing the height of the links, the
advance ratio can be larger than 1 (A short survey between
roboticist showed us that they all believed that AR = 1 is the
maximum possible speed).
We measured the speed of the robot and the speed of the
lower tip of a link using an Optitrack system. By measuring
the speed of the lower tip of the link, we found that it
contacts the surface in at a single point, implying that not
sliding does not occurs. We performed multiple experiments
and found that they are all within a few percentages from the
expected speed by the simulation. By applying 12 Volts to
the motors, the robot moved at up to 23 cm/s and no sliding
was detected even in this case. The robot was also capable of
climbing vertically when finely placed between two surfaces
polyurethane foam at a speed of 8.2 cm/s.
Our future work will focus on analyzing the locomotion
of this type of robots over compliant and slippery surfaces.
A. Turning using steering wheels
We added steering wheels to the front of the robot as seen
in Fig. . The robot is now controlled using a two channel
joystick (extracted from an RC toy car - see movie). We
performed multiple experiment in crawling straight and
turning and captured the position using our Optitrack set up.
The results show that the robot can turn to either direction and
that the radius of turning was nearly 0.3 m.
Fig. . The robot with steering wheels. The direction of turning is
controlled by a second motor.
The results are presented in Fig. in which the name of the
robot is written (SAW). All the letters were completed in a
single run with no external intervention.
Fig. . The position of the robot with steering wheels. The robot wrote his
B. Increasing the height to travel faster than the speed of
the wave
To increase the speed of the robot beyond the speed of the
wave, we developed three sets of links with different tips
which do not collide with each-others (see Fig. ). The height
r was nearly 1.75 cm. Using those links, the robot achieved a
speed which is 13% larger than the wave speed.
Fig. . The specially designed links that do not collide with each others.
C. Miniaturization
To Tthe single motor design allows for further
miniaturization of the robot. Our smallest version (Fig. 15) is
12 cm long and 3 cm wide and weighs 30 grams including the
motor and battery. It was tested and shown to be crawling at
nearly 3cm/s (see movie). Further miniaturization of the robot
is possible and depends on more precise manufacturing.
Fig. . The smallest version of the robot. The length is nearly 12 cm and
the width is about 3cm.
[1] N.K. Baek, I.H. Sung and D.E. Kim, “Frictional resistance
characteristics of a capsule inside the intestine for microendoscope
design,” Proc. Instn. Mech. Engrs, vol. 218 Part H: Journal of
Engineering in Medicine.
[2] X. Wang and M.Q.-H. Meng, “Study of frictional properties of the
small intestine for design of active capsule endoscope,” 2006 1st
IEEE RAS & EMBS International Conference on Biomedical
Robotics and Biomechatronics, 6 pp., 2006.
[3] K.D.Wang and G.Z.Yan, “Research on measurement and modeling of
the gastro intestine's frictional characteristics,” Measurement Science
& Technology, vol. 20, no. 1, 015803 (pp. 6), 2009.
[4] Fung. Y.C. "Biomechanics, Mechanical Properties of Living Tissues".
Springer-Verlag New York, Inc. 1993.
[5] P. Dario, P. Ciarletta, A. Menciassi, and B. Kim, “Modeling and
experimental validation of the locomotion of endoscopic robots in the
colon,” International Journal of Robotics Research, vol. 23, no. 4-5,
pp. 549-556, 2004.
[6] I. Kassim, L. Phee, W. S. Ng, G. Feng, P. Dario and C.A. Mosse,
“Locomotion techniques for robotic colonoscopy ,” IEEE
Engineering in Medicine and Biology Magazine, vol. 25, no. 3, pp.
49-56, 2006.
[7] L. Phee, A. Menciassi, S. Gorini, G. Pernorio, A. Arena, and P. Dario,
“An innovative locomotion principle for minirobots moving in the
gastrointestinal tract,” Proceedings of the IEEE International
Conference on Robotics and Automation, vol. 2, pp. 1125-1130, 2002.
[8] L. Phee, D. Accoto, A. Menciassi, C. Stefanini, M.C. Carrozza and P.
Dario, “Analysis and development of locomotion devices for the
gastrointestinal tract,” IEEE Transactions on Biomedical
Engineering, vol. 49, no. 6, pp. 613-616, 2002.
[9] L. Phee, A. Menciassi, D. Accoto, C. Stefanini, and P. Dario,
“Analysis of robotic locomotion devices for the gastrointestinal
tract,” Robotics Research, STAR 6, pp. 467-483, 2003.
[10] A. Menciassi, S. Gorini, G. Pernorio, and P. Dario, “ A SMA actuated
artificial earthworm,” Proceedings IEEE International Conference on
Robotics and Automation, pp. 3282-3287, 2004.
[11] B. Kim, S. Lee and J. Park, “Design and fabrication of a locomotive
mechanism for capsule-type endoscopes using shape memory alloys
(SMAs),” IEEE/ASME Transactions on Mechatronics, vol. 10, no.1,
pp. 77-86, 2005.
[12] B. Kim, H.Y. Lim and J. H. Park. “Inchworm like colonoscopic robot
with hollow body and steering device,” JSME International Journal,
Series C, vol. 49, no. 1, pp. 205-212, 2006.
[13] J. Lim, H. Park, J. An, Y.S. Hong, B. Kim, B.J. Yi, “One pneumatic
line based inchworm-like micro robot for half-inch pipe inspection,”
Mechatronics, vol. 18, pp. 315–322, 2008.
[14] J. Li, R. Sedaghati, J. Dargahi and D. Waechter, “Design and
development of a new piezoelectric linear Inchworm Actuator,”
Mechatronics, vol. 15, pp. 651–681, 2005.
[15] V.K. Asari, S. K. Irwan and M. Kassim, “A fully autonomous
microrobotic endoscopy system,” Journal of Intelligent and Robotic
Systems, vol. 28, pp. 325–341, 2000.
[16] A. Brett Slatkin, J. Burdick and W. Grundfest, "The Development of
a Robotic Endoscope", Experimental Robotics IV. vol. 223, pp. 162-
171, 1995.
[17] A. Menciassi, D. Accoto, S. Gorini, and P. Dario, “Development of a
biomimetic miniature robotic crawler,” Autonomous Robots, vol. 21,
no.2, pp. 155-163, 2006.
[18] B. Kim, M.G. Lee, Y.P. Lee, Y. Kim, and G. Lee, “An earthworm-like
micro robot using shape memory alloy actuator,” Sensors and
Actuators, A: Physical, vol. 125, no. 2, pp. 429-437, 2006.
[19] D. Chi and G. Yan. “From wired to wireless: a miniature robot for
intestinal inspection,” Journal of Medical Engineering & Technology,
vol. 27, no.2, pp. 71-76, 2003.
[20] K. Wang, G. Yan, P. Jiang and D. Ye, “A wireless robotic endoscope
for gastrointestine,” IEEE Transactions on Robotics, vol. 24, no.1,
pp. 206-210, 2008.
[21] K. Wang, G. Yan, G. Ma and D. Ye, “An earthworm-like robotic
endoscope system for human intestine: Design, analysis, and
experiment,” Annals of Biomedical Engineering, vol. 37, no. 1, pp.
210-221, 2009.
[22] N. Saga, T. Seto, H. Takanashi and N. Saito. “Development of a
peristaltic crawling robot using planar link mechanisms,” IEEJ
Transactions on Electrical and Electronic Engineering, vol. 3 no.1,
pp. 72-78, 2008.
[23] J. Dietrich, P. Meier, S. Oberthur, R. Preub, D. Voges, and K.
Zimmermann, “Development of a peristaltically actuated device for
the minimal invasive surgery with a haptic sensor array,” available
[24] D. Glozman, N. Hassidov, M. Senesh, and M. Shoham, "A self-
propelled inflatable earthworm-like endoscope actuated by single
supply line," IEEE Transactions on Biomedical Engineering, vol. 57,
no. 6, pp. 1264-1272, 2010.
[25] D. Zarrouk, I. Sharf, and M. Shoham, “Conditions for worm-robot
locomotion in a flexible environment: theory and experiments,” IEEE
Transaction on Biomedical Engineering, vol. 59, no. 4, pp. 1057-
1067, 2012.
[26] D. Zarrouk, I. Sharf, and M. Shoham, “Analysis and design of one
degree of freedom worm robots for locomotion on rigid and
compliant terrain”, ASME, Journal of Mechanical Design, vol. 134,
no. 2, 2012.
[27] H. Kimura, K. Shimizu, and Shigeo Hirose, "Development of Gnbu:
Active-Wheel Passive-Joint Snake-Like Mobile Robot". Journal of
Robotics and Mechatronics, Vol. 16, No. 3, 2004.
[28] Ostrowski J., Burdick J., "Gait kinematics for a Serpentine Robot",
Proceedings of the IEEE International Conference on Robotics and
Automation, 1996.
[29] Mori M., Hirose S., "Locomotion of 3D Snake-Like robots – Shifting
and rolling Control of Active Cord Mechanism ACM-R3". Journal of
Robotics and Mechatronics. vol. 18, no. 5. 2006.
[30] Chirikjian G., Burdick J.W., "The Kinematics of Hyper-Redundant
Robot Locomotion", IEEE Trans. On Robotics and Automation, vol.
11, no. 6, 1995.
[31] Burdick, J.W., Radford, J., and Chirikjian, G. S., "Sidewinding
Locomotion Gait for Hyper redundant robots". Advanced Robotics,
vol. 9, no. 3, pp 195-216, 1995.
[32] Lu Z., Ma S. Li B., and Wang Y., "3D Locomotion of a Snake-Like
Robot Controlled by Cyclic Inhibitory CPG Model". Proceedings of
the International Conference on Intelligent Robots and Systems,
[33] Hirose S., Fukushima E.F., "Snakes and Strings: New Robotics
Components for Rescue Operations". International Journal of
Robotics Research, vol. 23, pp. 341-349, 2004.
[34] Wolf A, Choset H,Brown HB, Casciola R, "Design and Control of a
Mobile Hyper-Redundant Urban Search and Rescue
Robot", International Journal of Advanced Robotics, vol 19 (8)
pp.221-248, 2005.
[35] PhD thesis. G.J. Goldman, “Design space and motion development
for a pole climbing serpentine robot featuring actuated universal
joints”, PhD thesis, Virginia Polytechnic Institute and State
University, 2009.
[36] G. Taylor, "Analysis of the swimming of microscopic organisms."
Proceedings of the Royal Society of London A: Mathematical,
Physical and Engineering Sciences. Vol. 209, No. 1099, pp. 447-461,
[37] G. Taylor, "The action of waving cylindrical tails in propelling
microscopic organisms." Proceedings of the Royal Society of London.
Series A, Mathematical and Physical Sciences, pp. 225-239, 1952.
[38] T. Hu, L. Shen, L. Lin and H. Xu, “Biological inspirations,
kinematics modeling, mechanism design and experiments on a
undulating robotic fin inspired by Gymnarchus niloticus”,
Mechanisms and Machine Theory, vol. 44, pp. 633-645, 2009.
[39] K.A. Daltorio, A. S. Boxerbaum, A. D. Horchler, K. M. Shaw, H. J.
Chiel, and R. D. Quinn “Efficient worm-like locomotion: slip and
control of soft-bodied peristaltic robots”, Bioinspiration and
Biomimetics. Vol. 8, doi:10.1088/1748-3182/8/3/035003, 2013.
[40] P. Phamduy, R. LeGrand, and M. Porfiri, “Robotic Fish”, IEEE
Robotics and Automation Magazine, DOI,
[41] A. S. Boxerbaum, K. M. Shaw, H. J. Chiel, and R. D. Quinn,
“Continuous wave peristaltic motion in a Robot”, The International
Journal of Robotics Research, vol. 31, no. 3, pp. 302–318, 2012.
[42] L. Wen, and G. Lauder, “Understanding undulatory locomotion in
fishes using an inertia-compensated flapping foil robotic device”,
Bioinspiration and Biomimetics, vol. 8, DOI:10.1088/1748-
182/8/4/046013, 2013.
[43] F. Liu, K.M. Lee, and C.J. Yang, “Hydrodynamics of an Undulating
Fin for a Wave-Like Locomotion System Design” IEEE/ASME
Transactions on Mechatronics, vol. 17, no. 3, pp. 554-5622012.
... A minimalistic approach is commonly utilized to achieve efficient design, which involves a small number of motors and actuators. Three types of locomotion have been explored in these studies: screw-like locomotion [5,6], worm-like locomotion and undulating locomotion, which mimics a continuously advancing wave [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. ...
... However, these speeds are significantly slower when compared to the two fastest wave-like robots, the SAW and AmphiSAW. The SAW robot achieved a maximum speed of 57 cm/s when crawling over a rigid surface [29], and its amphibious version, the AmphiSAW, boasts a remarkable maximum ground speed of 77 cm/s when crawling on a polypropylene fabric solely relying on its wave-like mechanism [44]. ...
... Drawing inspiration from the wave-like locomotion observed in snakes and flagella, as well as the swimming patterns of miniature organisms, we previously introduced the Single Actuated Wave robot (SAW) [29]. SAW generates its wave motion by employing a rotating helix in combination with numerous links that are connected to one another via rotational joints. ...
Full-text available
In a recent study, we developed a minimally actuated robot that utilizes wave-like locomotion and analyzed its kinematics. In this paper, we present an analysis of the robot’s locomotion between two highly flexible surfaces. Initially, we created a simulation model of the robot between two surfaces and determined its speed and the conditions of locomotion based on the flexibility of the surface, the geometrical parameters, and the coefficient of friction for horizontal locomotion and climbing at different angles. Our findings indicate that wave locomotion is capable of consistently advancing along the surface, even when the surface is highly flexible. Next, we developed an experimental setup and conducted multiple experiments to validate the accuracy of our simulation. The results indicate an average relative difference of approximately 11% between the speed and advance ratio of the wave crawling between the two surfaces of our simulation model and the experimental results were performed using an actual robot. Lastly, we compared the wave locomotion results to those of the worm locomotion and discovered that wave locomotion outperforms worm locomotion, especially at a higher surface flexibility.
... Bioinspired crawling robots have generated significant interest due to their ability to move on various surfaces and around multiple obstacles, which can be categorized into inchworm-like robots [12,13], earthworm-like robots [14,15], and snake-like robots [16,17]. Recently, a novel wave-like mechanism has been proposed, which imitates the locomotion of snakes and the flagellar swimming of microscopic organisms and can advance over anisotropic and flexible terrains with varying surface properties [18][19][20][21]. Based on this, it uses a single motor to actuate the locomotion of the entire mechanism, which meets the requirement of the high integration of RMM robots. ...
... Furthermore, the links have a length l l of 40 mm and a height h l of 12.5 mm. Increasing φ h /L and h l would improve the robot's velocity at the same motor speed; however, it may result in collisions between the links [18]. A compromise between the desired speed and collision avoidance was considered in our design. ...
... The linear velocity v s of a single SWC robot is equal to the motion velocity of the links contacting the ground and is approximately proportional to the rotation frequency f of the helix. The relationship between v s and f is [18] ...
Full-text available
Traditional mobile robots with fixed structures lack the ability to cope with complex terrains and tasks. Reconfigurable modular mobile robots have received considerable attention as they can automatically reassemble according to the changing environment or task. In this paper, a new self-reconfiguration wave-like crawling (SWC) robot is presented to improve the mobile robots’ locomotion capacity. First, the mechanical design of the wave-like crawling mechanism is detailed. Then, the series and parallel connections are introduced to achieve self-reconfiguration. In addition, the kinematic model of the SWC robot is established. Finally, experiments were performed to verify the robotic system with wireless data transmission.
... The recently developed AmphiSAW is a reliable, simple to design, light weight and low cost amphibious robot fitted with a wave propulsion mechanism which generates a travelling sine wave using a single motor. This simple mechanism, which is also energy efficient and simple to control, was originally conceived a few years ago by the last author of this manuscript [30][31][32] (see figure 1). It is composed of a helix and hollow links attached to each other using simple rotational joints (see figure 2). ...
... Later, it was found that it could imitate continuous inchworm locomotion to crawl over challenging slippery and highly flexible surfaces such the gastrointestinal tract [31]. Over a rigid flat surface, the original 30 cm long prototype [30] fitted with passive wheels under its motor housing to support the weight of the motor and battery (and reduce the resisting friction) reached a top speed of 56 cm s −1 . A smaller 6 cm-long version of the robot [31] crawled inside highly flexible (silicone rubber) tubes and even ex-vivo inside the intestines of a pig at a rate of up to 2 cm s −1 . ...
... The robot crawls in the same direction that the wave travels using a wave-like crawling gait. If no sliding occurs (which is generally not the case and not what is being assumed in the current paper) between the links and the surface, its speed over rigid surfaces can be approximated to [30]: ...
Full-text available
Multiple animals ranging from micro-meter scale bacteria to meter scale vertebrates rely on undulatory motion to propel themselves on land and in the water. This type of locomotion also appears in amphibious animals such as sea snakes and salamanders. While undulatory motion can be used for both crawling and swimming, it requires the coordination of multiple joints so that only a few robots have the ability to mimic this motion. Here, we report a new minimalistic method for both crawling and swimming based on producing a wave motion in the sagittal (vertical) plane. A robotic prototype AmphiSAW was developed to demonstrate this methodology in a variety of scenarios. AmphiSAW (using its wave mechanism only) crawled at 1.5 B/s and swam at 0.74 B/s. The robot can be fitted with legs or wheels at the front, which can further increase its performance especially when crawling on uneven terrains. In addition to its high speeds, the robot has the lowest cost of transport among all amphibious robots reported in literature.
... Peristaltic robots driven by a single actuator with a cylinder cam have recently been proposed [9,10]. A single actuator wave-like robot (SAW), consisting of a helical shaft with mechanical links, has been proposed [11,12]. This demonstrated on-ground mobility and underwater swimming by generating the surface waves. ...
... From these studies, we focused on helix-generated wave generation methods such as SAW robot [11] and mesh-like robot [14]. In developing a mobile robot, we thought that wave generation by helix would be useful because it could be driven by a single motor. ...
Full-text available
This paper presents a novel mobile robot system that uses a uniaxial wave locomotion mechanism. The proposed mechanism can mechanically produce uniaxial surface waves by a single actuator to rotate a helix component that has discrete helical wings. This involves multiple pins with springs and a link mechanism. We designed and developed a mobile robot consisting of a main body and two helical wave locomotion units arranged in parallel. This paper also presents a locomotion model based on the proposed mechanics. The developed robot prototype demonstrated mobility on various surfaces and its skid-steering performance was evaluated. The experimental results validated the feasibility of the proposed wave-locomotion mechanism.
... Penetration resistance increases with depth in sand, and the polychaete Thoracophelia exhibits behaviors that can Peristaltic crawling robot comprising fabric skin over servomotors (Kandhari et al., 2019b). (C) Undulating, worm-inspired robot crawling up between vertical walls with small undulations acting as anchors (reproduced from Zarrouk et al. (2016) with permission). This image was rotated to align with other images in the figure; the robot is moving vertically (toward the left) (D) Peristaltic robot with paired expanding and elongating segments moving through a tube underwater (toward the right) (Fang et al., 2021). ...
... Robotically, small undulations would have advantages, mainly in increasing the range of burrow diameters that a single robot could traverse. A worm robot that undulates using actuators can successfully climb up vertical pipes ( Figure 7C; Zarrouk et al., 2016). For example, a large burrowing head could be followed by a narrower body. ...
Full-text available
Creating burrows through natural soils and sediments is a problem that evolution has solved numerous times, yet burrowing locomotion is challenging for biomimetic robots. As for every type of locomotion, forward thrust must overcome resistance forces. In burrowing, these forces will depend on the sediment mechanical properties that can vary with grain size and packing density, water saturation, organic matter and depth. The burrower typically cannot change these environmental properties, but can employ common strategies to move through a range of sediments. Here we propose four challenges for burrowers to solve. First, the burrower has to create space in a solid substrate, overcoming resistance by e.g., excavation, fracture, compression, or fluidization. Second, the burrower needs to locomote into the confined space. A compliant body helps fit into the possibly irregular space, but reaching the new space requires non-rigid kinematics such as longitudinal extension through peristalsis, unbending, or eversion. Third, to generate the required thrust to overcome resistance, the burrower needs to anchor within the burrow. Anchoring can be achieved through anisotropic friction or radial expansion, or both. Fourth, the burrower must sense and navigate to adapt the burrow shape to avoid or access different parts of the environment. Our hope is that by breaking the complexity of burrowing into these component challenges, engineers will be better able to learn from biology, since animal performance tends to exceed that of their robotic counterparts. Since body size strongly affects space creation, scaling may be a limiting factor for burrowing robotics, which are typically built at larger scales. Small robots are becoming increasingly feasible, and larger robots with non-biologically-inspired anteriors (or that traverse pre-existing tunnels) can benefit from a deeper understanding of the breadth of biological solutions in current literature and to be explored by continued research.
... Images of the undulator are shown in Fig. 1a, b. The primary component of this design is a helical spine encased with a series of hollow, rectangular links that are interconnected through a thin top surface 33 (see SI and Supplementary Movies 1 and 2 for details). The links along with the top surface form an outer shell that transforms the helix rotation into a planar traveling wave of the form, δ sin½2πðx À V w tÞ=λ. ...
Full-text available
Examples of fluid flows driven by undulating boundaries are found in nature across many different length scales. Even though different driving mechanisms have evolved in distinct environments, they perform essentially the same function: directional transport of liquid. Nature-inspired strategies have been adopted in engineered devices to manipulate and direct flow. Here, we demonstrate how an undulating boundary generates large-scale pumping of a thin liquid near the liquid-air interface. Two dimensional traveling waves on the undulator, a canonical strategy to transport fluid at low Reynolds numbers, surprisingly lead to flow rates that depend non-monotonically on the wave speed. Through an asymptotic analysis of the thin-film equations that account for gravity and surface tension, we predict the observed optimal speed that maximizes pumping. Our findings reveal how proximity to free surfaces, which ensure lower energy dissipation, can be leveraged to achieve directional transport of liquids.
... The salamander was also able to crawl at 0.5 m/s on land. The minimally actuated Velox reached a swimming speed of 0.5 m/s but only traveled a few cm/s on land, whereas the SAW robot [24] reached speeds of up to 50 cm/s on land but only 6 cm/s in water. ...
Full-text available
The development, modeling, and performance of AmphiSTAR, a novel high-speed amphibious robot, are detailed in this paper. The robot is palm-sized and fitted with propellers at its bottom, enabling it to crawl on the ground and hover on the water at high speeds. The design of the AmphiSTAR is inspired by two members of the animal kingdom - the cockroach’s sprawling mechanism and the Basilisk lizard’s ability to hover on the water at high speeds. We developed a relatively simple physical model of the lift force as a function of the size of the propeller, its submersion level, and rotational speed. We built an experimental setup to validate the results, and the experimental results are consistent with the analytical model. The robot can crawl at 3.6 m/s (13.6 bodylengths/s) and hover continuously on water surfaces at 1.5 m/s (5.6 bodylengths/s) speeds, making it the fastest amphibious robot. Its elevation on the water surface reduces friction, and its high-speed motors provide forward thrust, enabling it to move at high speeds. Additionally, it can swim by rotating its propellers while floating at low speeds and transition from swimming to crawling (see video).
Conference Paper
In the interaction process with complex environment, compared with rigid structure robot, soft crawling robot has the advantages of high degree of freedom, strong adaptability to complex environment, and high human-computer interaction security. Therefore, it is necessary to conduct in-depth research on intelligent soft crawling robot oriented to environment interaction. This paper designs and manufactures an intelligent soft crawling robot system for environmental interaction. The main research contents include: 1) design and manufacture of intelligent soft crawling robot; 2) mathematical modeling and fluid-structure coupling simulation of soft crawling robot; 3) design and research of the interaction module between the soft crawling robot and the environments; 4) build a software crawling robot drive control platform for environmental interaction experiments. In this paper, the body of soft crawling robot is designed to simulate the motion of earthworm. The combination of ontology, flexible bending sensor, infrared digital obstacle avoidance sensor and ORB-SLAM algorithm framework enables the soft crawling robot to intelligently pass through maze channels, complete the environment mapping function in a closed environment, obtain accurate map information, and complete the interaction with the environment.
Full-text available
Soft robots can adapt to various unstructured environments and have received extensive attention. The integrated structure of sensing and actuation makes soft robots more miniaturized and integrated, enriching their usage scenarios. The multiple degrees of freedom of soft actuators facilitate flexible deformation but also bring challenges to precisely control the deformation. This work presents a novel Liquid Crystal Elastomer-based soft actuator with self-sensing. The kinetic model of a soft finger structure made of the above soft actuator is proposed to facilitate the controller design. Considering the non-predetermined external excitation, a deformation regulation strategy based on a sliding mode controller is designed. Under the action of the controller, the bending angle of the finger joint can be stabilized in a smaller range around the desired value based on the feedback of the self-sensing information. This research realizes the integration of sensing, actuation, and control, enabling the flexible structure can organically adapt to the environmental dynamics and uncertainty in nature, which cannot be achieved by the existing flexible structure deformation control.
This paper analyzes the crawling locomotion of a wave-like robot in curved tubes. We use an energy-based approach to determine the optimal crawling orientation of the robot that minimizes the surface energy while advancing. The results showed that the robot rotated its body along the roll direction so that the wave motion would be in the same plane as the curvature plane of the tube. The incorporation of a passive bending joint along the plane of the wave motion decreased the surface energy and enhanced the robot's ability to advance in even tighter curves. Given these findings we designed and manufactured two new robots with either one or two passive bending joints. We molded custom flexible surfaces and tubes and experimentally tested our robots in them. These validating experiments indicated that the bending joints substantially improved the robots' ability to traverse curved tubes (see video).
Full-text available
In this work, we present a dynamic simulation of an earthworm-like robot moving in a pipe with radially symmetric Coulomb friction contact. Under these conditions, peristaltic locomotion is efficient if slip is minimized. We characterize ways to reduce slip-related losses in a constant-radius pipe. Using these principles, we can design controllers that can navigate pipes even with a narrowing in radius. We propose a stable heteroclinic channel controller that takes advantage of contact force feedback on each segment. In an example narrowing pipe, this controller loses 40% less energy to slip compared to the best-fit sine wave controller. The peristaltic locomotion with feedback also has greater speed and more consistent forward progress.
Full-text available
We have developed several innovative designs for a new kind of robot that uses a continuous wave of peristalsis for locomotion, the same method that earthworms use, and report on the first completed prototypes. This form of locomotion is particularly effective in constrained spaces, and although the motion has been understood for some time, it has rarely been effectively or accurately implemented in a robotic platform. As an alternative to robots with long segments, we present a technique using a braided mesh exterior to produce smooth waves of motion along the body of a worm-like robot. We also present a new analytical model of this motion and compare predicted robot velocity to a 2D simulation and a working prototype. Because constant-velocity peristaltic waves form due to accelerating and decelerating segments, it has been often assumed that this motion requires strong anisotropic ground friction. However, our analysis shows that with smooth, constant velocity waves, the forces that cause accelerations within the body sum to zero. Instead, transition timing between aerial and ground phases plays a critical role in the amount of slippage, and the final robot speed. The concept is highly scalable, and we present methods of construction at two different scales.
Full-text available
Motivated by the interest to develop an agile, high-efficiency robotic fish for underwater applications where safe environment for data-acquisition without disturbing the surrounding during exploration is of particular concern, this paper presents computational and experimental results of a biologically inspired mechanical undulating fin. The findings offer intuitive insights for optimizing the design of a fin-based robotic fish that offers several advantages including low underwater acoustic noise, dexterous maneuverability, and better propulsion efficiency at low speeds. Specifically, this paper begins with the design of a robotic fish developed for experimental investigation and for validating computational hydrodynamic models of an undulating fin. A relatively complete computational model describing the hydrodynamics of an undulating fin is given for analyzing the effect of propagating wave motions on the forces acting on the fin surface. The 3-D unsteady fluid flow around the undulating fin has been numerically solved using computational fluid dynamics method. These numerically simulated pressure and velocity distributions acting on the undulating fin, which provide a basis to compute the forces acting on the undulating fin, have been experimentally validated by comparing the computed thrust against data measured on a prototype flexible-fin mechanism.
Full-text available
Unskillful operation and rough handling of conventional colonoscope, especially at the sigmoid colon, may lead to perforation or splitting the colon wall. Thus, it is crucial to develop autonomous or semi-autonomous colonoscopes that do not require physical force by the doctors for their motions. In this paper, we report the design and development of a colonoscopic robot system that has a locomotive function based on inchworm-like motion, with a hollow body and a steering system that consists of three pneumatic bellows of 7 mm diameter, each located 120 • apart from the others at the head part. The steering device can bend up to approximately 90 • . In order to evaluate the performance of the colonoscopic robot, in-vitro tests and in-vivo tests were carried out. The experimental results show the feasibility of the prototype colonoscopic robot being used for diagnosis and treatments in colon.
Worm-like robots for applications including maintenance of small pipes and medical procedures in biological vessels such as the intestines, urethra, and blood vessels, have been the focus of many studies in the last few decades. The robots must be small, reliable, energy efficient, and capable of carrying cargos such as cameras, biosensors, and drugs. In this study, worm locomotion along rigid and compliant terrain is analyzed, and a novel design of worm-like multicell robots actuated by a single motor is presented. The robots employ a screw-like axis for sequencing and coordination of the cells and clamps. This design allows for significant miniaturization and reduces complexity and cost. The design of the robots and analysis of their dynamics and power efficiency are described. Two earthworm and two inchworm prototypes were built to demonstrate their performance. The robots are capable of moving forward, backward, and vertically and consume low power, which allow them to climb for hundreds of meters using onboard batteries. [DOI: 10.1115/1.4005656]
In this article, we present the design, development, and characterization of a biomimetic robotic fish remotely controlled by an iDevice application (app) for use in informal science education. By leveraging robots, biomimicry, and iDevices, we seek to establish an engaging and unique experience for free-choice learners visiting aquariums, zoos, museums, and other public venues. The robotic fish incorporates a three-degree-of-freedom tail along with a combined pitch and buoyancy control system, allowing for high maneuverability in an underwater three-dimensional (3-D) space. The iDevice app implements three modes of control that offer a vividly colored, intuitive, and user-friendly theme to enhance the user experience when controlling the biomimetic robotic fish. In particular, the implemented modes vary in the degree of autonomy of the robotic fish, from fully autonomous to remotely controlled. A series of tests are conducted to assess the performance of the robotic fish and the interactive control modes. Finally, a usability study on elementary school students is performed to learn about students' perception of the platform and the various control modes.
This paper presents a proof-of-concept design of an inchworm-type piezoelectric actuator of large displacement and force (or power) for shape control and vibration control of adaptive truss structures. Applications for such actuators include smart or adaptive structural systems, auto and aerospace industries. The proposed inchworm-type actuator consists of three main components with frictional clamping mechanisms: two clamping or braking devices and one expanding device. The two frictional clamping devices provide alternating braking forces when the moving shaft, which is pushed by expanding device, walks inside the PZT tubular stack and emulates an inchworm, summing small steps to achieve large displacements. Since the development of a robust clamping mechanism is essential to realize the high force capability, a considerable design effort has been focused on optimizing the clamping device to increase the output force. CATIA is used as a platform to model the whole actuator and ANSYS is used to analyze and optimize the performance of the actuator. The proposed design avoids the tight tolerance of the tube diameters and reduces the clearance between clamps and the moving shaft with the adjustment device. The moving shaft of the actuator could also be replaced by one member of a truss structure for vibration suppression and position control purposes. In the proposed actuator the flexure clamps can also be easily replaced to outfit different dynamic characteristics. The complete design of the proposed actuator has been performed using the finite element analysis. The simulation result confirms that the output force of 160 N and incremental displacement in each step of 8.3 μm can be achieved using the proposed actuator. A prototype of actuator has been fabricated and static tests have been performed to validate the simulation results.
Large objects which propel themselves in air or water make use of inertia in the surrounding fluid. The propulsive organ pushes the fluid backwards, while the resistance of the body gives the fluid a forward momentum. The forward and backward momenta exactly balance, but the propulsive organ and the resistance can be thought about as acting separately. This conception cannot be transferred to problems of propulsion in microscopic bodies for which the stresses due to viscosity may be many thousands of times as great as those due to inertia. No case of self-propulsion in a viscous fluid due to purely viscous forces seems to have been discussed. The motion of a fluid near a sheet down which waves of lateral displacement are propagated is described. It is found that the sheet moves forwards at a rate 2pi 2b2/lambda 2 times the velocity of propagation of the waves. Here b is the amplitude and lambda the wave-length. This analysis seems to explain how a propulsive tail can move a body through a viscous fluid without relying on reaction due to inertia. The energy dissipation and stress in the tail are also calculated. The work is extended to explore the reaction between the tails of two neighbouring small organisms with propulsive tails. It is found that if the waves down neighbouring tails are in phase very much less energy is dissipated in the fluid between them than when the waves are in opposite phase. It is also found that when the phase of the wave in one tail lags behind that in the other there is a strong reaction, due to the viscous stress in the fluid between them, which tends to force the two wave trains into phase. It is in fact observed that the tails of spermatozoa wave in unison when they are close to one another and pointing the same way.
The action of the tail of a spermatozoon is discussed from the hydrodynamical point of view. The tail is assumed to be a flexible cylinder which is distorted by waves of lateral displacement propagated along its length. The resulting stress and motion in the surrounding fluid is analyzed mathematically. Waves propagated backwards along the tail give rise to a forward motion with velocity proportional to the square of the ratio of the amplitude of the waves to their length. The rate at which energy must be supplied to maintain the waves against the reaction of the surrounding fluid is calculated. Similar calculations for the case when waves of lateral displacement are propagated as spirals show that the body is propelled at twice the speed given it by waves of the same amplitude when the motion is confined to an axial plane. An externally applied torque is necessary to prevent the reaction of the fluid due to spiral waves from causing the cylinder to rotate. This is remarkable because the cylinder itself does not rotate. A working model of a spermatozoon was made in which spiral waves could travel down a thin rubber tube without rotating it. The torque just referred to was observed and was balanced by an eccentric weight. The performance of the model while swimming freely in glycerine was compared with the calculations. The calculated speed of the model was higher than was observed, but this discrepancy could be accounted for by the fact that the model has a body containing its motive power while the calculations refer to a disembodied tail.
The field of bio-mechanisms, which develops new machines that use motion and control of organisms as a model, is attracting attention. We examined the peristaltic crawling of an earthworm as a transport function in place of wheels or ambulation, and have developed a robot running inside a tube. In this robot, a joint corresponding to the earthworm's segment is driven by a DC motor. This paper presents the experimental result of the peristaltic crawling of an actual earthworm and the evaluation result of the transport mechanism of a prototype robot. Copyright © 2007 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.