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7/25/2019 A Strategy for Quadruped Walking on Uneven Terrain
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ICAR
97
Monterey,
CA,
July
7-9, 1997
A Strategy for Quadruped Walking on Uneven Terrain*
Gaurav
S.
Sukhatme, Scott Brizius, Scott Cozy and George A.
Bekey
gauravlbriziuslcotylbeAey@robotacs.usc.edu
Department of Com puter Science
Institute for Robotics and Intelligent Systems
University of Southern California
Los
Angeles, CA
90089-0781
Abstract
We describe the design and construction of Q
quadruped robot which walks on uneven terrain. A
control system which produces
a
statically stable
gait
has been implemented; results showing a straight and
turning gait are presented. The control of quadruped
robots poses interesting challenges due to a small sta-
bility margin when compared to hexapods for exam-
ple).
For
this reason most implemented systems for
outdoor walking on uneven terrain have been hexapods.
The system described here has the added virtue
o
us
ing very few inexpensive sensors and actuators. One
o
the aims
of
this work is to build a reduced complexity
low power, low mass and direct drive) walking robot
for statically stable walking. The other aim is t o corn-
pare the performance
o
this ro ot with a wheeled robot
roughly the same size and weight. In this paper we
re-
port on progress towards the first
o f
these two goals.
1
Introduction
The advantages that walking robots possess have
been extolled for many years. Chief amongst these
are the ability to reduce the mechanical coupling be-
tween the payload and the terrain and the ability to
traverse irregular terra in. Several successful walking
robots have been built that have walked on uneven
terrain; [ lo] , [l] are examples. All of them have ei-
ther been hexapods
or
eight legged frame walkers. In
this paper we propose a design for a quadruped robot
(called MENOII) which walks on uneven terrain using
a small number of inexpensive sensors and actuators.
A quadruped has the disadvantage of being less stable
This
work
is supported in part by Jet Propulsion Labs, Cal-
ifornia Institute
of
Technology under contract 959816 and the
Office of Naval Research under contract N0014-95-1-1152
but it is lighter than corresponding eight legged and
hexapod designs. This makes it better sui ted for appli-
cations where lightweight robots are preferable. One
such application is planetary exploration. The forth-
coming missions to Mars, planned by
NASA
[5],
all use
wheeled robot rovers but in the future it is conceivable
that a legged rover may prove preferable for exploring
planetary surfaces.
We have constructed two rovers (one wheeled and
the o ther legged) and a mockup of a Martian surface.
Experiments are in progress to evaluate the perfor-
mance of the two robots using a multicriteria approach
[ l l] In this paper we describe the design and con-
struction of
MEN011
and i ts control system
as
well as
results on walking and turn ing. The control systemis a
set of interacting sensor and actuator processes which
maintain balance while moving the robot forward or
turning i t in place). Due to uneven terrain, mechanical
and calibration errors and slippage on the ground an
open-loop, preprogrammed gait fails frequently. How-
ever with the control system operational we are able
to demonstrate stable walking and turning . Additional
sensing (for obstacle avoidance), navigation implemen-
tation and benchmarking results are the subjects of a
future paper.
Significant work on quadrupeds has been done by
Hirose et al.
[3] and [4] and by Jimenez et al.
[Z]
Early work on walking robots goes back to McGhee
[6] where a finite state machine was used to control a
quadruped. The design
of
gaits has been studied by a
number of researchers;
[7]
and [8] are examples of ap-
plying stability measures to evaluate gait quality. The
work reported here is based on statically stable walk-
ing. A good reference for dynamic legged locomotion
is [9].
0-7803-4160-0-7/97 10.00 1997 IEEE
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mailto:gauravlbriziuslcotylbeAey@robotacs.usc.edumailto:gauravlbriziuslcotylbeAey@robotacs.usc.edu7/25/2019 A Strategy for Quadruped Walking on Uneven Terrain
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Figure 1: MENOII in a simulated Martian environ-
ment
Q u a n t i t y
total mass
chassis length
chassis width
proximal limb length
distal limb length
minimum height
maximum height
2
Robot Design and Sensors
Value
0.18
m
0.15
m
0.09 m
0.11 m
0.14 m
0.29 m
5 kg
MEN011 is a
12
OF
statically stable quadruped.
Ea,ch leg is a RRP design. The body of the robot and
the first two links of each leg are in the horizontal plane
and the prismatic joints (the most distal joint of each
limb) are in the vertical plane. The robot chassis and
limbs are constructed out of Aluminum tubing. The
robot is actuated by
12
off-the-shelf servomotors.
A
lead-screw is used to convert the rotation of the motor
to translation
of
the foot in the case
of
the prismatic
joints. By retracting/extending the prismatic joints
the chassis height above the ground is varied. Figure
1 shows the robot and the table below gives some of
its mechanical parameters.
The robot is equipped with th e following sensors
0 Foot switches:
Measure contact (on/off) with
the ground. There
is
one on each of the 4 feet.
0 Two-axis inclinometer:
Measures the roll and
pitch
of
the robot chassis with respect to the local
gravitational vertical.
Resistive potentiometers:
One on each
of
the
8 rotational joints, to measure the joint angle.
Foot retraction microswitch:
To measure
when a foot is fully retrac ted (on/off). There is
one on each leg.
Compass:
Measures yaw of the chassis.
Onboard computing is all done on a custom board
built around a Motorola 68332 microcontroller.
A
tether is used to supply offboard power for extended
testing and for gathering telemetry. The testing is all
done in a
3 5
m ~ 3 . 5 sandbox. This same environ-
ment is also used for our experiments with the wheeled
robot we have built.
A
single camera suspended 3m
above the center of the sandbox is used for tracking
the robot's position. The sand surface is nominally
flat but not excessively
so.
No attempt is made to
smooth out the surface which is usually uneven as a
result
of
people walking in the sandbox, depressions
left by rocks that are constantly moved around and
other disturbances. It should be noted tha t we are not
dealing with excessive slopes or terrain that
is
likely
to fail. Experiments and an analysis
of
the kinematics
shows that the maximum slope that the robot is able
to navigate successfully is on the order of 25 .
3 The Control System
The control system for MENOII operates about
a nominal gait. The combined mass
of
the limbs,
the chassis and the control electronics was measured.
Since these are the most massive parts of the robot the
calculation of the center of mass uses only these val-
ues lumped at their geometric centers.
For
convenience
they are shown on one limb only, as partial ly filled cir-
cles in Figure 2a. Additional sensors that were added
later were not used in making center of mass calcula-
tions for the nominal gait generation. The assumption
was also made that the chassis and the first two links
of each leg always lie in the horizontal plane. Fur ther,
the nominal gait generation also assumes ideal actu-
ators and no slippage between the feet and the sand.
The gait generation imposes the constraint that under
the idealizations described above the projection of the
center of mass of the robot on the ground should lie in
the support polygon formed by the stance feet. The
nominal straight gait generation was done as part of
another project in our lab which investigates biologi-
cally inspired cerebellar approaches to quadruped and
hexapod walking.
The nominal stra ight gait is shown pictorially in Fig-
ure
3
The first two phases (Figures 3a, 3b and 3b , 3c)
are with 3 legs on the ground and are used to recover
29
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7/25/2019 A Strategy for Quadruped Walking on Uneven Terrain
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C
0 6
y
-
Global frame
Figure 2:
MEN011
parameters and a shift maneuver
0.4
0.2
E O
6
0.5 1.5 2 2.5
. 4
m
Figure 3: The nominal straight gait (korward is to-
wards the top of the page)
-2.5
W
0
-0.5 0.5 1 1.5 2.5
3
Figure 4: The nominal turn gait (iorward is towards
the top of the page)
the 4th leg to a forward position. The 3rd phase (Fig-
ure 3c, 3d) is with all four legs on the ground and is
used to move the center of mass of the robot forward
with respect to the ground. The next three phases are
mirror images
of
the first three.
The nominal turn gait shown in Figure 4 uses small
rotations to achieve a turn in place anda repositioning
sequence which displaces the center of the robot back-
ward. For brevity we do not describe the tur n gait
further here. In both Figures 3 and 4 he numbers
denotes the stability margin (in cm) prior to a swing
phase. The is the center of mass of the robot and
the
o
is the geometric center of the support polygon.
When the nominal gait is implemented on the robot
with no feedback it fails almost immediately.
Often
before the robot completes one gait cycle it is desta-
bilized enough to fall over while recovering a leg. The
stability margin under which the nominal gait operates
is small - see Figures 3 and
4.
The center of mass lo-
cation is quite sensitive to the configuration as shown
below. We show a sample sensitivity calculation to es-
timate the amount of error bscm in the position of
the center of mass
as
a function of a small error 601
of the proximal joint angle. T he center of mass along
the local 2 axis (attached to the chassis) depends on
the mass at locations
A
through E (Figure 2a) and
the mass of the chassis. The mass at A is the prox-
imal servo motor which is fixed t o the chassis. The
configuration dependent mass moments are due t o the
mass at points B through E. We write only those terms
explicitly below and ignore the rest.
1
m ga
2 c m
-(---cosBl+2 mcacosel
where M 5kg is the total mass of the robot,
xi
denotes the position
of
the point i in the chassis
frame, mi is the mass at point i 81 and 9 are the
proximal and distal joint angles
as
shown in Figure
2a and a
=
0.09m and b
=
0.llm are the link lengths.
By differentiating the above and bounding the sine and
cosine values we conclude for small 601,
l a
b
l nl
M Zmo+amc+amo+-mo+am~+~mE)/6e11
Using measured values for the masses from MEN011
(2)
and the appropriate link lengths we have
293
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--
Datamow
__ ControlFlow
I
The measured errors in 81 on MENOII are on the
order of
f10 .
Substituting into the equation above
we have the following error estimate
Ibz l 5 0.0041 m
(4)
There are 8 rotational joints if we assume th at all of
them are in error by
10
then we have an upper bound
on the error estimate Sz 5
8
x 0.0041 0.0328m.
This is an overestimate since the center of mass is not
as sensitive to the distal angle
8 2
as it is to the prox-
imal angle
81
but it serves as a good order of mag-
nitude estimate. The above calculation was for the z
component of the center of mass, a similar number for
the y component may be assumed and the resultant
error estimate in the center of mass position may be
calculated as
2/2
x 0.03282
0.0469m.
This estimate
exceeds the best stability margin available. In light of
the above calculation we may expect destabilization
quite routinely when a leg recovery is attempted if the
nominal gait is used without feedback. The reason for
this is the play in the rotational joints. Further con-
sider that there is unmodeled mass in the system in
the form of new sensors, connectors etc. This mass is
rigidly connected to the chassis and its moment does
not depend on the configuration of the joints . How-
ever it can serve to introduce destabilization into the
nominal gait which was derived without modeling it.
Redesign of the robot with lighter materials for the
legs and an indirect drive mechanism can be used to
move mass closer to the chassis thus increasing the
stability margin. This introduces both cost and com-
plexity into the design which we try to avoid. Further,
simulation results show tha t with this RRP design and
conventional materials there is no substantial gain in
stability with an indirect drive mechanism. A second
solution lies in making small corrections to the nomi-
nal gait at every leg recovery if the inclinometers show
excessive roll and pitch. This results in a slower walk
but is much more reliable than the situation discussed
above.
The magnitude of the correction to the nominal gait
that needs to be made at each leg recovery is calcu-
lated using the inverse kinematics of each leg. The
objective is to shift the center of mass away from the
leg being recovered since the robot tilt s towards the leg
being lifted. The assumption made is tha t the unmod-
eled mass is attached rigidly to the chassis. Hence if
the chassis is moved away from the recovering leg the
objective will be achieved. In Figure 2b we see two
locations of the chassis and a leg. While the foot re-
mains in contact with the ground the leg and chassis
are moved from the solid line to the dashed line. Us-
ing the inverse kinematics it is possible to calculate
Command
I
sequence I
Sequence
complete
Executive
Blackboard
I
Command
sequence
equence
complete
Executive
State ? Blackboard
I
Figure
5:
The control system architecture
appropriate final values for the two angles
61
and
82
given a desired shift in the geometric center of the
robot S
Sz,Sy)
nd a desired chassis rotation A
The same shift S and rotation X is used for all four
legs and the two angles are calculated for each leg sep-
arately. The new joint angles are then commanded to
each rotational joint and the leg recovery is attempted
again.
If
it fails the leg is lowered until contact and
another shift is commanded. The leg is not recovered
until it is safe to do
so.
We are now ready to describe the complete control
system as a set of interacting processes (see Figure 5).
The sensor processes run at the fastest rate and may
be considered as the lowest level processes. There is
one process
for
each sensor and each updates a cor-
responding global da ta structure. The main control
flow proceeds using an executive process that receives
a command from a planner. For purposes of the ex-
periments reported here the planner is
a
sequencer
which produces a nominal target sequence for the ex-
ecutive process to implement. No real time constraint
is placed
on
the planner which awaits
a
successful re-
turn from the executive process to advance its internal
clock and produce the next target sequence. When at-
tempting a leg recovery the executive process treats it
as a guarded motion and lifts the appropriate leg by
a small amount until contact is lost with the ground.
The resulting roll and pitch values are thresholded to
estimate whether the robot is tipping
or
whether the
leg can be recovered safely. In the latt er case th e leg is
raised higher and the inclination is monitored. At any
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stage in the leg raise phase if the inclination exceeds
the preset threshold the leg is lowered and a shift com-
mand is generated. The shift is executed
with
all legs
on the ground and the leg recovery is attempted again.
On completion of
a
shift
or a
successful leg recovery
the l e v e l ( ) process is executed.
The
l e v e l ( )
process tries to achieve two objectives
a. To level the plane of the robot, and
b.
To keep
the centroid of the plane of the robot a certain (pre-
defined) height above the ground in order to keep the
operating region of the prismatic joints near the center
of their region of travel. The l e v e l ( ) process finishes
when the roll and pitch values are below some preset
thresholds.
4 Results
n
Figures 6 ,
7
and 8 we show
a
sequence
of
steps
taken by the robot in the sandbox while executing a
straight walk and
a
turn maneuver.
In Figure 6 the
robot translates forward approximately
20
cm in one
complete gait cycle. The last frame of Figure
6
is the
same configuration as the first. In Figure 7 we show
a 10' turn maneuver composed of
8
frames. These
8 frames correspond to Figure 4a,c,e,g,i j , k and
1
re-
spectively. In Figure
8
we show the results
of
three
consecutive turn maneuvers resulting in a net turn of
30 . Note tha t in Figures 6, 7 and
8
the 'forward'
direction is to the right of the page and in Figures 3
and 4 the 'forward' direction is towards the to p
of
the
page.
Conclusion
We have described here the design, construction and
control architecture for a quadruped robot walking on
uneven terrain. Experiments with the robot and
our
approach show encouraging results. While it is pre-
mature to advocate the use of quadruped robots for
expensive missions, it is not out of the realm of possi-
bility in the future.
Our next priority is to implement a navigation
sys-
tem which sequences various gaits t o go from point
A
to point
B.
This will include deciding whether to
avoid obstacles
or
to step on (or over) them. Th e first
implementation of such a system will have sonar and
IR
sensors
for
obstacle detection in keeping with
our
philosophy to be minimalist with regard to the sensing
used. In previous work
[ll]
we have described
a
statis-
tical benchmarking technique for robot rovers which
measures performance over a large number of obsta-
cle placements drawn from the same statistical distri-
bution. To make a comparison between the wheeled
robot tha t we have already tested and MEN011 is one
of the main thrusts of future work.
Acknowledgments
The authors would like to thank
S.
Hayati, G. Rodriguez,
R. Volpe,
C.
Weisbin and
B.
Wilcox for stimulating discus-
sions over the past few months. The authors lso thank
J.
Hoff
for his help with the straight gait design.
References
[l]
J. Bares and W. Whittaker. Configuration
of
au-
tonomous walkers
for
extreme terrain.
International
Journal
of
Robotics Research, 12(6):535-559, 1993.
[2] P. G. de Santos and M. A. Jimenez. Generation of
discontinuous gaits for quadruped walking vehicles.
Journal
of
Robotic Syst ems , 12(2):599-611, 1995.
[3]
S.
Hirose, H. Kikuchi, and
Y.
Umetani. The standard
circular gait of
a
quadruped walking vehicle.
Adoanced
[4] S
Hirose and
0
Kunieda. Generalized standard foot
trajectory
for a
quadruped walking vehicle.
The In-
ternational Journa l of Robotics Research, 10(1):3-12,
February 1991.
[5]
L. Matthies,
E.
Gat, R. Harrison, B. Wilcox,
R.
Volpe,
and T. Litwin. Mars microrover navigation: Per-
formance evaluation and enhancement. Autonomous
Robotics, 1(2):143-164, 1986.
Robots, 2(4):291-311, 1995.
[6] R . B.
McGhee. Finite state control
of
quadruped loco-
motion.
Simulation,
pages
135-140,
September
1967.
[7] D. A . Messuri and
C
A. Klein. Automatic body reg-
ulation
for
maintaining stability of
a
legged vehicle
during rough terrain locomotion.
IEEE
Journal of
Robotics an d Auto mati on, RA-1(3):132-141, 1985.
[S] P. Nagy,
S.
Desa, and
W. L.
Whittaker. Energy-based
stability measures for reliable locomotion
of
statically
stable walkers: Theory and application.
The Inter-
national Journal of Robotics Research, 13(3):272-287,
June 1994.
[9] M. H.
Raibert.
Legged Robots t hat Balance.
The
M I T
[lo] S. Song
and
K. J. Waldron. Machines tha t Walk: The
Adaptive Suspension Vehicle.
The MIT Press, Cam-
bridge, Massachusetts,
1989.
[ l l ]
G. S Sukhatme and G.
A.
Bekey. Multicriteria eval-
uat,ion
of
a planetary
rover. In Proc. Workshop on
Planetary Rover Technology and Systems,
1996
IEEE
Int. Conf. on Robotics and Automation, April
1996.
Press, Cambridge. Massachusetts
1986.
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f
Figure
6:
Straight gait sequence
f
(g)
Figure
7:
Turn gait sequence
-
one gait cycle
Figure 8: Turn gait
sequence -
3 gait cycles
96
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