Drilling Mechanism of Autonomous Burrowing Robot
for Lunar Subsurface Exploration
Kenji NAGAOKA∗1 , Takashi KUBOTA∗2 , Ichiro NAKATANI∗2 , Satoshi TANAKA∗2∗1
The Graduate University for Advanced Studies, ∗2 JAXA/ISAS
E-mail:nagaoka@nnl.isas.jaxa.jp

Abstract
Lunar and planetary subsurface exploration is of
considerable significance. The authors have studied
the strategies for subsurface excavation and propulsion for the development of a lunar subsurface explorer. The authors have proposed an autonomous
robotic explorer which can burrow into the soils.
Based on the strategies the authors have already considered, this paper especially focuses on the excavation mechanism of a robotic system for near-future lunar subsurface exploration. The main objective of the
proposed robot is to bury a scientific observation instrument like a long-term seismometer under the lunar
surface, which is covered with very compacted lunar
regolith. Therefore, an eﬃcient excavation mechanism
is required. In this paper, the authors propose a newscrew drilling system with double rotation, which iscalled N-RDM (Non-Reaction Drilling Mechanism).
Through some experiments and analyses, this paper
discusses the feasibility and eﬀectiveness for the proposal of a burrowing robot system.

1 Introduction
Since the creation of time, the Moon is one of most
attractive celestial bodies for human beings. The outcomes of the Apollo missions by the U.S. is particularly recognized as significant achievement in spacedevelopment [1]. Many countries have tried to improve upon it. From various sample returns and measurements, a lot of important knowledge has been
gained in lunar and space science. However, theMoon still has a lot of unanswered questions such as
its origin, chemical components, and internal structure. To answer these questions, it is required to obtain global information about the Moon in future lunar exploration missions. Therefore, the authors propose a robotic system for burying a scientific observation equipment like a long-term seismometer under the surface to investigate the internal of the Moon
(Fig.1). In general, the lunar surface is covered withvery fine soils, called lunar regolith, and the lunar regolith has high adiabatic property. Given this, the instruments buried in the lunar regolith can be kept at aconstant temperature, even at night. To accomplish
this, some scientists say that the instrument shouldbe placed about 1 meter below the surface. Consequently, this enables it to function for a long time
without any heaters. Also, the buried seismometercan realize better contact with the surrounding lunar
regolith, so it would be able to capture very small lunar seism. This paper first describes the strategies for
subsurface propulsion of a burrowing robotic system
and its required mechanisms. Then, this paper especially discusses the excavation mechanism, which isvery important for such a system. Finally the authors
propose a novel excavating mechanism that is suitable
for a burrowing robot, and present the results of someexperiments.

2 Burrowing Robot
2.1 Subsurface mobile robots
So far, there have been numerous researches ofrobots with a locomotion mechanism. But, most ofthem have paid attention to just only mobility. There
are several environments for movement, such as on
the ground, inside of tubes, and under water. Meanwhile, some have developed biomimetic robots thatcan move like underground creatures, for instancean earthworm or a snake, and their locomotion ismostly restricted to the above. However, studies on
autonomous robots that can move underground are especially rare. That is because soils are too complex
and unsteady as a locomotion environment. Also, anysuch study would need to consider both the locomotion and how to generate the space for locomotion.

Fig.1: Lunar subsurface exploration mission

Table 1: Planetary excavation systems
Bucket Wheel
Penetrator
Drill
Burrowing Robotmechanism
simplesimplesimplecomplexsize
large
middle, longnarrow, longcompact

weightheavy
middlelight
light

robustness
××○△

purposesampling
investigation
sampling
investigation

Next, the authors define two phases for subsurface
propulsion by a burrowing robot, and consider diﬀerent strategies for each phase as follows.
1. Make space• Compress regolith• Remove and back transport regolith
2. Advance forward• Utilize contact with surrounding regolithFig.2: Overview of planetary excavating robots• Utilize excavated regolith• Self advancing without utilizing regolith

2.2

Conventional robots for planetarysubsurface exploration

Planetary exploration with excavation of soils hasreceived a lot of attention in the world. Table 1 shows
a comparison of planetary excavation systems. Here,the robustness refer to the capability to have diﬀerent
excavating opportunities. So far, there have been proposal for digging robots for planetary subsurface exploration [2]-[6]. However, it would be hard for theserobots to bury a large instrument such as a seismometer. An overview of some proposed ideas which areclassified by length and diameter is shown in Fig.2.
The ICEBREAKER of CMU and the Lunar-A penetrators of JAXA are not actually autonomous burrowing robots, but robotic systems for subsurface investigation or a similar objective. Hence, these two diﬀerent methods are included in Fig.2 for comparison.

2.3

Strategies for subsurface propulsion

Based on the past researches, the authors set thefollowing assumptions:• The burrowing robot is carried by the rover• Power is supplied by a cable from the ground station• Target depth is several meters from the surface• Target soil-layer is lunar regolith• The robot diameter is about 0.1 m(The seismometer’s diameter: about 0.05 m)

Now there are diﬀerent ways to achieve the above
strategies [7], and the proposed robots shown in Fig.2
can be classified by these strategies.
By applying Apollo’s data regarding compression
index [1], the authors have previously concluded that
it would be unlikely that the regolith can be compressed for making space. Also the authors concluded
quantitatively by applying the rankine’s soil pressure
theory that a burrowing robot needs to generate a
propulsive force [7]. Therefore, from the next section
this paper describes a concrete excavating mechanism
and uses it as a baseline.

3 Screw Drilling Mechanism
The earth-auger method is a screw mechanism usedin excavation systems on Earth. According to the referense [8], the screw drilling state can be in one of thefollowing 3 states.
h1i Auger moves forward one pitch forward after one
rotation, soils are not excavated, and there is noshear on the edges of the screw.
h2i Auger moves forward less than one pitch forward
after one rotation, and soils are excavated andtransported backward.
h3i Auger cannot move forward at all despite rotation.
In general, the state of an earth-auger is in the stateh2i. This paper also assumes this state. This excavating mechanism using a helical screw is one of the
major methods in the field of construction and civil

engineering. The shapes of these helical screws is determined by past empirical knowledge. The action
performance is the almost completely controlled byoperation, and there have been very few theoreticalstudies. The method involves human beings and large
scale systems in order to treat the behavior of complicated soils. Some researchers focus on the estimationof discharging soils and the description of the dynamics [9]. The results indicate a very good estimation,
but the objective is limited to such discharging estimation and some theoretical considerations are lacking.
Another use of screw mechanism is in screw piles.
The application is for improving soft ground, as acountermeasure against liquefaction almost all of theresearches are focused on the bearing capacity. Additionally, like the earth-auger its mechanism is notclearly understood.
A third use of the screw mechanism is found insystems for conveying materials. These researches
are principally focused on the screw conveyors, whichtransport materials obliquely upward, so it is hard to
apply the concept to a burrowing robot system.
From these, the authors have decided to do somebasic experiments for the analysis and clarification of
the behavior of the screw excavating mechanism.

4

Non-Reaction Mechanism

4.1

Proposal of Double Rotation System

With the above considerations, the required properties for a robotic excavation mechanism are the following:• Fore-soil removal and transportation backward• Generation of propulsive force(a) Contra-rotor(b) Twin-rotor(c) Dual-spin
Fig.3: Double rotation screws

evelop a new screw mechanism with N-RDM (NonReaction Drilling Mechanism) by separating thescrew parts, and applied it to a burrowing robot. Here,the double rotation methods are classified into three
types as shown in Fig.3. The contra-rotor type (a) has
one drilling unit which has the contra-rotation axis atcoincident with the rotation axis. The twin-rotor type(b) consists of two drilling units whose rotation axes
are fixed and parallel to each other. The dual-spin
type (c) has one drilling unit whose rotation axis isspinning around another spin axis. Each type has tworotation axes, so it is possible to cancel the reaction.
However, there are some notable diﬀerences. Firstly,
the contra-rotor type (a) is compact in size, and it canbe estimated that it would have an equivalent excavating performance with the single screw drilling mechanism. Secondly, the twin-rotor type (b) has an unexcavated space between the two drilling units, resulting
in an anomalous shape. It is impossible to make one
circular hole, and a constraint on the body shape must
be considered. Thus, it can be estimated that it would
have lower eﬃciency. Thirdly, the dual-spin type (c)has a driven part not used for drilling, so the eﬃciency
would be ever lower. According to these considerations, the authors adopt the contra-rotor type and will
do some experiments in the near future.

• Dust prevention mechanism
Therefore, a screw drill, which has a series of spiralwings, is one of candidates. However, a serious problem is that a single spinning drill results in a reaction
force to the body. This reaction can generate the friction between the body and the supporting soil reducing the drilling eﬃciency. It can also lead to the wobbling of the propulsion axis. This paper proposes a
new type of spiral screw drill unit as a novel excavation mechanism to improve this problem.
A mechanism using double rotations already exists as the doughnut-auger method. It has two rotating parts, an inner-screw and an outer-casing. The
mechanisms of the reaction reduction have not beenstudied so well. Thus, it cannot eﬀectively reduce thereaction. An outer-casing for reducing the reaction
is very useful for drilling a hole, but it increases thenumber of driven parts, which means an increase inpower consumption. It is also structural redundant fora burrowing robot. Due to these factors the authors d-

4.2 SSD
The schematic of the basic model, which is called
SSD (Single Screw Drilling) unit, is represented in
Fig.4(a). Also Fig.4(b) shows the prototype. The developed SSD is a conceptual model of the contra-rotor
type screw, and it serves as a basic dynamics modelfor theoretical analysis.
The SSD unit consists of a body part and an excavation part. Furthermore, the excavation part has an
inner cone, called CONE, and a helical screw wing
which winds around the CONE, called SCREW. As
shown in Fig.4, αSC [rad] denotes the angle of inclination of the SCREW s center position and p[m] denotes
the SCREW’s variable pitch. The screw length isL[mm], and the maximum screw diameter is D[mm].
In general, the SCREW model can be mathematically
expressed as a function of a logarithmic spiral.

(a) Simplified modelFig.4: SSD unit

4.3(b) Prototype

Contra-rotor

Figure 5(b) shows the prototype of a new contrarotor screw, which the authors developed. This prototype consists of the body, the front screw and therear screw. The two screws can be driven independently by separated motors to analyze the behavior.
Also Fig.5(a) represents the schematic. From this thelength of the front and the rear screw is both L/2, thefront’s diameter is D/2, the rear’s diameter is D, andthe ratio between the moment of inertia between thefront and the rear is approximately 1:31.

4.4

Basic experiments

4.4.1

Experimental set-up

Some experiments with the SSD and the contrarotor screw have been carried out as shown in Fig.6.
Also in the experiment, the soil is silica sand and thespecifications are shown in Table 2. The front screw
and the rear screw of the contra-rotor are independently controlled. The starting situation is that thescrew is completely buried and the body stands out
on the surface, and the propulsive force comes fromjust its weight. Through the experiments, the encoder
value which indicates motor rotation speeds, the active time and the average sinkage are measured, andthe average penetration speed is calculated.

Fig.6: Experimental environment

4.4.2 Drilling performance: SE
The Specific Energy, which is called SE, is a major index of drilling performance [10]. In this paper,
the authors evaluate the excavating properties by applying this index. The required energy per minute,E[MJ/min], is calculated as follows.
E=

W × πD × f × 10−9

(1)

W

=

w1 × g + w2(2)

where, D[mm] is the diameter of hole, f[rpm] is therotation speed, W[N] is propulsive force, w1 [kg] isthe robot mass, g[m/s2 ] is the gravity acceleration
and w2 [N] is all external forces without the weight.
Here, the volume of the soil removed per minute,V[m3 /min], is calculated by using the penetration
speed PR[m/hr] as following.
V =π×( D × 10−3 )2
2

×

PR
60

(3)

Thus, SE[MJ/m3 ] is defined by the following equation.
SE =E 0.24 · f=· (w1 g + w2 )V
D · PR(4)

From the above equation (4), an increase in SE meansthat its performance becomes lower.
4.4.3 Equivalent angular velocity
To apply the evaluation equation (4), an equivalentangular velocity of the double rotation screw is considered. By equating the rotating energies, the equivalent angular velocity ωS [rad/s] is derived. Here, theTable 2: Specifications of screw units(a) Simplified model(b) Prototype
Fig.5: Contra-rotor screw unit

SSD
Contra-Rotor

L
50 mm
50 mm

D
50 mm
50 mm

Mass
356-867 g
604 g

αSC
10 deg10 degtotal energy of rotations is described as follow, neglecting the body’s rotation.
1
1
1
I1 ω21 + I2 ω22 = (I1 + I2 )ω2S
2
2
2

(5)

where, I1 [kgm2 ] is the moment of inertia of the front
screw, I2 [kgm2 ] is the moment of inertia of the rearscrew, ω1 [rad/s] is the angular velocity of the front
screw and ω2 [rad/s] is the angular velocity of the rearscrew. Hence, from the above, ωS is derived by thefollowing equation.
√
ωS =I1 ω21 + I2 ω22
I1 + I2(6)

Through the experiments, ωS [rad/s] can be converted
to the rotation speed as following in order to utilize
the above equation (4). Also, the ratios of the angularvelocities and the rotation speed between screws areboth defined as follows.
K=

ω1 f1
=
ω2 f2

5

Experimental Results

5.1

Results: Non-reaction(7)

When the SSD driven only the body rotates while
the remain in place due to the frictional resistancefrom the soil against the screw. It is not really an
excavation or propulsion mode, and the result of the
SSD unit indicates the SSD is unsuitable for a burrowing robot. In contrast, a reduction of the bodyrotation is confirmed in the case of the contra-rotor
screw. Also, the non-reaction condition is confirmed
at around K=60. On the other hand, slight wobbling
motion of the body was observed even near the nonreaction condition. This could be the eﬀect of by theconnecting cords or the mass decentering. Alternativ-

Fig.7: Dynamics model of contra-rotor screw

ely, the wobbling could also arise from the skew symmetry of the screw. This could be resolved by using adual spiral structure. The authors plan to do more experiments for measuring the driving torques and consider the theoretical approaches to find out the mechanism. However, the small wobbling behavior is notregarded as a critical problem given the frictional resistance against the body underground.

5.2 Results: SE
Figure 8 and 9 show the experimental results. In
the case of the SSD, when the body is free the bodyrotates with any screw rotation. Hence the body isfixed by hands to stop the body reaction in order tomeasure the drilling properties. As shown in Fig.8(a),SE is directly proportional to W and would be saturated with increase of f in the experiments of theSSD. In Fig.8(a), the blue line denotes the approximate function about SE with constant f and variable
W, and the green line indicates average SE with constant W and variable f. The lower performance withincreasing W is due to the increase of frictional resistance. This is expected because an increase of W is
proportional to an increase of normal force between
the screw and soils below. This fact is confirmed in
Fig.8(b), which indicates relationship among PR, W,
and f. Given these results, PR is directly proportional
to f which is equal to the angular velocity and W has an
insignificant eﬀect on PR during these experiments. It
is obvious that with screw driving with no W, propulsion stop. So it is preferable for the burrowing robot
to be able to generate arbitrarily an optimal W.
Next the results of contra-rotor screw are shown in
Fig.9. The body is fixed by hand in Fig.9(a), the bodyremains free in Fig.9(b), and Fig.9(c) indicates a comparison of the relationship among SE, f and PR in (a)and (b). Also in Fig.9, the horizontal axis represents
the ratio K as referred to above under the constant W,
and each line denotes the approximates curve associated with the discrete data of SE, f, and K. As shown in
Fig.9(a), the property SE is directly proportional to K,
and also, PR and f heavily depends on K and shows asimilar approximate curve. At around K=1, SE is sustained compared with the SSD data, where the green
line is the estimated SE of the SSD at the same mass.
In other words, the eﬀectiveness is indicated if the
non-reaction state could be achieved. On the other
hand, although the curves shown in Fig.9(b) is very
similar with the curves in Fig.9(a), and it shows an obvious performance reduction at lower K. Instead, thenon-reaction state is confirmed at around K=60, andthe performances of Fig.9(a) and Fig.9(b) indicate indeed almost the same value near the non-reaction condition. Therefore, this result indicates the validity of
non-reaction mechanism.

(a) Body fixation(a) Relationship between SE, f, and W(b) Body free(b) Relationship between PR, f, and W
Fig.8: Experimental results of SSD

5.3

Analysis

According to the above results, the following results are obtained from the experiments:• The Penetration speed is proportional to the rotation speed• The best excavating performance condition: K=1(c) Comparison between the body is fixed and freeFig.9: Experimental results of contra-rotor screw• The Non-reaction condition: around K=60
5.3.1

Equation of rotation

Here, based on the simplified dynamics model asshown in Fig.7, the equations of rotation are defined
as follows.
I0 ω̇0I1 ω̇1I2 ω̇2= −T 1 + T 2 − sgn(ω0 ) · T F0
= T 1 − T F1
= −T 2 + T F2
2

(8)
(9)
(10)

where, I0 [kgm ] is the moment of inertia of the body,
ω0 [rad/s] is the angular velocity of the body, andsgn(·) is a signum function. The angular velocity indicates a positive value when the direction is anticlockwise direction along the rotation axis passing throughthe center of the robot (Fig.7). Also, T1 [Nm] is thedriving torque for the front screw, T2 [Nm] is the driving torque for the rear screw, TF0 [Nm] is the frictional torque against the body, TF1 [Nm] is the frictional torque against the front screw and TF2 [Nm] isthe frictional torque against the rear screw. These
torques are positive values, irrespective of the rotation
directions.
5.3.2 Non-reaction control
Next by using above equations (10), this paper
describes the mechanism of canceling the countertorque against the body. Given the state that the reaction against the body is approximately zero, the workof the friction TF0 would be zero. Thus, the driving

torques for the non-reaction are derived as follows.
ω̇0 (t) → 0 : T 1 (t) = T 2 (t)(11)

On the other hand, when the body rotates, the relationship between the driving torques is expressed as
the following equations.
ω0 (t + ∆t) =.. .
T 1 (t) − T 2 (t) =ω0 (t) + ω̇0 (t) · ∆t → 0
I0 ω0+ sgn(ω0 ) · T F0 (12)∆tHere, ∆t is the cycle of the input torque, and the relationship between torques would be described in thecase of controlling the body’s small reaction within
one cycle input.
5.3.3

Evaluation of DC motor

The electric properties of a DC motor are calculated as follows.
VM
T= I M · R M + ke · ω + VB
= kt · I M

(13)
(14)

where, VM [V] is the input power, IM [A] is the electric
current of the motor, RM [Ω] is the electric resistanceof the motor with the internal resistance, ke [Vs/rad]is the factor of counter electromotive force, ω[rad/s]
is the directed relative angular velocity, VB [V] is thevoltage drop by the friction of the brush, T[Nm] isthe driving torque, kt [Nm/A] is the torque constant.
Where, the no-load current of the motor is ignored.
In fact, ke is really equal to kt and VB by the metallic brush has almost negligible VB , hence the above
equation (13) is rewritten as follows.
V M = I M · R M + ke · ω(15)Also from an absolute coordinate, the motor stator’s
directed angular velocity is ω sh [rad/s] and a motor
shaft’s directed angular velocity is ω sh [rad/s]. So theω is defined as following.
ω = ω sh − ω st

(16)

In general, the relationship between the motor torqueand the angular momentum H[kgm2 /s] is written as
follows.
T = Ḣ = I sh ω̇ sh − I st ω̇ st(17)

where, Ish [kgm2 ] is the moment of inertia of the motor
shaft and Ist [kgm2 ] is the moment of inertia of the motor body including the stator. Thus, from these considerations, T is calculated as follows.
T = ke ·V M − ke · ω
Ra

(18)

From the above considerations, Figure 10 shows thesimulation result of an example indicating the DC motor characteristic. Here, the input voltage VM is assumed to be constant and the values regarding the fric-Fig.10: Simulation result of DC motor characteristic

tional resistances, which are given with the ratio between the surface area of the body and the screw,
assume much smaller than the torques. According
to Fig.10, the frictional resistance reduce directly the
motor’s rotation speed with a constant voltage. Therefore the output torque depends on the higher friction,
but the another rotation speed keeps accelerating until the driving torque would be equal to the resistancetorque.
In these experiments, the non-reaction state is indeed observed as a value around K=60. However,based on a theoretical analysis, given no-load state K
would be due around 105 with the gear reduction ratio, the moment of inertia and the voltage. Where, thegear reduction ratio of the front screw is 1.875 andthe rear one is 0.5. The ratios are indeed not equivalent values to f in Fig.8 or 9. Thereby, the eﬀects offrictional resistance reduce the rotation speed or K as
above considered. Even the ratio between surface areas of screws assumes 1:3, the diﬀerential can becomea critical problem for the control. There could be several other factors, but the most dominating factor isthe frictional resistance. The tendency depends on thefrictional resistance, and more considerations are required with the theoretical analysis. Thus, the theoretical approaches are significant future works for analysis of the soil frictional resistance against the screw
motion during the driving of the burrowing robot.

5.3.4 Sustaining the drilling performance
To sustain the excavating performance SE, or produce the required propulsive speed PR, the control of
K is necessary as mentioned above. The control law
also depends on the friction conditions. With the nonreaction control, the absolute values of each motor
torque retain same. In other words, the absolute angular accelerations of the motors depend on the torquehistory and the frictional resistances which include a
uncertainty. So it is surely needed to make the hybrid
control law with the non-reaction and the performancesustainment, and that is our future work.

6

Conclusion

In this paper, the authors have discussed an autonomous burrowing robot system for the lunar subsurface exploration. The authors especially proposeda novel excavation mechanism, called contra-rotor
screw with N-RDM, for the development of the burrowing robot for lunar subsurface exploration. In particular, this paper has presented the important andbasic guideline concerning a relationship among thepenetration speed, the rotation speed, the propulsive
force and the total performance SE. And then the authors have indicated the feasibility and the eﬀectiveness through some experimental analyses. Some experiments for the validation of the proposed excavating method are listed as future works. Also, further
theoretical analysis of the screw mechanism for excavating soils and its hybrid control law are in progress.

Acknowledgments
Dr.
Otsuki, who is an assistant professor at ISAS/JAXA, supported the experiments.
Mr.Edmondo, who is a doctoral course student in thelaboratory, helped in writing this paper. Here, the authors would like to express my appreciation for them.

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