Int. Journ. of Unconventional Computing, Vol. 6, pp. 145–161
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Amoeboid Locomotion having High Fluidity
by a Modular Robot
Masahiro Shimizu and Akio Ishiguro
Department of Electrical and Communication Engineering, Tohoku University, 6-6-05 Aoba,
Aramaki, Aoba-ku, Sendai 980-8579, Japan
E-mail: [email protected]; [email protected]
Received: December 23, 2007. Accepted: January 15, 2008.
Investigation has so far been with a fully-decentralized algorithm that can
control the morphology of a module robot called Slimebot comprised of
many identical mechanical modules in accordance with the environment
encountered. One of the most significant features of the approach of us,
the authors of this paper is that explicit exploitation has been promoted
with “the emergent phenomena” stemming from the interplay between the
control system and the mechanical system for the purpose of controlling
the morphology in real time. Confirmation has already been made with
the fact that the method in question brings about remarkable real-time
adaptivity and scalability. The paper discusses a control method by which
fluidity of the modular robot is enhanced. From a more specific standpoint,
it should be confessed that “sol-gel transition” was encouraging enough
for the authors to make a trial of inducing “protoplasmic streaming” in the
inside of the modular robot. It is shown from simulation results that as
fluidity is made higher, the modular robot is enhanced in its abilities. As
far as knowledge is concerned, attempts to develop modular robots of so
high fluidity have never been made.
Keywords: Amorphous robot, artificial amoeba, distributed intelligence.
1 INTRODUCTION
Organisms possess, even if at times they are believed to be classified as quite
primitive species, real-time adaptivity allowing themselves to be complied
with by converting their behaviors into self-organization in an appropriate
manner under the unpredictable environment. To discuss emergence of such
intelligence, it might be important to be positively aware of existence of
interaction dynamics among a control system (brain and nerves), mechanical
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system (body), and the environment surrounding the said two systems [1, 2].
Therefore when attention is anew paid to the fact that the control system and
mechanical system as direct objectives for design are in existence on the origin of the interaction dynamics, it might be intrinsically proper enough for
them to be dealt with as having the equalized weight. Meanwhile with conventional designing of robots, enhancement of systems has been made, as is
explicitly insinuated from the term of controlling system/controlled system,
by dividing the said two and by exclusively attaining high functions of control
systems positioned on the upper layer side based on a governing relation. Such
a method how to deal with the control and mechanical systems is, as a matter
of course, is linked to the requirement for forcible control. Thus as a result,
there appears to be issues that these systems are too fragile for environmental
perturbations or energy efficiency is very low.
Under these circumstances, the authors of this paper have come to be aware
of the importance of the working hypothesis shown below [3, 4]:
To allow a performance entity having finite physical/calculative resources to
make emergence of real-time adaptivity, there is no other method except exploitation of emergent phenomena. To achieve this, it is necessary to consider the
interaction dynamics between the control system and the mechanical system.
By taking up a modular robot (Slimebot) showing amoeboid locomotion as an
example and based on the working hypothesis referred to above, the authors
have discussed concerning the design measure of the control and mechanical
systems. With these types of research, introducing mainly spontaneous connectivity control mechanism (i.e., mechanical system) by exploiting functional
materials and mutual entrainment (i.e., control system) makes it possible to
make emergence of excellent real-time adaptivity. Meanwhile when attention
is paid to the amoeboid locomotion, fluidity of the constitutional elements
( protoplasmic streaming) can be regarded as one of the important features
generating the behaviors of the said locomotion. This stems from the reason
that application of the law of conservation of protoplasmic mass makes it possible, it is imagined, for the individual modules to hold dynamic long-distance
correlation [5], and such exploitation of embodiment will be influential enough
to make emergence of real-time adaptivity. However it is recognized that no
emergence is made with protoplasmic streaming of slimebot except under
specific situation. That is to say, the Slimebot never conducts exploitation of
the protoplasmic streaming regarded as an important feature of the amoeboid
locomotion. Thus it can safely be said that it is quite inadequate with the traditional Slimebot to discuss protoplasmic streaming making emergence from
such embodiment (i.e., the body made with protoplasmic streaming).
Therefore in this study, development is to be made with a modular robot
allowing continuous protoplasmic streaming to make its emergence based on
the Slimebot, and it is explained from the embodiment of the robot what kind
of real-time adaptivity will make their emergence. When realization of the
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Amoeboid Locomotion having High Fluidity by a Modular Robot
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protoplasmic streaming by means of the modular robot is considered at this
stage, antinomic properties, i.e., dispersion of the modules produced from high
fluidity and maintenance of the coherency as a swarm should simultaneously be
satisfied. For the said requirement in this study, attention is paid to the sol-gel
transition exhibited by a material comprised of polymer gels. Thus proposal is
made with a view to utilizing the transition to be applied to control of physical
connection among the modules. A report is hereby released stating to the effect
that as a result of execution of the simulation, a profoundly interesting realtime adaptivity as seen in an example of continuous protoplasmic streaming
generated in the modular robot accompanied with high fault-tolerance.
2 RELATED WORKS
In this section, some notable works concerning the robots that enables amoeboid locomotion are introduced.
Yokoi et al. [6] proposed some types of amoeba-like robots in both simulations and experiments. The simulation was conducted with the mathematical
model based on VPF (vibrating potential field). Simulation results showed that
the swarm exhibits amoeboid locomotion cooperatively through the interaction using the wavy signal propagated among the units. However, the real
physical system with this mathematical model has not been treated.
On the other hand, Yokoi et al. also proposed the real physical amoeboid
robot SMA-NET. The SMA-NET is driven by exploiting the SMA (Shape
Memory Alloy) actuators that is connected as a network. The robotic system
realized amoeboid locomotion with deformation. However, the topology of
the network, which makes the body of the robot, can not be reconfigured.
In contrast with these studies, the proposed approach discusses the reconfigurable amoeboid locomotion which can be realized with real physical robot.
3 METHODS
In this study, rearrangement of the mechanism system for the purpose of allowing protoplasmic streaming to be induced together with the control system was
made based on the slimebot.
3.1 Sol-gel transition and protoplasmic streaming
When protoplasmic streaming is to be induced in the modular robot, a problem is liable to be caused such as construction of a system having antinomic
properties as shown below owing to high fluidity of the streaming:
• Dispersion of the modules from the center of gravity of the swarm by
fluidity
• Aggregation of the modules to maintain coherency of the swarm
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When careful consideration is made at this stage with a spontaneous connectivity control mechanism with which functional materials are utilized, it
is understood that the dynamic characteristics are closely similar to crosslinkage in polymer gels. That is to say, the swarm consisting of modules that
can be utilized becomes closely similar to gel. On the other hand, polymer
gel, which is prone to be prevented from being cross-linked owing to outer
stimulants, e.g. heat, reversibly changes its structure into gel. Some types of
the gel occasionally bring about sol-gel transition. Therefore by mechanically
switching whether functional materials of the Slimebot are in existence or not,
it becomes possible to allow movement of sol-like modules having fluidity to
be composed.
From the above discussion, proposal is made in this study with a style with
which sol-gel transition is made by switching existence and non-existence of
the functional materials on the assumption that the peripheral part of the modular robot is in a gel-like state (i.e., outer surface) having functional material and
the inner side of swarm is in a sol-like state having no functional material. By
so doing, it is imagined that although fluidity (i.e., dispersion of the modules)
is kept preserved, maintenance of coherency as a swarm will become possible.
3.2 Contrivance of the mechanical system aiming at induction
of protoplasmic streaming
For the purpose of allowing high fluidity to make its emergence, details are
described with the contrivance concerning the mechanical system applied to
Slimebot. The individual modules are in possession of the mechanism system
illustrated in Fig. 1, and connection among the modules in a gel-like state
is made via functional material (i.e., genderless velcro strap). The strap is
endowed with dynamic characteristic allowing the individual modules to be
connected physically very easily when they are contacted and furthermore
they are separated automatically when force strong enough to be more than
removal strength is applied. To bring the sol-gel transition proposed in Sec. 2.1
to realization, it becomes necessary to switch whether the functional material is
in existence or not. Therefore with the sol-like module, a mechanism allowing
a functional material to be accommodated was introduced (Fig. 1(b)). On
the other hand, in a sol-like state, to bring high fluidity to realization at this
stage, ground friction is always minimized by raising a friction plate with the
modules in a sol-like state. More over, all types of modules (i.e., both gellike and sol-like modules) have the mechanisms that can control the ground
friction and the telescopic arms.
Utilization of ground friction and the telescopic arms make it possible
to produce locomotion of the individual modules. Note that the individual
modules itself have no mobility, and locomotion of the modules becomes
possible exclusively when plural modules cooperate appropriately. Furthermore sensors to detect a goal light (i.e., a destination) were to be possessed
concurrently.
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(a) Gel-like module
(b) Sol-like module
FIGURE 1
Mechanical structure of a module employed. (Left) Top view. (Right) Side view.
3.3 Induction of protoplasmic streaming by control system
In this section, a controlling measure enabling locomotion having high fluidity
maintaining coherence as a swarm to be accomplished is considered, when a
modular robot is composed by gathering plural modules that are to be proposed
(Fig. 1).
3.3.1 Locomotion allowing fluidity and coherent morphology
to be concurrently established
A noticeable thing in case locomotion is produced is that coherency of the
whole of the modular robot is apt to be in disorder very easily because of
high fluidity. To prevent this trouble, proposal is made with protrusion of the
inner-side module group caused by contraction locomotion of the periphery
module group in a forward direction as illustrated in Fig. 2 and a locomotion
measure making use of sol-gel transition. Hereunder detailed is the principle
of the description referred to above.
First of all, the connection of the periphery module group in the frontal part
in a proceeding direction is weakened. After that, movement directed towards
the inner side of the periphery modules is produced (Fig. 2(a)). Protoplasmic
mass of the inner-side module group is conserved at this stage, and the innerside module group is protruded in a forward direction (Fig. 2(b)). At that
time, the module, which is, as it were, regarded as the periphery among the
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Sol-like module
Gel-like module
Connection
Locomotion
Sol-Gel Transition
(a)
(b)
(c)
FIGURE 2
A schematic of the proposed method inspired by sol-gel transition.
inner-side modules protruded in a frontal direction makes sol-gel transition,
becomes a module having a functional material. Thus a periphery in a new
sol-like state is constructed (Fig. 2(c)). Repetition of these processes makes
it possible to produce the locomotion with which high fluidity is utilized in
parallel with maintenance of coherence as a swarm.
3.3.2 Active mode and passive mode
In this study, two fundamental action modes called the active mode where the
individual modules themselves make locomotion and the passive mode where
no locomotion is made by the modules themselves are reciprocally repeated.
With the active mode, the individual modules extend/contract their arms. Concurrently with this, ground friction with the ground is lowered. Meanwhile
with the passive mode, the individual modules recover their arms to the extent
of natural length. Concurrently with this, ground friction is heightened. The
module itself on this mode, which never moves, is functional enough to play
a role of a supporting point encouraging the module group on the active mode
to make progress with great efficiency.
3.3.3 Generation of driving force by converting the peripheral module
into a sol-like state
As has been referred to before, it is impossible for the modular robot in question
to locomote as a single module. That is to say, generation of locomotion is
impossible unless not less than two pieces of modules are available. For this
reason, it is necessary for the not less than two modules connected in gel-like
state in series in an inner-side direction. Therefore as illustrated in Fig. 3,
contraction force was to be generated by allowing two layers on the periphery
to be in a gel-like state.
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FIGURE 3
A schematic of the two-layered gel-like modules.
3.3.4 Composition of phase gradient utilizing mutual entrainment
among nonlinear oscillators
For switching timing generation as the two action modes, i.e. the active mode
and passive mode, the slimebot has VDP (van der Pol) oscillator with the individual modules as given in the equation shown below. A differential equation
stipulating the behavior of the VDP oscillator equipped onto the i-th module
(the module i) is shown below:
αi ẍi − βi (1 − xi2 )ẋi + xi = 0.
(1)
where αi is a parameter stipulating the frequency, whereas βi is another
parameter stipulating the speed converging to the limit cycle of the nonlinear oscillator. Secondly to encourage a mutual entrainment to be induced
between the nonlinear oscillators, an diffusion-like interaction allowing the
phase difference between the oscillators close enough to each other is adopted.
For convenience sake of explanation, let it be understood that an oscillation
tmp
state of the module before the interaction is expressed as xi , whereas a state
renewed by the interaction is expressed as xi . An equation used in a concrete
manner is shown below:


Ni
1
tmp
tmp
tmp
xi = xi + ε 
xj − x i  .
(2)
Ni
j =1
Ni in the equation indicates the number of the module approaching the module i at the time t. Here, Ni is a value dynamically and discretely changing
accompanied with configuration deformation.
Settling adequately the value of αi in Eq. (1) with a kind of oscillators at this
stage when plural VDP oscillators are in interaction in accordance with Eq. (2)
makes it possible to generate significant phase distribution in a modular robot.
With a view to generating phase distribution to initiate adequate contraction
locomotion, the value of αi was settled as shown below.


0.85 (module detected the goal light)
αi = 1.0 (sol-like module)
(3)


0.7 (in case of the other types)
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FIGURE 4
Phase distribution suitable for increasing fluidity.
Note that the value of αi is decreased with the modules in the inner side.
From this it is deduced that the frequency of the modules in the inner side
are made greater relatively for the modules in the periphery. As a result, it
becomes possible to generate phase gradient allowing the modular robot to do
contraction locomotion. Furthermore by adjusting the module that detected
a goal light in an intermediate value between the sol state and the module
in the inner side, the pivotal point toward which the contraction locomotion
is directed is settled slightly in a rear direction. The settlement is made for
the purpose of promoting the effect of the module to be thrust in a forward
direction. In Fig. 4, phase distribution obtained from mutual entrainment the
modules arranged in a disc-like style is illustrated.
3.3.5 Initiation of contraction locomotion
In this section, it is explained in what a manner mode switching of the individual modules and extension/contraction of the arms are controlled by making
use of the phase distribution initiated from mutual entrainment of the VDP
oscillator referred to previously. Mode switching of the individual modules is
allowed to correspond to the phase θi of the VDP oscillator. The current study
is promoted on the assumption that the phase 2π in a period T of the VDP
oscillator is equally divided into Np and likewise on the supposition that duty
ratio γ of the active mode to the passive mode is settled at the time T /Np equivalent to the individual phase interval. In other words, the definition equation
of the duty ratio γ is given as shown below on the assumption that the phase
(n − 1)π ≤ θi (t) < (n + 1)π of the optional VDP oscillator where a general
angle of the rotational number n is in consideration is equally divided into Np
pieces and likewise on the supposition that the terms of the active mode and
passive mode on the individual intervals are respectively Tα /Np and Tp /Np :
Tp
Ta
T
=
+
,
Np
Np
Np
γ =
Ta
Ta + Tp
(4)
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At that time, the individual modes are actually executed as shown below:

nT
(n + 1)γ T


(Active mode)

 Np ≤ θi <
2Np
, (0 ≤ n ≤ Np − 1).

(n + 1)γ T
(n + 1)T


≤
θ
<
(Passive
mode)
i

2Np
Np
(5)
where θi represents the phase of the VDP oscillator, and is determined by the
equation shown below:
θi = arctan
x˙i
.
xi
(6)
On the other hand, the extension/contraction of the individual arms equipped
onto the module i in a state of the active mode is determined corresponding
to the phase difference between each of itself and the modules approached. At
this stage, force required for the extension/contraction of the arms is given in
accordance with the equation shown below:
Arm j
Fi
= −k{θj − θi }eij ,
eij =
ri − rj
.
|ri ||rj |
(7)
Arm j
where Fi
is the force of the extension/contraction applied onto the m-th
arm of the module i, and k is proportional constant.
The degree of the extension/contraction of the arms of the individual modules becomes the most remarkable one in a direction of the phase gradient
(Fig. 4), and timing of mode switching is propagated as a traveling wave
directed from the inner-side module to the periphery module. As a result, contraction movement brought about by the sol-like module on the periphery is
spontaneously generated.
3.3.6 Induction of the continuous protoplasmic streaming obtained
by exploiting convection
Based on the design referred to above, locomotion by the contraction locomotion is made. At that time, the sol-like module group on the periphery obtains
driving force in a longitudinal (frontal) direction, and makes locomotion in
combination with the sol-like module group in the inner side in a proceeding
direction. However, at this stage, the protoplasmic streaming often suffers
from the problem of its not being continuously induced. To solve the problem,
convection brought about accompanied with the module is considered with a
view to encouraging more continuous and safe enough protoplasmic streaming to be induced (Fig. 5(a)). In this study, speed difference is made produced
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(a)
(b)
FIGURE 5
A schematic of the convection in the modular robot by exploiting velocity difference. (a) is the
convection of modules. (b) is the proposal method which exploit velocity difference of modules.
between the periphery modules and the inner-side modules to accomplish the
method referred to above (Fig. 5(b)). Details of the method are hereunder
described.
With a view to producing the speed difference of the module group, the
speed of the periphery modules in the lateral side in a proceeding direction is
at first reduced. As its realization method, attention is paid to the duty ratio
in Eq. (4). The duty ratio is a time-dependent ratio of the active mode to the
passive mode, by which the reduction of the said ratio enables the ratio of
the passive mode to be increased. For the module in a passive mode to allow
itself to be ceased, it is possible at this stage to reduce the moving speed of
the module by decreasing the duty ratio.
At the next stage, explanation is made with a decentralized autonomous
method allowing the duty ratio on the lateral side in a proceeding direction to be
reduced. Keeping in mind reaction diffusion of the virtual chemical materials
and utilizing its concentration in this study, it is discerned that periphery on
the lateral side in a proceeding direction is dealt with. To be concrete with this,
the reaction diffusion equation actually used is shown below. For convenience
sake of explanation, let the concentration of the virtual chemical material of
tmp
the module before reaction diffusion was made be ui , whereas let the state
renewed by the reaction diffusion be ui :


Ni
1
tmp
tmp
tmp
tmp
ui = ui + κinc ulight − κdec ui + εu 
uj − ui  .
Ni
j =1
1.0 iImj,
ulight =
0
ij.
(8)
(9)
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FIGURE 6
Concentration distribution of the hypothetical chemical created through the reaction-diffusion
equations.
The terms ranging from the 1st to the 3rd in the equation show the reaction
terms. In the meanwhile, κinc represents the speed where the virtual chemical
material is produced by the module that detected a goal light. On the other
hand κdec represents a proportional ratio obtained when the material is decomposed in proportion to the concentration. In addition, the 4th term represents a
diffusion ratio, whereas Ni is the number of the module where the module i is
approached at the time t. Figure 6 shows the concentration of virtual chemical
material in case the modular robot is in locomotion. As seen above, a concentration gradient is formed from a proceeding direction to a rearward direction.
Here when the gradient exceeds a settled threshold value uγ is obtained, the
duty ratio is made reduced:
0.5 (ui ≤ uγ )
γi =
(10)
0.2 (ui > uγ )
At that time, the modules, that are in a sol-state in the inner side, is never
influenced by the speed because installation friction is always small. Thus it is
possible to reduce the speed of the module on the lateral side in a proceeding
direction. As seen above, generation of the speed difference between the lateral
side in a proceeding direction and the inner side makes it possible to induce
continuous and stabilized protoplastic streaming.
4 SIMULATION RESULTS
4.1 Verification of the protoplasmic streaming induction by means
of computer simulation
To verify in accordance with a proposed method in relation to the fact that
continuous and stabilized protoplasmic streaming will be induced, computer
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simulation was conducted. Conditions concerning the simulation are as shown
below:
Module number
Initial configuration
Goal light
VDP oscillator parameter
Reaction diffusion
equation parameter
: 144
: disc-like configuration
: radiated from the upper side of the paper
: βi = 1.0; ε = 0.01
:
κinc = 0.015; κdec = 0.0015; εu = 0.2;
uγ = 0.5
Typical results are illustrated in Fig. 7. Each illustration takes up the center of
gravity of the modular robot performing locomotion onto the upper side of the
(a) Initial state
(b) 14000 steps
(c) 36000 steps
(d) 64000 steps
(e) 70000 steps
(f) 110000 steps
FIGURE 7
Time evolution of the convection of the module (see in alphabetical order).
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FIGURE 8
Trajectory of the marked module, of which origin is center of the modular robot’s mass.
surface of the paper as a pivotal point of the illustration. The black circle in the
illustration expresses the gel-like state, whereas the white circle expresses the
sol-like state. Furthermore the gray circle is the module that detected the goal
light. At this stage, note that emphasis is attached to the module. (The said
emphasis-attached circle shall be called the module A for convenience sake
of explanation.) On the other hand, Fig. 8 shows a trajectory of the module
A settled taking up the center of gravity of the modular robot as an original
point of the graph.
From both the figures, it is explained that the module A is transferred in the
inner side of the modular robot in a direction of the frontal part (b), the frontal
part on the left lateral side (c), the rear side on the left lateral side (d), the rear
side (e), and the frontal side (f) in this order. From this it can be observed that
convection brought about owing to utilization of the speed difference, which
is referred to in Sec. 2.3.6, is produced. On the other hand, it is understood that
between (b) and (c), sol-gel transition is produced accompanied with module’s
transfer from its pivotal point to the lateral side. Meanwhile between (d) and
(e), locomotion of the periphery module is activated because it is established
that ui ≤ uγ (see Eq. (10)). As a result, sol-gel transition ranging from the
lateral side to the pivotal point is produced. As seen above, it is confirmed
that locomotion inducing continuous and stabilized protoplasmic streaming
has been brought to realization owing to the contrivance of the contraction
locomotion by periphery modules and convection of the modules for which
speed difference is utilized.
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4.2 Spontaneous discharge of the malfunctional module for which
protoplasmic streaming is utilized
In the previous section, it is confirmed that continuous and stabilized protoplasmic streaming has been induced. At this stage, it is guessed that utilization
of such a kind of protoplasmic streaming makes it possible for the transportation function to make emergence in the inner side of the modular robot. When
the transportation function in question is considered from a point of view of
real-time adaptivity, it is expected that a very interesting function will come
to make emergence with spontaneous discharge of impurities. Keeping such
a situation in mind, verification is made in this study to explain what kind
of transportation function will come out when impurities are contained in
the inside of a modular robot having protoplasmic streaming (malfunctional
modules in this case).
Condition of the simulation was equally established as is determined in
Sec. 3.1. However as an initial state, four malfunctional modules arbitrarily
chosen from the sol-like modules are included. At that time, the malfunctional
modules have lost all the functions such as extension/contraction of the arms,
communication between approaching modules, function for sol-gel transition.
Meanwhile for analysis of individual data obtained in the simulations, an average of five trials having respectively four malfunctional modules is adopted.
The results obtained are shown in Figs. 9, 10, and 11. It is explained in Fig. 9
in what a manner the typical malfunctional modules in case ground friction is
low (large circles in the figure) are discharged, whereas the time required for
discharge of the malfunctional modules in case the ground friction is changed
is depicted in Fig. 10. On the other hand, it is explained in Fig. 11 from which
position of the modular robot the modules in function are discharged.
FIGURE 9
Time evolution of discharging the malfunctional modules. Each malfunctional module is low
ground friction.
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FIGURE 10
Time step of discharging the malfunctional module varying ground friction.
FIGURE 11
Vertical position from which the malfunctional module is discharged varying ground friction.
First it can be recognized from Fig. 9 that spontaneous discharge of
the malfunctional modules is in progress accompanied with locomotion of
the modular robot. Secondly it is understood from Fig. 10 that discharge
of the malfunctional modules is in progress at the time step approximately
40000 when the ground friction is small or great, whereas malfunctional modules with which the time step required for the discharge becomes very great
when the ground friction is settled in a value between the said two cases.
Emergence of such a phenomenon stems from the reason that speed of
the malfunctional module kept adrift by the protoplastic streaming is made
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reduced as the ground friction becomes great. At that time, the malfunctional
modules, which are transferred accompanied with the convection-like protoplasmic streaming so long as the ground friction is small, are discharged
from a relatively frontal part. Contrarily to the above, the malfunctional modules, which are liable to willingly remain the place where they are now when
the ground friction is small, are discharged from rear side of the modular
robot (Fig. 11). In other words, rapid discharge is made because speed difference between the modular robot and the malfunctional modules is great
(The speed difference direction becomes reverse depending on how great the
ground friction is.)
On the other hand, the modular robot and malfunctional modules are occasionally equal in transfer speed when the ground friction is settled to a value
the said two cases. This can particularly be seen in the vicinity of the pivotal
point of the modular robot when the direction of the protoplastic streaming to
be produced and the transfer speed of the malfunctional modules are equal.
At that time, the malfunctional modules are in inclusion for a long period.
Therefore even when the ground friction is settled as a value between the said
two cases, discharge of the malfunctional modules is made very easily in the
vicinity of the rear part of the modular robot where the protoplastic streaming
is produced in a lateral (transverse) direction.
As seen above, it is explained that making smaller or greater the ground
friction makes it possible for the malfunctional modules to make spontaneous
discharge respectively from a frontal part or rear part.
5 CONCLUSIONS
In this paper, an attempt was made to bring amoeboid locomotion driven by
protoplasmic streaming to realization by using a modular robot consisting of
many modules. In this study, generation of protoplasmic streaming was made
under antinomic requirement as seen in diffusion and cohesion of the modules
produced when high fluidity should be brought to realization. Furthermore proposed method was made with convection-like protoplastic streaming utilizing
speed difference among the modules with a view to inducing continuous protoplasmic streaming, and the proposal was brought to realization by utilizing
reaction diffusion of virtual chemical materials.
By conducting simulations, it is confirmed that interesting property such
as spontaneous discharge of malfunctional modules for which protoplasmic
streaming is utilized has made emergence. At that time, it is explained that
changing ground friction of the malfunctional modules makes it possible for
the discharge position of the malfunctional modules to be changed. Meanwhile
with a kind of ground friction, the malfunctional modules are allowed to be
in inclusion with continuation for a long time evolution. From the above, it is
expected that controlling the ground friction of each module makes it possible
for the module to be transported to relatively desired destination.
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Amoeboid Locomotion having High Fluidity by a Modular Robot
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ACKNOWLEDGMENTS
This work has been partially supported by a Grant-in-Aid for Scientific
Research on Priority Areas “Emergence of Adaptive Motor Function through
Interaction between Body, Brain and Environment” from the Japanese Ministry of Education, Culture, Sports, Science and Technology. We thank Noriaki
Kono for many helpful suggestions concerning the simulation of Slimebot.
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