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12th IFToMM World Congress, Besançon (France), June18-21, 2007
Structure Design and Locomotion Analysis of a Novel Robot for Lunar
Exploration
Zhiying Wang * Xilun Ding † Alberto Rovetta ‡
Beihang University Beihang University Politecnico di Milano
Beijing, China Beijing, China Miliano, Italy
Abstract— 1 Two kinds of hexapod robot, for lunar
exploration, are investigated: hexagonal and rectangular. II. Hexapod Legs
Typical gaits are analyzed for these two kinds of hexapods’
locomotion. A comparative study, based on agility, stability and Humans, with two legs, are the most agile animal, but
redundancy, concludes that the robot with hexagonal need a very complex controller: a brain. Lunar rovers
architecture is better than the rectangular one. Finally, cannot have that kind of brain because of knowledge and
simulations are done based on a novel hexagonal lunar technology limitations. Other mammals have four legs
exploration robot. and are also every agile. It seems that a four-leg-rover is a
good choice. However, the Moon is far from Earth,
Keywords: optimal design, accuracy, parallel robot traveling to the Moon costs a lot, we cannot afford
maintenance if one or two legs are broken. On the other
hand, almost all insects have six legs. According to
I. Introduction bionics, six-leg/hexapods robot may be a better choice.
Planetary rovers have become a popular topic in recent There are several benefits for hexapods rover.
years. Several types robot systems for planetary (a)Hexapod robot is easy to keep balanced.
exploration have been proposed [1], wheeled types, (b)Hexapod technology is a redundant locomotion
legged types and hybrid wheel/leg types. The wheeled system which increases reliability. It is workable even if
type robot includes the single wheel of Gyrover [1], four one, two or three legs broken.
wheels of RATLER [2] and others. The most famous (c)Hexapods makes it possible for the robot to use one,
Mars Rovers, Opportunity and Spirit have six wheels [3]. two or three legs to work as hand and perform complex
The legged type includes Ambler, Dante and Dante II of operations.
Carnegie Mellon University, and many others. Both
Dante and Dante II have eight legs [4]. Go-For from JPL III. The structure of the robot
and Chariot II from Tohoku University of Japan is a
There are two basic architectures of hexapod robots (see
leg/wheel robot. Track 1 of VNIITRANSMASH,
Fig.1) [6], rectangular and hexagonal. Generally, the
ANDROS Mark V-A from USA and ACEC robot from
hexagonal architecture is axi-symmetric. It can have many
ACES are pedrail robots. Other types such as hopper robot
kind of gaits and can easily change direction. For
can jump forward. However, until now, the robots that
example, to realize 0o, ±60 o, ±120 o and ±180 o turning
have landed on planets successfully are all wheeled type.
with the waving gait, it needs only regroup its legs and/or
The lunar environment is very different from that on
change the leader leg. The leader leg changes from leg 1
Earth. It is far from Earth, there is almost no air, the
to leg 3 in group ‘1+3+5, 2+4+6’, the direction will
gravity on the Moon is 1/6 of that on Earth and there is a
change from 0o to 120 o ( see Fig.2). In contrast, for the
deep layer of dust on the Moon. The strong friction
rectangular architecture, a special gait is required for
prevents wheels from running well. Wheels can also get
turning action. Generally, it requires four steps for a
stuck easily in dust. The leg-type robot is more agile than
rectangular robot to realize a turning action(see Fig.3).
wheel-type robot; however, it has very low locomotion
1
velocity. Legs incorporated with wheels can integrate the 2
advantages of these two kinds of locomotions [5]. 3 2
Therefore, leg/wheel-type rover have becomes our main
selection for lunar exploration.
4 3 4
1
*E-mail: wzy_sc@sina.com
† E-mail: xlding@buaa.edu.cn 6
‡ E-mail: alberto.rovetta@polimi.it 5 5
1 This work is partially supported by China NSFC Grant #50475001 and 6
by HI-TECH RESEARCH AND DEVELOPMENT PROGRAM OF Fig. 1 hexagonal and rectangular robots [6]
CHINA (863 PROGRAM: Grant # 2006AA04Z207)
12th IFToMM World Congress, Besançon (France), June18-21, 2007
Leg 2
Leg 1
Leg 3
Group 2
1 2 3 4
Group 1
Leg 4
Fig. 2 120 o turning Leg 5
Leg 6
Fig.5 Wave gait
z θi1
Bi
x
e θi2
d
Hi
θi3
Fig. 3 Four steps to implement a turn [7] b
a
Li Ai
S (a)
Fig. 4 Configuration of rover R
R
Compared with recetangular structure, a hexagonal
chassis with a hemisphere body is better for lunar R
rover(Fig. 4) R R R
R
IV. Implementation and results Gait analysis and R
simulation
R
For hexagonal hexapod robot, the wave gaits were
studied mostly. However, it can have several different R
gaits even for straight walking. S
A. Wave gait
(b)
Robot with wave gait (Fig.5) is the easiest gait to turn
around. But it is very complex to control because every Fig.6 Structure of a wave leg
leg has a different gait. For the wave gait, the leg’s
During walking, there will be three legs to support the
structure is as in Fig. 6. There are two revolute joints
body, and three legs wave ahead (Fig. 5). The whole
along axes Y, one along axes Z, its foot, contacting with
body’s simple structure is as Fig. 6(b). There are 12 links,
the ground becomes a spherical joint (with three revolute
13 revolute joints, two spherical joints in this
freedoms).
12th IFToMM World Congress, Besançon (France), June18-21, 2007
configuration. The positon is described in a space 9 and Fig. 10 listed the steps of 60 degrees and 90 degrees
coordinate frame. turning cases.
The number of degrees of freedom of the robot is
computed as follows :
F=12*6-5*12-3*2=6
In this case, every supporting leg has three freedoms,
which makes control very complex.
B. Crab gait
Fig.8 Small angle turning while walking
Another gait for hexagonal robot is ‘crab gait’ or ‘kick-
up gait’ [8], which is a continuous gait.. Six legs are also
grouped into two patterns, 1+3+5 and 2+4+6. There will
be 3 legs for supporting while three legs rise to walk
ahead at every time. The track of foot is a parabola ( see
Fig.7):
y=-ax^2+b
‘b’: is the maxmimal height that the robot’s feet can
raise.
While passing small obstacles, ‘b*fh’ is the height of Fig9. Three steps to realize turning left (60 o)
obstacle, ‘2*sqrt(b-y)*fw’ is the width of obstacle, given
that, ‘fh’ and ‘fw’ are factors of obstacle’s height and
width, 0<‘fh, fw’<1.
Fig10. Four steps to realize turning (90 degrees)
Quadrangles in the above figures are areas of support; the
white circle is the robots’ mass centre. It can safely turn
through 90 degrees using four steps (Fig. 10).
(a) B.2 Simulation
L2 When the robot walks in a straight line, the body should
L be kept horizontal. Three drivers are needed. The
L1
θ1 kinematics can be simply denoted by geometric equations.
The relationship between joint angles are shown in the
h following equations:
θ4
θ1 =θ1
(b) θ2 =π-arcsin[(h+L 1sinθ1)/L2] - θ1
Fig. 7 crab gait and simple structure θ3 =π-arcsin[(h+L 1sinθ4)/L2] - θ4 (1)
L2cos(θ4)+L1 cos(π- θ4 -θ3)
In figure 7(a), legs in solid line are in the supporting = L1cos(θ1)+L2 cos(π- θ1-θ2) + L
phase, legs in dashed line are in the walking phase.
From simple structure (see Fig.7 (b)), the number of
degrees of freedom of the robot is: F=3*5-2*6=3. Therefore, the result can be obtained as follows:
From the above analysis, the crab gait is simpler than θ1 =θ1
(2)
the wave gait. However, it also needs special gaits for θ2 = f1(θ1)
turning. θ3= f2(θ2)
B.1 Turning
Figure 11 shows the simulation of the robot walking
To realize turning motion, there are two cases. For small straight using ADAMS with crab gait.
angle turning, turning can be realized during walking, the
robot does not need to stop. The turning angle must be
less than 30 degrees to avoid walking legs colliding with
supporting legs. See in Fig.8.
For large angle turning, three steps are needed. There are
always four legs standing on the ground to support the
body, and the other two legs rise to adjust direction. Fig. Fig. 11 Simulation of walking (3 3 gait)
The trajectories of joints are shown in Fig.12
12th IFToMM World Congress, Besançon (France), June18-21, 2007
The simulation results for the displacement of the mass
centre using MATLAB & ADAMS are shown in Fig.13-
Fig. 16.
B.3 Gaits with sick legs - Fault Tolerant Locomotion
Because of the complex lunar environment, the robot’s
legs may be damaged during working. If one or two legs
(a) The thigh joint (b) The thigh joints of leg 2 are broken, it still can run with wheels and walk with the
of leg 1 and leg 6 other four or five legs with two kinds of gait. Even if three
legs are broken, the robot can still walk with a suitable
gait [8]. However, if two interphase legs are out of action,
the crab gait is impossible. It is still possible for
supporting and running, but if three adjoining legs are
broken (see Fig. 17) walking is almost impossible. Figure
18 shows how the robot can run with two legs out of
action.
(c) The thigh joints of (d) The thigh joints of
leg 3 and leg 5 leg 4 4
5 6
Fig.17 Three adjoining legs broken case Fig.18 Two legs broken case
B.4 Gaits with wheels
(e) The calf joint of (g) The calf joint of
leg 1 leg 2 and leg 6 Because wheels can provide higher speed locomotion
than legs, our robot will run with wheels in the case of a
smooth surface on the Moon.
All wheels will be grouped into two branches, one on the
left, the other on the right. The robot runs like a car. It can
realize turning through changing the velocity difference
between these two groups of wheels, which had been
studied intensively.
(h) The calf joint of leg 3 (i) The calf joint of leg 4 The ideal velocity for forward motion[9] is,
and leg 5 v(t)=(vl(t)+vr(t))/2 (3)
Fig.12 Curves of joints’ angles vl (t):velocity of left group;
vr (t):velocity of right group.
The radius of turning is,
p=D*( vl (t)+ vr (t))/(2*( vl (t)- vr (t))) (4)
D-the distance between group one and group two.
The angular velocity of turning is:
w(t)=(v1(t)- vl (t))/D (5)
If |vl (t)|=|vr(t)|, then w(t)=0, robot runs straightly;
If | vl (t)|>|vr (t)|, then robot turns right;
If | vl (t)|<|vr (t)|, then robot turns left;
Fig.13 Horizontal displacement of mass centre
Fig.14 Vertical displacement of mass centre If vl (t)=- vr (t), then w(t)>0 and v(t)=0, robot
turns without displacement.
According to experience, Fuzzy Logic is most suitable
for controlling the wheel velocities.
V. Prototype test
Based on system design and simulation, one prototype
was build (see Fig.18). The prototype has 24 motors
Fig.15 Horizontal displacement of a single leg (Servos Hitec HS-475HB) and a main board (Servopod).
Fig.16 Vertical displacement of a single leg The Servopod has the ability to control more than 26
12th IFToMM World Congress, Besançon (France), June18-21, 2007
servos, it is the best choice for a limited budget prototype, [5] Shigeo Hiros. Three Basic Types of Locomotion in Mobile Robots.
Advanced Robotics, 1991. 'Robots in Unstructured Environments',
but it will be changed in the next stage when more
91 ICAR., Fifth International Conference, Page(s):12 - 17 vol.1,
computational power will be needed. Figure 19 also June 19-22, 1991.
shows the motion of the prototype. [6] Reumoat, P.Alezandre, Ff D.Ghuya. GAIT ANALYSIS AND
IMPLEMENTATION OF A SIX LEG WALKING MACHINE,
Advanced Robotics, 1991. 'Robots in Unstructured Environments',
91 ICAR., Fifth International Conference, Page(s):941 - 945 vol.2,
June 19-22, 1991.
[7] SU Jun, CHEN Xue dong, TIAO Wen gang. A Study of the
Omnidirectional Gait for a Hexapod Walking Robot. Mechanic and
Electron, pages:48-52, 2004 (3).
[8] Yun-Jung Lee, Shigeo Hirose. Three-Legged Walking for Fault
Fig.19 Prototype walking on smoothing surface
Tolerant Locomotion of a Quadruped Robot with Demining
Mission. Proceedings of the 2000 IEEE/RSJ International
VI. Conclusion and Future work Conference on lntelligent Robots and Systems. Pages :973-978,
2000.
Robots with wheel type locomotion can have high [9] Ruan Feng, The Research on Mobile Robot Control System,
velocity on smooth surfaces, but cannot run on rough issertation of Master's Degree of Zhejiang University, Feb. 2004.
terrain. Robots with leg type locomotion are more agile, Mechanism and Machine Theory, 38(3):227–240, March 2003.
but usually only walk with low speed. Therefore, the
robot with a hybrid locomotion using both legs and
wheels will be a good choice for a lunar rover.
From the above analysis, the hexagonal structure for a
hexapod is more agile than the rectangular one. Because
the crab/kick-up gait is like a human’s gait, it is simpler
to control and easier to implement. The wave gait is more
complicated,. However, when one or two legs are
damaged, the crab gait is very hard to use while the wave
gait is still available. Therefore, the locomotion of the
crab gait coupled with the wave gait is more suitable for a
lunar rover.
This papaer mainly focus on a comparative study of
rectangular hexapod robot and hexagonal hexapod robot,
and the analysis of the wave gait and crab gait was
investigated. There are still many other gaits for this kind
of lunar robot, such as climbing slope, overtaking gouge,
and detailed gaits when one or two legs are broken. As for
fault tolerant gaits, only runing with wheels is studied
here, more work will be done on fault tolerant leg-
walking gaits in the future.
VII. Acknowledgment
Thanks to the China NSFC (Grant no. 50475001), HI-
TECH RESEARCH AND DEVELOPMENT PROGRAM
OF CHINA (863 PROGRAM: Grant no. 2006AA04Z207)
AND the S&T cooperation program (2006-2009) of the
governments of China and Italia for financial support, and
also thanks to Professor Alberto Rovetta and his research
group on the Italian side for joint research work.
References
[1] http://www.ri.cmu.edu/projects/project_102.html
[2] http://www.sandia.gov/isrc/fuelcellrat.html
[3] http://apod.nasa.gov/apod/ap040803.html
[4] Su Jun. The Research of the Gait Planning and Control of the
Multilegged Walking Robot. A Thesis of Submitted in Partial
Fulfillment of the Requirements for the Degree of Master of
Engineering, 2004.03.
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