Proceedings of the 2000 IEEE/RSJ
International Conference on
Intelligent Robots and Systems
Mobility of a Microgravity Rover using Internal Electro-Magnetic
Levitation
31 ,
Yoshihiko NAKAMURA
31
32 ,
Shingo SHIMODA
31
Sanefumi SHOJI
Dept. of Mechano-Informatics, University of Tokyo
7-3-1 Hongo Bunkyo-ku Tokyo, 113-8656 Japan
32 Dept.
of Environmental Studies, University of Tokyo
fnakamura,
Abstract
A new type of mobility is discussed for space projects
such as the MUSES-C aiming at small asteroid exploration. Since the environment of asteroids is of vacuum and microgravity, oatation is a possible choice
for enhancing a new mobility of the rover. In this
paper, we propose the use of electro-magnetic levitation in order to integrate a mobility into the microgravity rover. The rover has a spherical shape and
a smaller spherical shell inside. Four electro-magnets
are symmetrically located between the outer sphere
surface and the inner sphere shell with one end of
each directed to the center of the shell. With electromagnetic force of the magnets, a sphere iron ball inside
the shell is controlled and levitated. When the rover
lifts the ball inside with the electro-magnetic force,
the rover is in return pressed down the ground by the
reaction force, due to which the rover system not only
gains upward momentum for oatation, but also obtains friction that enables its rolling on the ground.
The prototype microgravity rover was developed and
provided experimental results indicate eectiveness of
the proposed mobility.
1
Introduction
The Mars Pathnder of NASA/JPL succeeded in
soft-landing on the equator of Mars in 1998[1]. Sojourner[2], the micro-rover was released on Mars and sent
us numerous observation and image data. In the investigation of the planets, satellites and asteroids, the
importance of robot rovers that move and investigate
on the surface is increasing[3][4]. For micro-rovers,
Nakatani[5] listed up the following requirements:
1. wide area of investigation (dozens ∼ several hundreds [km])
2. underground investigation (dozens [cm] ∼ several [m] in depth)
3. long time investigation
4. investigation of crust exposures such as craters
and precipices
5. sample selection and analysis
6. settlement of observation and experimental devices
In addition to the restrictions on weight, size, and
electric power, rovers must survive in an unknown environment with high/low temperatures, cosmic rays,
vacuous, regolith and so on.
0-7803-6348-5/00/$10.00 ©2000 IEEE.
g
shimoda, shoji @ynl.t.u-tokyo.ac.jp
The Institute of Space and Astronautical Science
designed the satellite MUSES-C for investigation of
asteroid Nereus, and scheduled its launch in 2002[6].
MUSES-C discharges a rover for sampling the surface
of the asteroid[7]. The microgravity environment on
asteroid is not suitable for the conventional rovers,
that move using the gravity and friction forces between the rover and the ground. It is required to develop a rover with new type of mobility. In this paper, we develop a microgravity rover that moves using
electro-magnetic levitation.
2
Requirements for the MUSES-C Microgravity Rover
The conditions on the rover for MUSES-C are as
follows [8]:
mass: 1 kg or less including the separation system from MUSES-C
size: within 10 2 10 2 10cm3
life: several weeks
communication: earth-reachable via MUSES-C.
temperature: durable within -100 ∼ 140℃
Mobility is, however, the most essential requirement.
The rover should move and reorient in any direction in
the unknown environments, since none of the gravity,
the escape velocity, and the surface friction is precisely
predictable.
3
3.1
Mobility
Structure
In order to move on the asteroid, a common rover
would rely on the friction force with the asteroid surface. Since the gravity of Nereus is estimated in the
order of 1004 m/s2 , it is dicult to obtain sucient
friction force from the gravity force. On the other
hand, taking an advantage of microgravity and vacuous, the rover can move for a long period of time and
for a long distance, once it oats with a horizontal
velocity.
In this paper, we adopt the oating mobility due to
electro-magnetic levitation using four electro-magnets
and an iron ball installed within the rover body, as
shown in Figure 1. The rover attracts the iron ball
and thereby gets the reaction force, that presses itself
against the ground. In turn, the rover gains the lifting
force, the friction force, and the momentum. This
rover can jump and reorient itself in the air.
Figure 3: Mobility control of spin
electromagnet
iron ball
Figure 1: Structure of Microgravity rover
Figure 4: Mobility control of horizontal jump
Figure 2: Mobility control of vertical jump
3.2
Floatation
The mobility of the rover is oatation and reorientation, whose combination allows it to move freely on
the asteroid. We explain in this subsection the principle of oatation using Figure 2.
Initially assume the rover stays on the ground and
that the iron ball is at rest in the bottom of the spherical cavity inside the rover (Figure 2 (a)). First, the
rover pulls up the iron ball with the electro-magnets,
and, in turn, is pressed against the asteroid due the
reaction force of the electro-magnetic force(Figure 2
(b)). The iron ball with the upward momentum collides at the top of the spherical cavity(Figure 2 (c)).
The collision transfers a part of the upward momentum of the iron ball to the rover, and the whole rover
oats(Figure 2 (d)).
3.3
Reorientation in the air
There are two conceivable ways to reorient the rover
in the air. One method is to rotate the iron ball like
a spherical induction motor generating eddy currents
on the iron ball. Through the rotation of the iron ball,
the rover obtains the reaction moment to reorient itself. However, this would require more than seven
electro-magnets in addition to gap sensors, and precision control using them.
Another simpler method is to employ only four
electro-magnets and control the position of the iron
ball. We explain the principle using the basic equation. From the angular momentum conservation, we
have:
Ib!b + mb rb 2 r_b + Ir !r + mr rr 2 r_r = 0
(1)
Ib : inertia matrix of the iron ball
Ir : inertia matrix of the rover without the iron ball
mb : mass of the iron ball
mr : mass of the rover without the iron ball
rb : vector from the center of gravity of the whole
rover to that of the iron ball
rr : vector from the center of gravity of the whole
rover to that of the rover without the iron ball
!b : angular velocity of the iron ball
!r : angular velocity of the rover
From the abobe equations !r is resolved as follows,
!r = 0Ir 01(Ib !b + mbrb 2 r_b + mr rr 2 r_r )
= 0Ir 01(Ib !b + mb(mmr 0 mb) rb 2 r_b) (2)
r
where the equation of momentum conservation was
used. From Eq.(2), we can conclude
1. When mr =mb , !r and !b is simple mapping,
where the rover can rotate in proportion to the
rotation of the iron ball.
2. When mr 6= mb , in addition to the rotation due
to !b, the rover can rotate even without the rotation of the iron ball using the second term of
Eq.(2).
Therefore, we propose to choose mr 6= mb. Note that
with only four electro-magnets we can directly control
rb. However, indirectly we have an access to control
!b by rolling the iron ball in frictional contact with
the inner surface of spherical shell as shown in Figure
3.
3.4
Horizontal Jump
During the rover is pressed against the asteroid,
the gravity is virtually generated. Horizontal jump becomes possible depending upon the virtual gravity and
Table 1: Specications of microgravity rover
electro- iron core
magnet
coil
iron ball
inner spherical shell
rover body
4
Figure 5: Mesh used for FEM analysis of electromagnetic force
Figure 6: Electro-magnetic force v.s. distance (maximum gap : 2.5cm; iron ball : 3cm; electro-magnet
: 1cm 2 2cm (iron core), 5A (current))
the surface friction. When a rover would have more
than seven electromagnets and an iron ball would
possessed independent six degrees of freedom like a
spherical induction motor, we could independently rotate the rover while generating the virtual gravity.
This allows to have horizontal velocity when it starts
to oat. Since the natural gravity is in the order of
1004 0 1005m/s2 , the rover would have a reasonable
horizontal jump ever with a small vertical jump.
Another method is feasible with only four magnets.
By pulling up an iron ball in the inclined direction as
much as angle from the vertical of momentum from
the ground if
tan > 1
Where is the frictional coecient between the asteroid and the rover.
1cm 2 2cm
1000 turns
3cm, weight 100g
4cm
14cm, weight 1000g
Magnetic Levitation System
4.1
System Design
4.2
Simulation of Magnetic Floatation
Using a FEM software, we analyzed the relationship between the electro-magnetic forces and the distance from the iron ball to the electro-magnet. The
whole model was subdivided into nite elements as
shown in Figure 5. Since the gravity of the asteroid is estimated in the level of 1003 ∼1005 m/s2, the
electro-magnetic force on the iron ball needs more
than F = 1002 ∼1003 N .
The electro-magnetic force was calculated assuming the iron core of the electro-magnet (1cm2 2cm),
the coil (5000 turns), current (5A), the maximum gap
(2.5cm), and the iron ball (3cm). Figure 6 shows the
result. Since the large electric power over 5A is demanded to generate 1003 N when the gap is 2.5cm, it
would be unrealistic under the imposed constraints.
Figure 7, on the other hand, shows the electromagnetic force versus the radius of the iron ball under the condition of constant distance between the
iron ball and electromagnet. The longer the radius of
the iron ball becomes, the larger the attracting force
grows.
Figure 8 shows the maximum velocity of the iron
ball versus the initial gap between the surface of the
iron ball to the electro-magnet. Note that the maximum velocity saturates against the growth of the gap.
From these considerations, we can conclude that
the combination of the the small space and the large
iron ball is more eective in obtaining momentum than
that of the large space and small iron ball. We determined the dimensions of the electro-magnets and the
iron ball as shown in Table.1, where the initial gap
between the electro-magnets and the iron ball is 1cm.
Assuming 7V and 500mA for the battery, we designed the coil as follows: 0.3mm copper wire of 50
m in length, and of 14 [9] in resistance.
The electro-magnetic force that attracts the iron
ball is approximated by F= ax2 +1bx+c [10], where x
is the distance between the iron ball and the magnet.
Figure 9 shows the computational result.
Figure 10 shows the velocity of the iron ball when
the initial gap is 1cm. Figure 11 shows velocity versus
position of the iron ball when it starts from 1cm of the
initial distance. From these analysis, we obtained the
following results:
1. The iron ball collides with the rover body after
0.7 second 0.12m/s.
15
2.5
1.5
force (N)
Force(N)
2
10
5
1
0.5
0
0
0.01
0.02
0.03
radius(m)
0.04
0
0.05
Figure 7: Electro-magnetic force v.s. radius of iron
ball (electro-magnet : 1cm 2 2cm (iron core), 5A
(current))
0.5
1
1.5
2
2.5
3
x 10 3
distance (m)
Figure 9: Electro-magnetic force v.s. distance
(approximated computation due to Sugie at al.[6])
0.14
0.1
velocity (m/s)
velocity (m/s)
0.12
0.1
0.08
0.06
0.04
0.02
0.08
0.06
0.04
0.02
0
0
0.02
0.04
0.06
distance (m)
0.08
0
0.1
Figure 8: Initial gap v.s. maximum velocity of iron
ball (electro-magnet : 1cm 2 2cm (iron core),
500mA (current); iron ball : 3cm)
2. Based on the momentum conservation low, the
whole body obtains 0.012m/s of velocity after
the collision if we assume complete non-elastic
collision and zero restitution coecient.
3. The rover ies for 200 seconds up to the maximum height of 40cm when we assume gravity
acceleration 1004 m/s2.
4. When the friction coecient of the surface is assumed 0.5, the friction force is represented by
f = 0:5F
(3)
where F and f are the virtual gravity force and
the friction force. If we also assume the virtual
gravity as shown in Figure 11, the friction force
of Eq.(3) provides the horizontal momentum and
velocity indicated by Figure 12. Figure 12 suggests that the rover jumps 90cm in the horizontal direction with the initial horizontal velocity
of 4.503
210 m/s.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
time (s)
Figure 10: Result of theoretical computation; velocity
of iron ball v.s. time (initial distance : 1cm)
5
Experiments
5.1
Prototype of the Microgravity Rover
To evaluate the mobility of the rover, we prototyped
of the microgravity rover. Figure 13 shows the photograph of the rover. The preliminary experiments were
conducted under the gravity. To approximate the microgravity environments, the rover was hung by a long
string, and the experiments were done in the horizontal plane. The experiments were then conducted in the
microgravity environments using the drop-shaft facility, JAMIC(Kamisuna-gawa-cho Hokkaido, Japan).
5.2
5.2.1
Preliminary Experiments under the
Gravity
Method of Experiments
We hung the rover body with long strings(6.44m
and 23.58) and measured its motion in the horizontal
direction. The iron ball was also hung with a short
inner
spherical shell
velocity (m/s)
0.14
0.12
battery
electro magnet
0.1
0.08
0.06
0.04
0.02
0
0
0.002 0.004 0.006 0.008 0.01
distance (m)
Figure 11: Result of theoretical computation; velocity
v.s. position
4x 10
-3
outer
spherical shell
velocity (m/s)
3.5
iron ball
3
Figure 13: Prototype of microgravity rover
2.5
2
1.5
1
0.5
0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
time (s)
Figure 12: Result of theoretical computation; horizontal velocity v.s. time
string xed to the rover body. The experiments were
on the free rotation in the air and on the horizontal
jump from the vertical wall.
In the drop-shaft experiment, to avoid the initial
vibration, the rover is xed by an external electromagnet for a second after drop. To investigate the
inuence of the remaining magnetic eld of the external magnet, we also user an electro-magnet xed on
the vertical wall.
5.2.2
Theoretical Analysis
As shown in Figure 11, the iron ball collides with
the rover body with 0.12m/s under the microgravity.
Under the normal gravity and with the strings as seen
in Figure 14, the height of horizontal jump is estimated
by the following equation:
x=
s
2 2
p2
2 m
2
2
l 0 l1 0 2gM 2 v 0 2g l2 0 l2 0 a
2
1
l1 : length of string hanging the rover
l2 : length of string hanging the iron ball
a : initial distance of the iron ball and the rover
g : the gravity acceleration
v : colliding velocity of the iron ball with the rover
Figure 14: Preliminary experiments hanged by strings
m : mass of the iron ball
M : mass of the rover body
By substituting m=0.1kg, M =0.8kg, v=1.2m,
a=5.0 1003 m, and g =9.8m/s2 into the equation, we
obtain x = 0:602 1003m for l1 =6.44m, and x =
1:15 1003m for l1=23.58m. The period of the vibra-
2
2
2
tion is
s
T
l12 + 6M l1
= 2 62M
g + 3l1 g
(4)
: string mass of the unit length of the
We also conducted the experiments of the inclined
jump, where friction was approximately = 0:21.
From Eq.(3), we can estimate that the rover jumps
in the direction of 10 degree inclined from the normal
of the wall. The theoretical results are summarized in
Table.2.
Table 2: Result of experiments hanged by a string
normal jump(m)
Spin rate(rad/s)
inclined jump(m)
string(m)
6.44
6.44*
23.58
23.58
6.44
theory
6:02
10
6:02
10
11:5
10
0.22
1:52
10
2
2
2
2
03
03
03
03
experiment
5:72
10 3
2:88
10 3
13:2
10 3
0.16
1:43
10 3
2
2
2
2
0
0
0
0
* : with electro-magnet xture
5.2.3
Result of Experiments
The results of experiments is shown in Table.2. The
rover could spin in the air and jump, which clearly
shows the eectiveness of the proposed mobility. The
experimental results closely followed the theoretical
results, without the external electro-magnet for the
xation of the iron ball. The result with the electromagnet shows the inuence of the remaining magnetic
eld.
5.3
Drop-shaft Experiment
5.3.1
Method of Experiment
5.3.2
Result of Experiment
We conducted the drop-shaft experiments in
JAMIC, on December 2nd and 3rd 1999. The dropshaft distance(free drop) is approximately 490m, and
the microgravity lower than 61005 m=s2 keeps for 10
seconds. The rover was xed by the external electromagnet. The xture force of the magnet was gradually
released in 3 seconds. By this method, we reduced the
eect of the remaining magnetic led. After 3 seconds from the drop, the inner electro-magnet started
to attract the iron ball, and the rover oated after 3.7
seconds from the drop.
The result of experiment is in Figure 15. After
3.7 seconds from the drop, the iron ball attracted
by the inner electro-magnets collided with the rover
body. After the collision, the rover oated with approximately 5mm/s of upward velocity. 7th result are
summarized as follows.
Until the iron ball collided, the rover was in the
rest, which indicates that the inuence of the
initial vibration was eciently removed.
The rover oated after the collision, which clearly
shows that the rover obtained the momentum
from the iron ball through the collision. The
upward velocity was approximately 0.005m/s,
which was less than that of the theory.
The rover rotated in the drop-shaft experiments.
The angular velocity was approximately 0.017
rad/s, while that on the experiment under the
gravity was approximately 0.16rad/s.Through additional experiments, it turned out that the spin
control inside the shell as shown in Figure 3 was
not stable although it was stable in the experiment under the gravity. The renement of spin
control is a issue to be solved.
Figure 15: Floatation of the rover in the drop-shaft
experiment: The left side are images from the camera
over the rover and the right side are images from the
camera under the rover
6
Conclusion
The results of this paper are summarized as follows:
1. The microgravity rover with a new mobility was
proposed using internal magnetic levitation, where
the rover obtains the reaction force to move by
attracting an iron ball inside.
2. The FEM magnetic eld analysis enable the theoretical design of the rover.
3. The prototype spherical rover(14cm in diameter, and 1kg of mass) was fabricated. By the
preliminary experiments under the gravity using string, we conrmed the oating mobility,
and compared the experiments and the theory.
4. We conducted the experiments under the microgravity environment at JAMIC. The rover successfully oated with approximately 0.005m/s of
upward velocity and rotated with approximately
0.017rad/s of angular velocity.
This research was supported by the Japan Space
Utilization Promotion Center.
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