MOBILITY PERFORMENCE OF CILIARY LOCOMOTION FOR
AN ASTEROID EXPLORATION ROBOT UNDER VARIOUS
EXPERIMENTAL CONDITIONS*Kenji Nagaoka1 , Kazuki Watanabe2 , Toshiyasu Kaneko3 , Kazuya Yoshida4
1

Tohoku University, Aoba 6-6-01, Aramaki, Aoba-ku, Sendai, Japan, E-mail: nagaoka@astro.mech.tohoku.ac.jp
Tohoku University, Aoba 6-6-01, Aramaki, Aoba-ku, Sendai, Japan, E-mail: watanabe@astro.mech.tohoku.ac.jp
3
Tohoku University, Aoba 6-6-01, Aramaki, Aoba-ku, Sendai, Japan, E-mail: kaneko@astro.mech.tohoku.ac.jp
4
Tohoku University, Aoba 6-6-01, Aramaki, Aoba-ku, Sendai, Japan, E-mail: yoshida@astro.mech.tohoku.ac.jp
2

ABSTRACTThis paper investigates the mobility of ciliary locomotion based on experimental and theoretical analysis. A
ciliary locomotion mechanism actuated by an eccentric
motor is one possible solution for enhancing mobility ona microgravity asteroid with environmental uncertainties.
The proposed mechanism is also feasible for space applications because it is eﬃcient, simple, and reliable. So
far, we have evaluated the feasibility of ciliary locomotion based on mobility experiments using a microgravity
emulation system and model-based numerical simulations
under limited conditions. Thus, this paper discusses themobility performance of ciliary locomotion under various
environmental conditions like gravity and friction via experiments and simulations. As a result, we introduce theinteraction mechanics of ciliary locomotion within a more
systematic framework.

1 INTRODUCTION
The robotic exploration of small bodies such as asteroids has received attention in recent years. The Hayabusa
project is the world’s first sample return mission demonstrated by the Japan Aerospace eXploration Agency(JAXA). The Hayabusa spacecraft carried a small exploration robot named MINERVA [1]. MINERVA has an inner torquer and can hop using the torquer’s reaction torquein microgravity. Although MINERVA’s landing onto thesurface was unsuccessful, the development of MINERVA
has enhanced the research on robotic locomotion under
microgravity. Following this mission, JAXA is now operating the Hayabusa 2 mission [2]. The Hayabusa 2
spacecraft targets the near-Earth C-type asteroid 1999 JU3(Ryugu) and aims to arrive at Ryugu in mid-2018. Observation and analysis from Earth shows that Ryugu has
an eﬀective diameter of 870 ± 30 m, a rotation period of
7.6 h, and its shape is also nearly spherical [3]. To advance robotic exploration on the asteroid surface, several
MINERVA-II rovers are installed in the Hayabusa 2 spacecraft [4, 5]. Figure 1 shows the MINERVA-II2 system,

Figure 1 : Flight model of the MINERVA-II2 systemc MINERVA-II Consortium.
⃝
which is one of the MINERVA-II systems developed by
the MINERVA-II University Consortium [5].
Hopping mobility is one possible solution to locomotion on a microgravity asteroid. So far, various otherhopping mechanisms have been proposed for an asteroid
exploration robot in addition to the MINERVA’s hopping
mechanism [6–14]. We proposed a ciliary locomotion
mechanism actuated by a vibration motor [9, 10], whereas
most of the other hopping mechanisms hop by a relativelylarger impulsive force from the ground surface. The ciliary locomotion robot can crawl and perform micro-hops,
and achieves more accurate locomotion in microgravity.
This mechanism was equipped with the MINERVA-II2
Rover 2 and will be demonstrated on the mission as one of
the engineering challenges [5]. Although the fundamental
mobility performance and feasibility of ciliary locomotion
robot has been discussed based on theoretical and experimental analyses [9, 10], the eﬀect of the environmental
parameters, such as gravity, friction, or surface irregularity, on performance remains to be elucidated.
We address ciliary locomotion mechanics with environmental variations in microgravity. In particular, theenvironment on the surface of an asteroid is highly uncertain. To maximize and appropriately control the mobility of ciliary locomotion, a more systematic understanding

(1) Deflecting

based on experimental and theoretical approaches is necessary. In this paper, the interaction mechanics of ciliary
locomotion is shown through an analysis of the mobility
performance, which is examined by experiment and simulation.
This paper is organized as follows. Section 2 presents
the locomotion principles of the ciliary locomotion robot
based on microscale observation by a camera. The fundamental framework of the locomotion performance is also
described. Section 3 introduces the experimental analysisof the ciliary locomotion robot under various environmental conditions: gravity, friction, and surface slope. The experimental results exhibit the mobility performance more
systematically. Section 4 presents a theoretical model ofthe locomotion system, and then the results of the experiments and simulation are compared. The comparison
yields a key relationship from the viewpoint of interaction
mechanics. Section 5 summarizes the results and contributions of this paper.

(2) Recovering(2) Slipping(a) Crawling mode(3) Hopping(1) Deflecting(2) Recovering(2) Slipping(b) Hopping mode

2 CILIARY LOCOMOTION
PRINCIPLES
Ciliary locomotion is an innovative mobility system thatutilizes the elastic force of cilia attached to the robot
surface at an angle. Utilizing vibratory actuation andthe deflection/buckling of the cilia, the robot is propelledsmoothly on the surface. The inclined cilia exert thrustforce repeatedly by deflection and buckling based on contact with the locomotion surface. Here, the period of vibrating motion of the robot significantly aﬀects mobility
performance. In this study, we utilize an eccentric motor
to exert vibratory force on the robot.
In a microgravity environment, dynamic forces become quite small. Hence, ciliary locomotion in microgravity can perform two diﬀerent locomotion modes:
crawling and hopping [9, 10]. Figure 2 illustrates thesemodes. In particular, the hopping height is quite small ina nominal case, and thus we call it micro-hopping. Ciliary
locomotion is based on a complicated dynamic interaction between the cilia and locomotion surface. To better
illustrate the locomotion principle, this paper first presents
observed results of microscale cilia behavior during locomotion.

2.1 High-Speed Camera Observation
2.1.1 Experimental Setup
We observed the precise microscale motion of a cilium
through planar microgravity experiments. Figure 3 shows
an overview of the experimental environment. For the experimental analysis, we developed an air-floating test bedof the ciliary locomotion robot that can emulate planar
motion in microgravity, as shown in Figure 4. The test bed
weighs 3.85 kg, and its size is 200 × 200 mm in the X-YFigure 2 : Schematic illustration of ciliary locomotion.
plane. Figures 5(a) and (b) also show the eccentric motor
unit and cilia unit mounted on the test bed. The eccentricweight weighs 12 g and the eccentric distance is 3.9 mm.
The cilia in the cilia unit are made of nylon, and their inclination angle is 80◦ . The cilia bundles are attached in fiverows and eight columns. Throughout these experiments,
the gravity level was set to 1 × 10−3 G. The test bed can becontrolled by an on-board micro-controller, and we input
the motor frequency as a command via wireless communication. Figure 6 shows the electrical system configurationof the test bed. The planar motion of the test bed was also
obtained by an external motion capture camera system.
We observed the microscale behavior of the cilia
using a VW-9000 high-speed camera produced by
KEYENCE Corporation, Japan. A VW-Z2 lens was used
(KEYENCE Corporation), and close-up views within a
5 mm radius were obtained during the locomotion experiments. The obtained video resolution is 640 × 480 pixels,
and the frame rate was set to 1 kHz.

2.1.2

Results and Discussion

An example image taken by the camera is shown in Figure 7. From these observations, the cilium motion canbe summarized as the mode of which the deflection andbuckling of the cilium is (i) increasing or (ii) decreasing.
Furthermore, in principle, each mode can also be divided
into the following four motion states.
• Negative slip:
The cilium slips in a negative direction with respect
to the locomotion. The ciliary thrust works in a positive direction with respect to the locomotion.

Motion tracking camera

Reflective marker

Simulatedsurface

Micro-controller(w/ motor driver)Stoneflat pate

RecordingcameraBattery

Test bed

Cilia unit

Air tank

Simulatedsurface
X

Y

p
Stone

Figure 4 : Ciliary locomotion robot test bed for microgravity experiments.
DC motor(w/ encoder)late

Locomotion direction
Φ

Figure 3 : Experimental overview of the microgravity emulation and measurement system.
• Sticking:The cilium tip sticks to the surface. Basically, the ciliary thrust works in a positive direction with respect
to the locomotion.
• Positive slip:
The cilium slips in a positive direction with respect
to the locomotion. The ciliary thrust works in a negative direction with respect to the locomotion. Large
locomotion velocities induce this state.

Eccentric weight

3 EXPERIMENTAL MOBILITYPERFORMANCEThis section presents the results of the experimental mobility performance obtained using the air-floating test bed,(b) Cilia unit

Figure 5 : Overview of the test bed actuation system.
LaptopSD cardBattery• Hopping:
The cilium does not contact the surface. No reaction
force is assumed.
Based on the observation results, we confirmed thatciliary locomotion is achieved by alternating modes (i)and (ii). In particular, we observed that the tip of a cilium holds onto the surface when it is deformed in mostsituations. In contrast, the tip mostly slips in a directionthat is opposite to that of the locomotion when recovering from deflection and buckling. When the cilia maintaincontact with the surface, stable ciliary locomotion can be
performed. The observed motion was basically the crawling mode because of the irregular properties of the cilia
at microscale. This result is also the same behavior as reported for ciliary locomotion on a surface under 1 G [15].

Cilia(a) Eccentric motor

Micro-controller

wireless
communication
XBee

Motor driver

DC Motor(w/ encoder)Figure 6 : Electrical system configuration of the test bed.
which emulates motion in a microgravity environment. In
particular, the eﬀects of gravity level and roughness of
surface on the mobility of ciliary locomotion were experimentally investigated.

3.1

Flat Surface Experiments

3.1.1

Experimental Conditions

For the locomotion experiments on an acrylic flat surface,
we investigated the eﬀects of diﬀerent levels of the emulated gravity and motor frequencies to analyze the locomotion parameters. The experimental conditions were as
follows:• Gravity: 1 × 10−2 G, 5 × 10−3 G, and 1 × 10−3 G• Motor Frequency: 5 Hz ∼ 80 Hz in intervals of 5 Hz

t = 0 [s]t = 5 [s]t = 10 [s]Figure 8 : Example image of the experimental motion of
the test bed: g = 1 × 10−3 [G] and f = 30 [Hz].

For each condition, we conducted five trials and averaged the locomotion velocity with error bars. The levelof the emulated gravity was adjusted by changing the inclination angle of the stone plate. We then quantitatively
evaluated the gravity by analyzing the free motion of thetest bed. The gravity in the x-axis direction was set within
a ±5% error, and in the y-axis direction was adjusted to beless than ±1% of the value in the x-axis direction.

20
Robot Linear Velocity [mm/s]

Figure 7 : Example high-speed camera image of cilia during locomotion.

g = 1x10-2 [G]

10

5

0

3.1.2 Results and Discussion
Figure 8 shows example images of the experimental motion of the test bed. In almost all of the cases, the test bed
moved smoothly without body rotation. Figure 9 depicts
the relationship between the motor frequency and linear
locomotion velocity of the test bed. This graph summarizes the results for each gravity condition, and shows thatgravity aﬀects the locomotion velocity. That is, a larger
gravity results in a smaller locomotion velocity in thesecases. Friction force is a major factor here. A larger gravitational force leads to more deflection and buckling of thecilium because of the greater robot weight. Although thisexerts a larger elastic force on the robot, at the same time,
the friction force works as a larger negative factor when
the cilia are recovering from the deflection and buckling.
In addition, under g = 1 × 10−3 [G], a clear peakin velocity is seen at around f = 35 [Hz]. We call thisthe state transition point. Whereas the velocity is proportional to the motor frequency from 0 Hz to 35 Hz, it increases as a second order curve of the frequency at morethan 40 Hz. These observed results come from the resonant characteristic of elastic deflection and buckling of
the cilia at around f = 35 [Hz]. Therefore, at frequencies higher than the resonant frequency, a decline in thelocomotion velocity was generated because the amplitudeof the test bed vertical motion decreased. In contrast, atmore than f = 80 [Hz], the locomotion velocity rapidly
increases. This comes from a resonant characteristic of themechanical stiﬀness of the test bed. This mechanical resonant frequency was also observed by a vibration sensor attached to the test bed. The resonant frequency generates alarger vertical motion amplitude, aﬀects the cilia’s deflection and buckling, and as a result, the locomotion velocity

15

g = 1x10-3 [G]g = 5x10-3 [G]

0

20
40
60
Motor Frequency [Hz]80

Figure 9 : Experimental results for steady locomotion velocity on an acrylic flat surface for various levels of emulated gravity.
increases. This tendency is notable at g = 1 × 10−3 [G],but it is a characteristic that is not of particular note in theother gravity cases.

3.2 Frictional Sloped Surface Experiments
3.2.1 Experimental Conditions
The mobility performance on a discontinuous sloped surface was experimentally investigated. In the experiments,
the gravity was set to g = 1 × 10−3 [G]. The motor frequency was selected from 10 Hz to 80 Hz in interval of
10 Hz. Figure 10 shows the flat and sloped surface used.
Moreover, a sheet of sandpaper was attached on the locomotion surface to investigate the eﬀects of friction on
mobility. As the key experimental conditions, the slope
inclination angle and grit of the sandpaper were set as follows:• Sandpaper: #120 (rough), #320, and #1000 (smooth)• Slope angle (α): 2◦ , 4◦ , 6◦ , 8◦ , and 10◦

3.2.2

Results and Discussion

Figure 11 shows the experimental results of locomotion
velocity on the sandpaper and acyclic board (for reference), where the velocity was obtained from trials on aflat surface area (not a slope). The results confirm thatlower friction works better for the locomotion velocity.
Although higher friction generates larger propulsive thrustTest bedg

4.1 Dynamics Model
4.1.1 Equations of Motion

Y
X

α
100 m

m

200 mmFigure 10 : Schematic of ciliary locomotion experiments
on a discontinuous surface with a slope.

Robot Linear Velocity [mm/s]

20
#120
#320
#1000
Acyclic board

15

10

In this section, we introduce a planar dynamics modelof the ciliary locomotion robot. This paper assumes a
two-dimensional dynamics model. Figure 12 illustrates
the schematic of the ciliary locomotion robot dynamics
model. We extended the fundamental dynamics model
developed in [16]. In this study, the locomotion surface
is assumed to be uniform and flat. We first define the inertia coordinate ΣO {X, Y}, in which X is the horizontal axis
parallel to the terrain surface and Y is the vertical axis
normal to the X-axis. The origin of the Y-axis is fixedat the locomotion surface. In addition, ΣR {x, y} denotes
the robot-fixed coordinates as shown in Figure 12(a). The
equations of motion of the robot with n cilia bundles arederived as follows:

5

M ẌG =F m · X +

n
∑

Ffi

(1)

i=1

0

0

20
40
60
Motor Frequency [Hz]80

M ŸG =F m · Y − Mg +n∑Fi · Y(2)

i=1

Figure 11 : Experimental results for steady locomotion velocity on flat sandpaper: g = 1 × 10−3 [G].

J θ̈ =g m ⊗ F m − τm +n∑(ri ⊗ Fi − T i )

(3)

i=1

from a general standpoint, it simultaneously creates larger
resistance. Therefore, as a design factor, the cilia must be
designed to maximize the mobility on an uncertain asteroid surface considering its frictional properties.
Table 1 shows the experimental results of slope traveling, where a check-mark (✓) indicates that the test bed
was able to move on the slope. The locomotion on asurface covered with #320 sandpaper, which is a surface
with medium friction, showed better slope traveling performance. This comes from the trade-oﬀ between thrustforce and frictional resistance. The results also show thatthe slope traveling performance depends on the locomotion velocity. In contrast, the locomotion on the acyclicboard (low friction) achieved higher velocity than on thesandpaper. Although a trade-oﬀ exits, the results confirm
that lower friction leads to better locomotion performance.

4 THEORETICAL ANALYSISThis section introduces the dynamics model of ciliary locomotion, and then presents its numerical analysis. The
theoretical model is validated by a comparison with theexperimental results, and we provide key remarks regarding the mechanics of ciliary locomotion.

where M is the robot mass, XG and YG are the position of
the center of gravity (COG) of the robot in ΣO , X and Y
are the unit vectors of the X- and Y-axis, respectively, J
is the moment of inertia of the robot around its COG, θis the rotation angle of the robot around its COG (wherecounter-clockwise is positive), F m is the centrifugal force
exerted by the eccentric motor, F f i is the friction force
between the i-th cilia and the terrain, g is gravitational acceleration, Fi is the force exerted by the i-th cilia on the
robot body, ri is the vector from the COG to the base of
the i-th cilia in ΣR , g m is the vector from the COG to therotational axis of the motor, and T i is the viscous-elastic
torque exerted on the based of the i-th cilia. Here, we canassume τ ≈ 0 because of the very small moment of inertiaof the eccentric weight. Furthermore, gmx and gmy are also
approximated as 0 in the actual test bed design.

4.1.2

(

Contact Detection and Mechanics)
Given piX0 , piY0 is the ideal tip position of the i-th cilia
without deformation in ΣO (where i = 1, · · · , n), piX0 and
piY0 can be geometrically written as follows: piX0 = XG + rix cos θ − riy sin θ − hi0 cos (θ + ϕi0 )
(4)



 piY0 = YG + rix sin θ + riy cos θ − hi0 sin (θ + ϕi0 )where rix and riy are the x and y components of ri in ΣR ,respectively. In addition, hi0 and ϕi0 are the natural lengthand implant angle of the cilia, respectively.

Table 1 : Experimental ability of the test bed to climb slopes with various frictional surfaces.
Sandpaper
Slope angle
f = 10 [Hz]f = 20 [Hz]f = 30 [Hz]f = 40 [Hz]f = 50 [Hz]f = 60 [Hz]f = 70 [Hz]f = 80 [Hz]

2◦
✓
✓
✓
✓
✓
✓
✓
✓

4◦

#1000
6◦ 8◦

10◦

✓
✓
✓
✓
✓

✓
✓

✓

COG

2◦
✓
✓
✓
✓
✓
✓
✓
✓

4◦
✓
✓
✓
✓
✓
✓
✓
✓

#320
6◦ 8◦
✓
✓
✓

10◦

✓
✓
✓

4◦
✓
✓
✓

#120
6◦ 8◦

10◦

Furthermore,

MotionBody
Eccentric
Motor
Microgravity

Fhi = khi (hi0 − hi ) − chi ḣi(7)

T i = kϕi (ϕi0 − ϕi ) − cϕi ϕ̇i(8)Surfacewhere Fhi is the elastic deflection force, T i is the viscoelastic torque, and hi and ϕi are the equivalent cilia length andbucking angle, respectively. Furthermore, khi and kϕi are
the elastic stiﬀnesses, and chi and cϕi are the damping coeﬃcients. When restoring the cilia from a deformed state
to a natural one (i.e., ḣi ≥ 0 and ϕ̇i ≥ 0), the damping
coeﬃcients chi and cϕi are assumed to be zero.

(c) Deformation of cilia

The contact point must be determined to calculate the reaction force when contact is detected by Eq. (4). We here
assume a small time step for the integral calculation of adiscrete-time system as a quasi-static analysis. First, contact force FiX is calculated based on the assumption thatthe cilia are sticking to the surface. When this conditionis satisfied, i.e., FiX < µ0 FiY , where µ0 is the maximum
coeﬃcient of static friction, contact point piX maintains
its contact in the last time step. If the condition is notsatisfied, ϕi is iteratively changed so that FiX < µ0 FiY ,piX decreases with respect to negative slip (FiX > 0) andincreases with respect to positive slip (FiX < 0). On thebasis of this analysis, we can define the cilia’s deformation
parameters, hi and ϕi , as follows:

Cilia(a) Fundamental schematic

4.1.3(b) Interaction mechanics

2◦
✓
✓
✓
✓
✓
✓
✓
✓

Figure 12 : Dynamic model of ciliary locomotion robot.
Assuming the cilia deformation (deflection and buck()ling) is quite small, the reaction force Fi ≡ FiX , FiY in
ΣO generated by the cilia can be given as follows:• piY > 0:
F i X = F iY = 0(5)• piY ≤ 0:

T i sin (ϕi + θ)Fi = Fhi cos (ϕi + θ) −



hi
 X



(ϕi + θ)
T
cos
i



 FiY = Fhi sin (ϕi + θ) +
h
i

(6)

Contact Point Determination• Negative and positive slip:

YG + rix sin θ + riy cos θ hi =sin (θ + ϕi )
 ϕ = ϕ̂ − sgn (F ) s∆ϕiiiX• Sticking:
{(

)2


h
=
YG + rix sin θ + riy cos θ

i





(
)2 } 21


+
X
+
r
cos
θ
−
r
sin
θ
−
p̃

G
ix
iy
i
X






 ϕ = ϕ̂
i

i

(9)

(10)

• Hopping:{hi = hi0ϕi = ϕi0

4.2.1
(11)

Here, p̃iX is the tip position of piX on the last calculation
step in ΣO is satisfied, s is the minimum value so that FiX <µ0 FiY , ∆ϕ is a small calculation step for incrementing ϕi ,sgn (·) is a signal function, and ϕ̂i is given as follows:()
YG + rix sin θ + riy cos θ−1
ϕ̂i = tan−θ
(12)
XG + rix cos θ − riy sin θ − p̃iX
The deflection and buckling states of the cilia underslip are determined by the iterative calculation, and we canthen compute the definitive reaction force Fi to be appliedat the current time step.

4.1.4 Frictional Characteristics
We apply the static and kinetic friction forces dependingon the motion velocity. For the four motion states definedin the previous section, F f i can be given as follows:• Negative slip:• Sticking:• Positive slip:

F f i = µFiY
F f i = F iX()
< µ 0 F iY

(13)
(14)

F f i = −µFiY(15)

Ffi = 0(16)

• Hopping:where µ is the coeﬃcient of kinetic friction.

4.1.5 Eccentric Motor()
The centrifugal force F m ≡ FmX , FmY in ΣO exerted by
the eccentric motor can be represented as follows:

2



 FmX = mrm ω cos (Ω + θ)
(17)



 FmY = mrm ω2 sin (Ω + θ)
where m is the mass of the eccentric weight, rm is the eccentric distance between the motor’s rotational axis andthe position of the center of mass of the eccentric weight,
ω is the motor angular velocity, and Ω is the motor’srotating∫ t angle. According to its definition, we deriveΩ = 0 ω·dt (boundary conditions: Ω = Ω0 and ω = ω0
at t = 0). In the analysis, we define motor frequency f as
f = ω/2π [Hz].

4.2 Comparative Analysis
The model-based numerical simulations were performed
for comparison with the experimental results. This paper
presents comparative analysis of ciliary locomotion in microgravity. In particular, this analysis focuses on the statetransition point at around f = 35 [Hz].

Simulation Parameter

The fundamental simulation parameters are shown in Table 2. Most of the parameters were determined so that they
simulated the specifications of the test bed. Here, hi0 and
ϕi0 were given as constant values, defined as h0 and ϕ0 ,respectively. The elastic stiﬀness of the cilia, khi and kϕi ,were experimentally determined by applied weights andstatic deformation. In contrast, the damping coeﬃcients,
chi and cϕi , were tuned through parametric analysis. Assuming no diﬀerence between the cilia, khi , chi , kϕi , and cϕican be given as constant values kh , ch , kϕ , and cϕ , respectively. The time step was 0.1 ms in the integral calculation.

4.2.2

Results and Discussion

Figure 13 compares the results of the experiments andmodel-based simulations. These plots show the dataof the locomotion velocity on an acyclic flat surface in
g = 1 × 10−3 [G]. The model can qualitatively simulate the experimental mobility performance. In particular,
the results confirm that the simulation produces the samestate transition point as the experiments at around aroundf = 35 [Hz]. This arises from the resonance of the motor
frequency with the cilia’s stiﬀness. Assuming the robot isa simple mass-spring model, the natural frequency of thecilia is close to 35 Hz. The simulation results before thetransition point match the experiments quantitatively. In
contrast, the experimental and simulated velocities after
the transition point have a few diﬀerences. Although mostof the physical parameters of the cilia were set to constantvalues, variable and nonlinear parameters need to be introduced to improve the model.

5

CONCLUSION

This paper presented the experimental mobility performance of ciliary locomotion under various values of gravity, friction, and slope. In an initial approach, the locomotion principles of ciliary locomotion were observed andanalysed by microscale images of a high-speed camera.
Locomotion experiments were next conducted using an
air-floating test bed that can emulate free motion in planar
microgravity, and the results confirmed that the locomotion velocity is improved in lower gravity. Furthermore,
we found that the state transition point, around 35 Hz in
the test bed, results from the resonance of the motor frequency with the cilia’s stiﬀness. The locomotion velocity
was proportional to the motor frequency before the transition point, whereas the velocity descends rapidly and increases again as a quadratic curve above this point. In
addition, locomotion experiments were performed on various roughness of sandpapers and slopes. As a result, although higher friction lowers locomotion velocity on a flat
surface, some friction is required for the test bed to climb
slopes. This reveals an important trade-oﬀ relation in the

ROBOT SYSTEM
SymbolValue
M
3.85 kg
J
0.046 kgm2m
0.012 kgrm
0.0039 m
gmx
0m
gmy
0m
Ω0
0 rad
ω0
0 rad/s

ELASTIC CILIA
SymbolValuen8h00.015 mϕ04π/9 rad (= 80◦ )µ (< µ0 )0.25 (< 0.28)
kh
10000 N/mch
2 Ns/mkϕ0.01 Nm/rad
cϕ
0.00001 Nms/rad

design process. On the basis of the observed results, wedeveloped and extended the dynamics model of the ciliary
locomotion. Slip detection and frictional characteristics
were introduced into the model. In particular, the modelbased simulations can produce the state transition point
observed in the experiments. The comparative analysis of
the experiments and model-based simulations confirmedthat the developed model can simulate the mobility experimentally observed on a microgravity surface.

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Robot Linear Velocity [mm/s]

Table 2 : Fundamental simulation parameters.

20

15

Experiment
Simulation

10

5

0
0

10

20

30

40

50

60

70

80

Motor Frequency [Hz]Figure 13 : Comparative results of locomotion velocity on
a flat acyclic surface: g = 1 × 10−3 [G].
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