Ciliary Micro-Hopping Locomotion of an Asteroid Exploration Robot
Kenji Nagaoka† ‡ , Riku Takano† , Takayuki Izumo† , Kazuya Yoshida††

Tohoku University, 6-6-01, Aramaki-Aoba, Aoba-ku, Sendai 9848579, Japan‡
E-mail: nagaoka@astro.mech.tohoku.ac.jp

Abstract
Locomotion capabilities form the basis for accomplishing robotic exploration by a rover on an asteroid.
While traditional locomotion gears, such as wheels andtracks, are promising candidates for traversing extraterrestrial terrains, their capabilities lower in such an environment due to its micro-gravity. Here, we propose a
new idea of ciliary micro-hopping mechanism for an asteroid exploration robot. In this paper, we deliver fundamental locomotion characteristics of the mechanism basedon ground experiments by using an air-floating test bed.
Through the experimental analyses, we indicate the proposed mechanism can be one of the possible solutions on
locomotion principle under micro-gravity.

Table 1. Estimated parameters of 1999 JU3 [4–6]
Parameter
diametergeometric shape
period of rotation
inclination of the axis
albedo coefficientgravitational constantnominal gravity
escape velocity
surface material
temperature
distance from the sunthermal inertia

Value
0.87 ± 0.02 km
0.92 ± 0.12 km
subglobular (1.3:1.1:1.0)7.63±0.1 hlongitude 331±10 deg
latitude 20±10 deg
0.070±0.006
11∼92 m3 /s2
3×10−4 m/s2
10.9∼31.6 cm/s
regolith and/or rocks
average -60∼+80 deg C
0.96∼1.42 AU
200∼600 Jm−2 s−0.5 K−1

1 Introduction
Exploring primitive bodies such as asteroids is expected to bring key findings of the origin of the solar system or terrestrial life [1]. As one of the successful asteroid missions, the world first sample return mission, named
Hayabusa, was demonstrated by Japan Aerospace Exploration Agency (JAXA). The Hayabusa spacecraft recovered dust samples from an S-type asteroid 25143 Itokawa,
and after a seven-year cruising, the spacecraft broughtback them to the Earth on June 2010 [2]. In the Hayabusa
mission, the spacecraft carried a small rover that can perform surface exploration on the asteroid Itokawa. This
rover is named MINERVA (MIcro/Nano Experimental
Robot Vehicle for Asteroid), and it has a mobility system
in micro-gravity environment. It has an inner torquer analogous to a reaction wheel and can hop using body rotation reacted by the torquer’s reaction torque [3]. Although
MINERVA’s landing onto the surface was unsuccessful
due to an unexpected release altitude from the spacecraft,development of MINERVA has promoted a pioneer technology in robotic locomotion under micro-gravity.
Following the Hayabusa mission, JAXA is now planning to launch the Hayabusa 2 spacecraft in 2014. This
upcoming mission will target a C-type asteroid 162173
1999 JU3. On the basis of latest observation and analysis,an estimate of environmental parameter of the target asteroid has been reported as shown in Table 1. According
to this, the environment is harsh for a mobile rover.

In the Hayabusa 2 mission, some small explorationrovers will be equipped, which are expected to obtain scientific findings by demonstrating in-situ surface observation. A series of these rover systems is named MINERVAII. With respect to nominal design requirements for the
MINERVA-II rovers with their mechanical interface attachments with the Hayabusa 2 spacecraft, the following
remarks must be satisfied;• total mass: less than about 1.5 kg,• size limitations: 175 mm in diameter and height,• mobility system: reliable mechanism under microgravity with environmental uncertainties,• limited power resources without chemical batteries.
Toward the development of the MINERVA-II rover,various hopping locomotion systems are currently being
intensively studied. However, for the in-situ science observation, achieving accurate mobility based on hopping
is technically one of the significant challenges because theasteroid surface environment accompanies uncertainties,
such as a gravity field and terrain irregularity. To negotiate
such environment, we propose a ciliary micro-hopping locomotion system for the MINERVA-II rover. We first designed the proposed system driven by an eccentric motor.
According to this idea, the proposed locomotion systemcan exert both a reaction torque of the motor and a centrifugal force of an eccentric weight attached to the motor.
These forces are exerted based on different driving variables of the motor: rotational acceleration and velocity.
Therefore, the rover can perform various hopping motions
by controlling the eccentric motor. In addition, employing
elastic cilia on the rover surface prolongs contact duration
with the unknown asteroid surface before lifting-off. Although the contact duration is generally determined by thegravity and the coefficient of restitution with the asteroid
surface, the cilia enables the rover to control contact dynamics because of their smaller elasticity. As such, thecilia are expected to militate for the rover mobility in an
unknown asteroid.
This paper presents fundamental locomotion characteristics of the ciliary micro-hopping mechanism. The
ground experiment was carried out in order to investigate
the characteristics by using an air-floating test bed. In thedeveloped test bed, planar motion under micro-gravity canbe emulated using air bearings on a flat plate. The characteristics were experimentally evaluated with several typesof the input motor rotational velocity and different cilium
properties. According to the experiment, we provide key
remarks for mechanical design and motion control of thecilia mechanism of an asteroid exploration rover. The experimental results also contribute to develop mathematicalmodels of the rover motion under micro-gravity environment.

2 Ciliary Micro-Hopping Locomotion
2.1 Related Works
Hopping locomotion is one of the feasible solutions
for a mobile rover on micro-gravity asteroid surface.
Generally, gravitational attraction of asteroids becomesminute. It is hard for a rover to maintain contact with asteroid surfaces during its locomotion. Therefore, not only
the torquer-typed hopping method of MINERVA [3], several hopping mechanisms have been proposed and elaborated for applying an asteroid exploration rover [7–12].
Locomotion principles of these proposals are divided inlocomotion using: external movable legs/arms [7, 11, 12],multi-wheels with swingable struts [9], internal electromagnetic levitation [8], and elastic sprigs and linear actuators [10]. Basically, the locomotion method of these isbased on hopping by utilizing active contact forces withthe asteroid surface. On the other hand, the first hopping
rover in space missions was PROP-F by the former Soviet Union in 1988 [13]. The PROP-F rover was carriedby the Phobos 2 spacecraft for Phobos, the moon of Mars,
but the spacecraft went astray before reaching Mars due
to communication faults by a malfunction of the on-board
computer [14]. Hence, any of the hopping rovers has notexperienced locomotion on small celestial bodies yet.

On the other hand, there have been some researcheson cilia mechanism as a conveyor or a pipe-inspection
robot. Most of these, however, are a lot different froman asteroid hopping rover from a viewpoint of contact dynamics. Recently, Ioi has elaborated dynamics modelingof the micro-robot with elastic cilia driven by the centrifugal force of a rotary motor [15]. In a practical application,
Konyo et al. has developed the active scope camera using
ciliary vibration for rescue in disaster sites [16]. Whilethese previous works discussed theoretically dynamics ofciliary locomotion, their locomotion principle is based ona ground gravitational constraint. As such, these cannot
simulate locomotion under micro-gravity since a motor’s
micro-reaction torque affects body rotation.

2.2

Locomotion Principle of Micro-Hopping
under Micro-Gravity

On robotic locomotion over rigid surface such as indoor floor or paved road, a mobile robot needs to exert
propulsive forces. The forces are basically divided into
frictional contact with the ground, external force with environment (without ground contact) or additional thrusterfrom the robot. However, moving on the surface accompanies frictional effects against the ground as thrust or resistance. In such locomotion, the frictional propulsion has
been the most common method. Given locomotion gear
drives on the ground, the reaction force F exerted by theground contact friction has the following relation.
0 ≤ F ≤ µMg(1)where M is robot mass, µ is a static frictional coefficient
between the robot and the ground, and g is a gravitational acceleration. Furthermore, Mg is a normal force
and thereby µMg acts as a static friction. Because deformability of the surface can be ignored, the reacted force
F is determined not by a contact surface area of the robot
but by only M. Therefore, degrees of freedom of a direction of a propulsive force become significant in robotic
surface mobility on the rigid ground. While locomotion
velocity or explorable area is a key factor for an exploration rover in time-limited space missions, g becomesmuch smaller under micro-gravity environment. That is,
micro-g exerts only micro-velocity for rover locomotion.
As a result, the frictional forces based on system weightcannot be expected to utilize as an effective surface locomotion method on most asteroids.
Locomotion principle varies greatly depending on
gravity environment. On a micro-gravity asteroid, agravity-based propulsive thrust for hopping locomotion
becomes much small. Hence, a rover ought to actively
generate additional contact forces with the asteroid surface to achieve an adequate locomotion velocity. At thesame time, the locomotion velocity must be less than an
escape velocity (∼ a few 10 cm/s) on the asteroid. Further-more, one of the key challenges is locomotion accuracy onan unknown asteroid with environmental uncertainties. In
this paper, we newly investigate micro-hopping locomotion reducing the locomotion error by repeating a microhop.
At first, we introduce the basic theory of microhopping under micro-gravity. Consider that a robot with
M in mass hops under micro-gravity on a flat surface,where gravity acceleration g assumes to vertically work
as a constant value. We here define coordinates are set tobe z-axis in a vertical direction and x-axis in a propulsive
direction normal to z-axis. Given the robot obtains a vertical impulse Fz ∆t from the surface, an initial velocity vz
in z-axis is written as follows.
vz =

Fz ∆t
M

(2)

Accordingly, the maximum height Hz and the horizontal locomotion distance H x of a micro-hop can be expressed as follows.
Hz

=

v2z
2g

(3)

Hx

=

v x vz µv2z
=
g
g

(4)

where the horizontal velocity is assumed to be represented
as µvz in Eq. (4). The time period of the micro-hop fromlifting-off of to landing on the surface becomes 2g/vz .
Based on these equations, the rover needs to control
the square of impulse obtained from the surface (Fz ∆t)2 toachieve a desired H x .

2.4

Micro-Hopping by Eccentric Motor under
Micro-Gravity

In accordance with the above description, the impulse from the surface is importance of controlling microhopping. The eccentric motor militates for locomotion because it can exert both a centrifugal force and a reaction
torque to obtain the impulse. Figure 1 illustrates different
locomotion modes based on these forces.
A centrifugal force exerted by an eccentric motor isexpressed as mrω2 , m is mass of an eccentric weight, r is
distance between a rotational axis of a motor and the masscenter of the eccentric weight, and ω is angular velocity ofthe eccentric motor. Thus, the eccentric motor can exert
periodic vibration force from the motor’s rotational axis to
the robot’s center of gravity, depending on the rotationalenergy of the eccentric weight.
Likewise, the robot moves or rotates under microgravity by applying reaction torque induced when the motor accelerates or decelerates. The motor’s reaction torqueis written as I ω̇, where I is moment of inertia of the eccentric weight, ω̇ is angular acceleration of the eccentricweight. Note that the actual torque acts around the centerof gravity of the robot.

3

Experiments

3.1

Overview of Tet Bed

Figure 2 shows the test bed for micro-gravity experiments. The test bed weights 1.56 kg, and its dimension is

Eccentric Motor

2.3 Advantage of Ciliary Micro-Hopping
The ciliary micro-hopping mechanism can offer thefollowing advantages.
Cilia

An eccentric motor exerts:• a centrifugal force (a function of motor velocity)• a reaction torque (a function of motor acceleration)
An elastic cilium assists:

step 0static state

step 1
rotating

step 2
hopping(a) Hopping based on reaction torqueEccentric Motor• a workable contact duration with asteroid surface• a controllability of hopping directivity• soft-landing onto asteroid surface
A magnitude of one-hop amount affects as an error ina landing position. Equipping completely-accurate landing mechanism is quite difficult for a rover on an asteroid
terrain with various uncertainties. Thus, micro-hops allow
the rover to reduce accumulation of an error in locomotion
accuracy.

Cilia
step 0static state

step 1
crouching

step 2
hopping(b) Hopping based on centrifugal force
Fig. 1. Locomotion principle of ciliary micro-hoppingwith eccentric motor under micro-gravity

Tracking markers

XBee (wireless communication)

Dry cells (for circuit)
H8 micro-controller
DC/DC converter
Motor driver
⅙Li-Ion battery(for driving motor)
Air tank

Elastic cIlia

Air bearings
Eccentric motor
Fig. 2. Test bed of ciliary micro-hopping rover

18 cm in length, 15 cm in width and 20 cm in height. To
emulate micro-gravity environment, the test bed equips
three air bearings, produced by New Way Air Bearings,
are embedded on bottom of the test bed as an air-floating
system. An air-tank is also mounted on the test bed.
With respect to the eccentric motor, 1.2 g of an eccentricweight is attached on a rotary shaft of a brushed DC motor.
The motor is driven and controlled by H8/3684F microcontroller produced by Renesas Electronics Corporation.
Practically, we sent a pulse width modulation (PWM) input of the DC motor to the micro-computer via Xbee wireless communication modules produced by Digi International. In particular, the main objective of the experiments
is investigating effects of the centrifugal force and the cilia
properties on the locomotion characteristics.

Throughout the experiment, the robot position was
tracked by using four IR motion capture cameras, named
OptiTrack. This camera system can provide tracking data
every 1 ms. On preliminary camera calibration, the position error was ±88 µm in the experimental setup.
As illustrated in Fig. 5, an acrylic board is laterally attached on the stone plate as a flat surface for locomotion.

3.2 Experimental Environment

D : implant diameter of cilia bundles

Let us define the coordinates for representing motionof the robot. Motion of the robot is constrained in twodimensional plane onto the stone plate, the robot behavesas it under planar micro-gravity. The initial position of
the geometric center of the tracking markers before driving, (x, z), shall be the origin of coordinates. As shownin Fig. 5, the locomotion direction is set to be +X direction and the gravitational direction be −Z. As such, thisapproach allowed one to consistently evaluate the relative
motion of the test bed through the experiments.
Next, we calculated gravity level acting to the robot
during the experiments. Through preliminarly free-falling
experiments, we calculated the emulated gravity field byapplying least-square method to the time histories of theposition data. Consequently, the emulated gravity condition was 4×10−3 m/s2 in −Z direction and 5×10−4 m/s2 in−X direction.

3.3

Experimental Conditions

In the experiments, we used five cilia units (#1∼#5).
Nomenclature of geometric parameters of the cilia units
are described as follows:d : diameter of ciliumh : effective height of cilia bundles
θ : inclination angle of cilia bundles
w : weight of cilia unit
Variable specification of the cilia units is shown in Table 2. Constant parameters of them are also w = 115 g,
D = 3 mm, and h = 15 mm. Schematic of the cilia unit isshown in Fig. 3. Elastic stiffness of cilia materials lowers
wool, nylon, and Corebrid B, in that order. In the experiments, we input PWM duty cycle 30, 50, 70, and 100 %to the eccentric motor in order for examining effects ofthe motor’s rotational speed. We also confirmed the experimental data was a reasonably reproducible result bycomparison with several trials.

Locomotion Surface

Cilium Angle

O

Cilia

Z
X
Base

Robot
Fig. 3. Geometry of cilia unit

Marker 3
Motion Capture Camera

X

Locomotion
Surface

Z
O

m

0c

10

100cm

Stone
Plate

Marker 2

Marker 1

Fig. 5. Coordinates of micro-gravity experiments

Fig. 4. Overview of test environment
Table 2. Cilia unit parameters in experiments

3.4 Results
Figure 6 shows effect of the rotational speed with thenylon cilia #1. Here, x, z and roll represents X and Y position and rotational angle around an axis normal to XZ
plane of center of the three attached markers in respectively. From these results, the locomotion velocities in x
direction increased in response to the motor’s rotational
speed. For instance, the locomotion distance changed
based on an increase of the PWM duty cycles: 21, 30,
32, 38 cm by PWM 30, 50, 70, 100 % at the distance x of
t=25 s. Also, the robot largely rotated in which the PWM
duty cycle set 30 %. As a result, the locomotion distancein x direction decreased due to reduced contact area ofthe cilia with the locomotion surface. Furthermore, we
can confirm that the test bed periodically performs microrotation and micro-hops as seen from the closeup views in
Fig. 6.
Next, Fig. 7 shows experimental results of the nylon cilia units with a different θ: #2 and #3. Comparedto the unit #1, the locomotion velocity in x direction increased with an increase of θ. However, an improvement
by increasing θ obviously had a certain limitation. Therefore, the result suggests θ has an optimal value, at leastθ=30 deg would be proper in these experiments. To investigate the optimization of θ, detailed elaborations are
required with an analysis of theoretical modeling.
Figure 8 shows the experimental results using cilia
made by wool (#4) and Corebrid B (#5). While we could

#1
#2
#3
#4
#5

Material
Nylon
Nylon
Nylon
Wool
Corebrid Bd [µm]
70
70
70
100
40

θ [deg]
20
10
30
20
20

not observe a key difference between #4 and #5, the cilia#1 exerted the propulsive force more than #4 and #5. As
such, the result suggests that the elastic cilia induce energy losses, although the cilia elasticity assist the rover tocontrol the contact dynamics.

4 Discussion
In this section, we provide an experimental analysis
based on the results in the previous section. Figure 9shows analytic results of the experimental data, indicating the locomotion velocity in x direction. As an analysis
method, in this paper we computed the velocity in processing the difference of the x position data with a threedimensional Butterworse filter, a kind of lowpass filters.
In the closeup view (10 ≤ Time ≤ 15 [s]) in Fig. 9, thelocomotion accelerations were averagely distributed from
0.7 m/s2 to 1.4 m/s2 . Immediately after the test bed started
moving, locomotion accelerations had a lot of difference.
But, in the closeup view range (the steady accelerated
range), all the resulting plots indicated a linear increase.

50
30 [%]

50 [%]

70 [%]

100 [%]

x [cm]

40
30
20
10
0
0

5

10

15

20

25

30

Time [s]10.2

30 [%]

50 [%]

70 [%]

100 [%]

0.5

closeup view

0
20

29

Time [s]z [cm]

0.1
0
−0.1
0

5

10

15

20

25

30

Time [s]60

430 [%]

50 [%]

70 [%]

50

100 [%]

40

2roll [deg]closeup view

25

29

Time [s]

0
−2
−4
0

5

10

15

20

25

30

Time [s]Fig. 6. Experimental results of cilia unit #1 with various PWM duty cycles
In the experiments, the cilia angle and the PWM duty cycle had much influence on the accelerations in this range.

5 Conclusion
This paper elaborated on the fundamental locomotion characteristics of the ciliary micro-hopping mechanism driven by the eccentric motor based on micro-gravity
experiments emulated by using an air-floating test bed.
We especially investigated the effects of the driving con-ditions and the cilia properties on the locomotion velocity. On the whole, we indicated that the ciliary microhopping locomotion proposed in this paper is capable ofadequate mobility under micro-gravity. Furthermore, thispaper suggests the cilia elasticity should be designed withconsideration of gravity environment. As future works,
the dynamics modeling and its theoretical analysis are thenext challenge to be addressed. The locomotion capabilityof the cilia mechanism in sandy and/or rocky terrain under
micro-gravity will be investigated as well.

60

60
x [cm]z [cm]
roll [deg]

50
40
30

40
30

20

20

10

10

0

0

−10
0

5

10

x [cm]z [cm]
roll [deg]

50

15

20

25

30

35

−10
0

40

5

10

15

20

25

30

Time [s]Time [s](a) Cilia unit #2 with PWM duty cycle 100%(b) Cilia unit #3 with PWM duty cycle 100%
Fig. 7. Experimental results with various cilia angles

60

60
x [cm]z [cm]
roll [deg]

50
40
30

40
30

20

20

10

10

0

0

−10
0

−10
0

5

10

x [cm]z [cm]
roll [deg]

50

15

20

25

30

35

5

10

15

20

25

30

35

40

Time [s]Time [s](a) Cilia unit #4 with PWM duty cycle 100%(b) Cilia unit #5 with PWM duty cycle 100%
Fig. 8. Experimental results of different cilia

Velocity in x [cm/s]

3#2: PWM 30 %2

#2: PWM 50%

2

1#2: PWM 70 %#2: PWM 100 %10closeup view15

#1: PWM 100 %1#3: PWM 100 %#4: PWM 100 %#5: PWM 100 %

0
0

5

10

15

20

25

30

Time [s]Fig. 9. Analysis results of experimental data: locomotion velocity in x direction

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