a strategy for quadruped walking on uneven terrain

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

[email protected]

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

29

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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

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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

294



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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.

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R.

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and T. Litwin. Mars microrover navigation: Per-

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Robots, 2(4):291-311, 1995.

[6] R . B.

McGhee. Finite state control

of

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motion.

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pages

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[7] D. A . Messuri and

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W. L.

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national Journal of Robotics Research, 13(3):272-287,

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[9] M. H.

Raibert.

Legged Robots t hat Balance.

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M I T

[lo] S. Song

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G. S Sukhatme and G.

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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

a strategy for quadruped walking on uneven terrain

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