Yangsheng Xu, Yongsheng Ou. Control of Single Wheel Robots

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tro

duction

polygonofsupportrequired forstatic stabilityprovides aleveragemecha-

nismfor thegenerationofdynamic torquedisturbances. Further, thesupport

points must comply with the surface, statically as well as dynamically,bycon-

trol

suppo

(e.g

usp

ension)

d/or

iclea

ttitudec

nges.

Sophisticated

hicle

sus

nsionsh

een

dev

elo

inimize

namic

disturbances,

but

passiv

e-sp

ring

sus

nsionsd

ecrease

static

stabilit

lowing the center of masstomovetoward theoutside of thesupportpolygon.

Activesuspensions mayovercome thisproblem, but require additionalcom-

plexity andenergyexpenditure.

As asecond example, consider abicycle or motorcycle whichhas two

wheels in the fore-aft (tandem) conﬁguration. Such avehicleisstatically un-

stable in the roll direction, butachieves dynamic stabilityatmoderate speed

through appropriate steering geometry andgyroscopic action of the steered

fron

heel.

Ste

ering

abilit

enerally

increases

with

eed

duet

yroscopic

eﬀects. Dynamic forces at the wheel-groundcontactpointact on or near the

vehicle center (sagital) plane, and thus produceminimal roll disturbances.

Additionally,the bicycle can remain uprightwhen traveling on side slopes.

Thus, sacriﬁcing

static roll stabilitye

nhancesthe

dynamic roll stabilitya

permits thevehicletoautomaticallyadjust to side slopes.

As alogical extension of this argument,consider awheelrollingdownan

incline. Under the

inﬂuence of

gravity,

gyroscopic action causest

he wheel to

precess(the axis of wheel rotationturns)about thevertical axis–rather than

simply falling sidewaysasitdoeswhen notrolling–andthe wheel steers in the

directioni

eaning. The

resulting curve

ath of

motion of

thewheelonthe

ground producesradial ( centrifugal)forcesatthe wheel-groundcontactpoint,

tending to rightthe wheel.Dynamic disturbances duetosurface irregularities

act throughornear the wheel’s center of mass, producing minimal torques

in roll,pitchand yaw. The angular momentum of the wheel, in additionto

providing thenaturalg

yroscopic steeringm

echanism, tendstostabilize the

wheel with respect to roll andyaw.Interms of attitude control, the wheel is

relative

ly insensitivet

ore/afta

nd side slopes.T

he resultisah

ighly stable

rolling motion wi

th minimal

attitude disturbances and tolerance to fore/aft

and verticaldisturbances. Onecan readilyobservethis behavior by rolling an

automobile tire down abumpyhillside.

Thereare precedentsfor single-wheel-likevehicles. In 1869,R.C. Hem-

mings [43] patented a Velocipede ,alarge wheel encircling the rider, powered

by hand cranks.Palmer [82]describes several single-wheel vehicleswith an

operatorridinginside. A1935 publication [72] describes the Gyroauto,which

carried the riders between apair of large, side-by-side wheels, andwas claimed

capable of aspeed of 116mph (187kph). Also in [72], thereisadescription

of the Dyno-Wheel, aconcept having abus-like chassis straddling ahugecen-

tral wheel. The relatively large diameterofasingle-wheel vehicle enhances

its obstacle-crossing ability, smoothnessofmotion androllingeﬃciency [12].

Further, asingle-trackvehicle can more easily ﬁndobstacle-freepathson

the ground, andits narrow proﬁlecan improve maneuverability. However,

1.1 Background 3

problems with steering, low-speed stability and aerodynamics, have kept such

vehicles from becoming commonplace.

1.1.2 Problems of Stable Robots

Traditional Research on mobile robotics has placed heavy emphasis on per-

ception, modeling of the environment and path planning. Consequently, ve-

hicles have been designed to be compatible with these planning limitations,

and the need for high speed has not been evident. Ultimately, as sensing and

computation capabilities improve, robots will be limited less by planning and

more by dynamic factors. Wheeled robots, capable of dynamic behavior - i.e.

high-speed motion on rough terrain - and of exploiting vehicle dynamics for

mobility, represent an exciting and largely unexplored area.

The purpose of our research is to exploit the natural steering behavior and

stability of the rolling wheel in the development of a highly dynamic, single

wheel mobile robot. We have built several prototypes of such a vehicle, and

demonstrated some of the potential capabilities.

1.1.3 Dynamically Stable Mobile Robots

Researchers have viewed mobile robots largely as quasi-static devices for

decades. Numerous robots with four, six or more wheels have been devel-

oped to maximize mobility on rough terrain. (See, for example, [13] [30] [45]

[52] [55].) Likewise, legged robots, which may have potentially greater mobil-

ity, have been built and demonstrated, as described in [60], [110]. Generally

these robots have featured low center-of-mass placement and broad base sup-

port, along with control and planning schemes designed to keep the center-

of-mass gravity vector within the support polygon (e.g. monitoring of slopes,

coordination of legs). Many designs have attempted to maximize mobility

with large wheels or legs, traction-enhancing tires or feet, multi-wheel driv-

ing, large body/ground clearance, articulated body conﬁgurations, etc. These

robots were often limited by motion-planning constraints and hence designed

for low-speed operation, typically 1 kph or less. Dynamic factors have little

inﬂuence on such systems, and consequently, have been largely ignored.

Traditional research on mobile robotics has placed heavy emphasis on per-

ception, modeling of the environment and path planning. Consequently, ve-

hicles have been designed to be compatible with these planning limitations,

and the need for high speed has not been evident. Ultimately, as sensing and

computation capabilities improve, robots will be limited less by planning and

more by dynamic factors. Wheeled robots, capable of dynamic behavior, i.e.

high-speed motion on rough terrain, and of exploiting vehicle dynamics for

mobility, represent an exciting and largely unexplored area.

A number of researchers have explored the possibilities of utilizing dynamic

behavior in various robot linkages, legged locomotors and other dynamic sys-

tems. Examples include Fukuda’s Brachiator [88] and Spong’s robot acrobat

tro

duction

[100], both of whichutilized dynamic swinging motions. Koditschek [22] and

Atkeson [92] andtheirstudents studied the dynamics of juggling.McGeer built

arobot that walked down slopes without additionalpowerorcontrol input,

utilizing

winging

motiono

legs

[70

Raib

ert’s

oupb

series

dynamically

balanced,

pping

andr

unning

robo

that

jump

ob-

stacles, climbedsteps [44], andperformedﬂips. Arai [3] andXu’s group[14]

developed an underactuatedrobot system by using thedynamic coupling be-

tween the passiveand activejoints.Dynamic motion in these systems allowed

the emergence of behaviorsthatwould nothavebeen possible quasi-statically.

In parallel with the work on linkage dynamics,other researchers have fo-

cused on thedynamics and balance of wheeled robots. Vos[109] developed

aself-contained unicycle that mimickedthe behavior of ahumancyclist in

maintainingroll andpitchstability. Koshiyama andYamafuji [59] developed

astatically stable, single-wheel robot with an internal mechanismthatcould

could move fore andaft andturn in place;theirworkemphasized the control

of the(non-inverted)pendulumcarriedonthe wheel, utilizing momentum

transfer in changingdirection.

The in

vention of the wheel

predates recorded history,but man

eresting

wheeled vehicleshaveappeared within thepass fewcenturies. According to

the historian [79], the

bicycle originated in

the

late 1700sasanunsteerable

vehicle known as the”HobbyHorse”. In theearly 1800s, steeringwas added

to the front wheel to facilitate changingvehicle direction; serendipitously,the

front-steeringc

onﬁguration pro

elf-stabilizing. Prior to

this

develop-

ment, the thoughtofavehicle travelingstably on two wheels would have been

considered ludicrous. In [82], Palmer describes several,

single-wheel ve

hicles.

One, an 8-foot diameter, cage-likew

heelw

drive

hroughfoottreadlesand

hand cranks by the driverinside. Presumably it wasstabilized by gyroscopic

action, andsteered by

shifting the drive

r’s weight. A”

unicycle”, builtaround

1904, provided aseat forthe driver insidealarge, annular wheel, powered by

agasolineengine.

The stabilizinge

ﬀect of gyroscopeshas in

trigued inve

orsf

or centuries,

andiscentral to anumberofinventions andpatents. Twointerestingvehicles

appearedina1935 publication [47].The ”Gyroauto” carried the driverand

apassenger between apair of large, side-by-side wheels, andwas claimed to

be capable of attaining aspeed of 116mph. The ”Dyno-Wheel” comprised a

bus-like

chassis straddling ah

ugecentral wheel. Outriggerw

heels apparent

were usedtocontrol steering, acceleration andbraking.(It is doubtful that

theDyno-Wheel waseverbuilt.)Ina1968 patent [102], Summers proposed

gyroscopicallystabilizing the roll axis of vehicles, enablinganarrowtrack for

passing throughtightspaces(e.g. forloggingequipmentinforests). Several

inventions relate to placing stabilizinggyros on the front [42]orrear [79] wheel

of abicycle. A1933 patent [111] proposed agyro stabilizer to reduce shimmy

on thefront wheels of automobiles.

More recently, Koshiyama,etaland K. Yamafuji, et al [59]developeda

single-wheel robot with internal mechanism. The statically stable, spherical

1.2

sign

wheel can apparently turn in place throughinertialeﬀects of theinternal

mechanism, giving it good maneuverability. Muchofthe eﬀortisdirected at

thecontrol aspects forturning andgenerating forward motion. D.Vos andA.

Floto

109]

elo

utonomous

trol

hemef

nicycle

that

comp

osed

heel,

rame,a

table

(inertia

wheel).

motors

driv

unicycle

eelf

d/rev

ersem

otion,a

the

table

forgenerationofyaw torques. The size andmass of theinertialdrivemecha-

nismislarge-2to3times that of thewheelitself-limitingmaneuverabilityand

the abilitytorecoverfromfalls. ProfessorYuta’s group[122] at University of

Tsukuba designed aunicycle that hasanupper andlowerpartfor steering,

anddeveloped algorithms on navigation andcontrol.

Pertinenttothe issue of attitudedisturbances on wheeled vehiclesisthe

work of Lindemannand Eisen at JetPropulsionLaboratory[67]. They simu-

lated the dynamic behavior of conventionalterrestrial construction equipment,

andpointedout thevulnerabilityofmulti-wheeled vehiclestodynamic dis-

turbances. The related researchworkonmulti-wheeled robots canbefounded

extensively in

papers published recently,

fore

xample, in

[91] and[117].

1.2 Design

1.2.1 Concept and Compromise

Gyrover is a novel, single wheel gyroscopically stabilized robot, originally

developed at Carnegie Mellon University [21]. Figure 1 shows a schematic of

the mechanism design. Essentially, Gyrover is a sharp-edged wheel, with an

actuation mechanism ﬁtted inside the wheel. The actuation mechanism con-

sists of three separate actuators: (1)a spin motor, which spins a suspended

ﬂywheel at a high rate, imparting dynamic stability to the robot; (2)a title

motor, which controls the steering of Gyrover; and (3)a drive motor, which

causes forward and/or backward acceleration, by driving the single wheel di-

rectly.

The behavior of Gyrover is based on the principle of gyroscopic precession

as exhibited in the stability of a rolling wheel. Because of its angular momen-

tum, a spinning wheel tends to precess at right angles to an applied torque,

according to the fundamental equation of gyroscopic precession:

T = J × ω × Ω (1.1)

where ω is the angular speed of the wheel, Ω is the wheel’s precession rate,

normal to the spin axis, J is the wheel polar moment of inertia about the

spin axis, and T is the applied torque, normal to the spin and precession

axes. Therefore, when a rolling wheel leans to one side, rather than just fall

over, the gravitationally induced torque causes the wheel to precess so that

it turns in the direction that it is leaning. Gyrover supplements this basic

concept with the addition of an internal gyroscope — the spinning ﬂywheel

tro

duction

Tilt Motor

Rear View

Side View

Forward

Axle

Tile Surface

Wheel

Structure

Main CPU

Board

and Gearing

Drive Motor

Gyro Rotor

Battery

Fig. 1.1. Thebasic conﬁguration of the robot

—nominallyaligned with the wheel and spinning in the direction of forward

motion. The ﬂywheel’s angularmomentum produceslateralstabilitywhen the

wheel is stopped

ving

slo

wly.

Gyroverhas anumberofpotential advantages over multi-wheeled vehicles:

1. Thee

ire system can be

enclosedw

ithin the

wheel to prov

ide mec

hanical

ande

ironmentalprotectionf

or equipmenta

nd mech

anisms.

2. Gyrove

esistanttogetting stucko

bstacles because it

hasnob

ody

to hang up,noexposed appendages,and theentire exposed surface is live

(driven).

3. Thetiltable ﬂywheel can be used to rightthe vehicle fromits statically

stable, rest position (onits side). The

wheel has no

“backside” on

which

to get stuck

4. Withouts

pecial steeringm

echanism, Gyrovercan turn in

place by

simply

leaningand precessing in the desireddirection forenhancing maneuver-

ability.

5. Single-pointcontactwith the ground eliminates the need to accommodate

uneven surfacesand simpliﬁescontrol.

6. Full drivetractionisavailable because allthe weightisonthe single drive

wheel.

7. Alarge pneumatictire mayhavevery lowground-contactpressure,result-

ing in minimal disturbance to the surface andminimum rolling resistance.

The tire maybesuitable fortraveling on soft soils, sand,snoworice; riding

over brush or other vegetation;or, with adequate buoyancy,for traveling

on water.

Potentialapplicationsfor Gyroverare numerous. Because it cantravelon

both land and water, it mayﬁnd amphibioususe on beaches or swampy areas,

for generaltransportation,exploration, rescue or recreation. Similarly,with

appropriate tread,it should travel well over soft snowwith good tractionand

1.2

sign

minimal rolling resistance. As asurveillance robot, Gyrovercould useits slim

proﬁle to pass throughdoorwaysand narrowpassages,and its abilitytoturn

in place to maneuverintightquarters. Anotherpotentialapplication is as a

high-spe

lunar

hicle,w

here

the

sence

aero

dynamic

sturbances

and

vity

uld

rmite

ﬃcien

gh-sp

eed

mobilit

its

lopmen

progresses, we anticipate thatother,morespeciﬁc uses will become evident.

1.2.2Mechanism Design

We have studied the feasibilitythroughbasicanalysisand simpleexperiments,

and designed andbuilttwo,radio-controlled (RC) working models. These

have proventhe conceptworkable,and have veriﬁedmanyofthe expected

advantages.

Given abasicunderstanding of thegyroscopic principle and wheel dynamic

stability, ourﬁrst task wastoﬁnd amechanism for steering the wheel along

esired path. Turning (steering)ofthe wheelisthe result of

gyroscopic

precession aboutthe yawaxis, caused by roll torquesasexplained above. We

considered two

mec

hanisms forproducing this torque: lateral shiftingo

eight

within the vehicle;and leaningofthe wheel.With regardtothe ﬁrst approach,

the need to prov

ide adequate in

ternal space for shiftingl

arge massesw

ithin

thevehicle is asigniﬁcantdrawback.Moving the mass outside the wheel’s

envelopeisunappealing because of theeﬀectivebroadeningofthe vehicle

andp

otential for the

mova

ble mass

con

tact theg

round or other obstacles.

Allowing the entire wheel to lean employs the complete weightofthe wheel

to shiftl

aterally–

notjust ar

elatively small,

mova

ble mass

–togenerate the

needed roll torque.Leaning of the wheel, canbeeﬀected by the useofinternal

reactionwheels or masses, butthesetend to acquirekinetic energy,become

locity-saturated, andgenerate angular momentum that

cancorrupt ve

hicle

behavior.Anotherway is to react against an internalgyroscope as described

abov

e; this mechanism hasb

een implemented andoperatedsuccessfully.

Several alternative conﬁgurations were considered. Asphericalshape,

whichcan be statically stable, does notexhibit the natural steering behavior

resulting fromthe interactionofgravitational (overturning)torqueand the

gyroscopic eﬀect. In fact, anarrowtire-contact area is desirable for steering

responsiveness (dependentonthe gravitational torque for agiven leanangle).

Twowheels,side-by-side provide static stability, but aresensitivetoroll dis-

turbances, do notexhibit the same natural steeringbehavior, and will not roll

stably on two wheels aboveacritical speed. (Observe thebehavior of ashort

cylinder, suchasaroll of tape, rolled alongthe ﬂoor.) Outboard wheels, either

on the sides or front/back, were considered forstatic stabilityand steering ef-

fects,aswell as acceleration and braking enhancement;but in additionto

mechanical complexity, these defeat thebasicelegance and controlsimplicity

of theconcept. Actually, therobot hasthe potential to be statically stable to

provide asolidbase of supportfor sensors, instruments or small manipulators,

tro

duction

etc., simply by resting on its side. The presentconcept, totallyenclosedinthe

single wheel,provides asimple, reliable, rugged vehicle.

Experimental work to date includes several simple experiments to verify

the

abilit

steering

princ

iple,

hree

rking

hicles.

1.2.3 Sensors and Onboard Computer

Thelatest modelweare using currently is Gyrover III.Itisbuiltwith alight-

weightbicycle tire andrim andaset of transparentdomes. It includes aradio

system forremote control, on-board computer and anumberofsensors to

permitdata-logging andon-boardcontrol of themachine’s motion.

Thereare 3actuating mechanisms in Gyrover:(i) Gyro tilt servo,(ii) Drive

motor, and (iii) DC gyro motor. Table 1.1gives adetailed description of each

of them.

Actuator Symbol Descriptions

Gyro tiltservo u

The tiltservocontrols the relative

angle of

the gyro spin

axiswith respectt

othe wheel axis. In

fact, by

controlling

the tiltservo, we

are able to

controls the lean angle angle

of the robot indirectly.

Drivem

otor

The robot forward/backward drivesystem uses a2-stage,

tooth belt system to amplifythe torque from the drive

motor.

DC gyro motor u

This motor cause the internal gyro to spin at adersirable

operating speed, increase the angular momentum of the

gyro.

Table 1.1. Table of diﬀerentactuating mechanisms in Gyrover.

Anumberofon-boardsensors have been installed on Gyrovertoprovide

information aboutthe statesofthe machine to the on-board computer. The

information includes:

• Gyro tilt angle, β

• The servocurrent

• Drivemotor current

• Drivemotor speed

• Gyro speed, ˙γ

• Angular rate (3-axes: Roll-Pitch-Yaw),

β ,˙γ and˙α

• Accleration (3-axes: Roll-Pitch-Yaw),

β ,¨γ and¨α

• Robot tilt angle (Roll),

All these signals, plusthe control inputs fromthe radio transmitter, can

be readbythe computer. Acustom-builtcircuit boardcontains thecontrol

computer and ﬂashdisk, interface circuitry for the radio system and servos,

1.2

sign

Fig. 1.2. Communication equipment: radio transmitter (left) and

laptops with wireless Modem (right).

Gyro

Accelerometer

SensorsA

ssembly

Radio Receiver

I/O Board

PowerCable

Tilt Servo

Battery

DriveMotor and Encoder

Gyro Tilt Po

tentiometer

Speed Controller

Fig. 1.3. Hardware conﬁguration of the robot.

components andlogic to control powerfor theactuators, andaninterface for

the on-board sensors. The on-board processing is performedbya486 Cardio

PC.

In addition, several more sensors areplanned to be incorporated with our

control

algorithms in

the

near future. Visual

pro

cessing capabilityo

Global

Positioning System (GPS) is abig issue forautonomous control, however, due

to the structurallimitationofthe robot, we have notequippedthe robotwith

this kind of device yet.

An on-board100-MHZ 486 computerwas installed in the robot to deal

with on-board sensing and control. Aﬂash PCMCIA card is usedasthe hard

diskofthe computer. It communicateswith astationary PC via apair of

wirelessmodems. Based on this communicationsystem, we can download the

sensor data ﬁle fromthe on-boardcomputer, send supervising commands to

the robot, andmanually control the robot throughthe stationaryPC. More-

duction

over, another radio transmitter is installed forhuman operatorstoremotely

control the robotvia two joysticks of the transmitter(Fig 1.2).One usesthe

transmittertocontrol thedrivespeed and tilt angle of therobot, hence, we

can

cord

the

ator’s

dri

ving

data.

Numerous sensors areinstalled in therobot to measure the state vari-

ables(Fig1.3). Twopulseencoders were installed to measurethe spinning

rate of ﬂywheel and the wheel. Furthermore, we have twogyros andanac-

celerometertodetect the angular velocityofyaw,pitch, roll, and acceleration

respectively.A2-axis tilt sensor is developedand installed fordirect measur-

ing the lean angle andpitchangle of therobot. Agyro tilt potentiometer is

usedtocalulatethe tilt angle of theﬂywheel and it’s rate change.

Theonboardcomputer is run on an OS,called QNX, whichisareal-

time microkernel OS developed by QNX Software SystemLimited. Because

of handling numerous sensors and communicating with the stationary PC,the

robo

t’s soft

ware system is dividedi

hreemain programs:(1)communica-

tion server, (2)sensor server and (3)controller.The communication server is

usedtocommunicate between the onboardcomputerand thestationary lap-

top computer via RS232, while as

ensor serve

sed to

handlea

ll the sensors

and actuators. The controller program implementsthe control algorithm and

communicates amongtheses

ervers.

All

these programs arerun independently

in order to allowreal-time control of therobot.

1.2.4 Implementation

The ﬁrst vehicle, Gyrover I, shown in Figure 1.4, was assembled from RC

model airplane/car components, and quickly conﬁrmed the concept. The ve-

hicle has a diameter of 29 cm and mass of 2.0 kg. It can be easily driven and

Fig. 1.4. The ﬁrst prototypeofthe robot

1.2

sign

steered by remote control; hasgood high-speed stabilityonsmooth or rough

terrain; andcan be kept standing in place.This vehicle hastraveled at over

10 kph,negotiated relatively roughterrain (a small gravel pile), and traversed

5-degree

ramp

75%

itsh

eigh

iameter.

Reco

fromf

alls(

resting

ther

ound

side

thew

heel)

een

hiev

with

strate

ing

the

wheel

forw

ard

dri

andg

yro-tilt

con

trol.

The

ortcomings

areits lackofresilience andvulnerabilitytowheeldamage;excessivebattery

drain due to dragonthe gyro (bearingand aerodynamics); inadequate torque

in the tilt servo; andincompleteenclosure of thewheel.

Fig. 1.5. The second prototypeofthe robot

Thes

econd ve

hicle,Gyrove

I, (Figure 1.5) wasdesigned to address these

problems.Itisslightly larger than Gyrover I(34 cm diameter, 2.0 kg), and

alsoutilizes manyR

Cmodel parts. Tilt-serv

otorqueand trav

were both

approximately doubled. GyroverIIuses agyro housed in avacuum chamber

to cut powerconsumption by 80%, whichincreasesbatterylife fromabout

10 minu

tes to

minutes. The

entire robot

housed insideas

pecially de-

signed pneumatic tire whichprotectsthe mechanismfrommechanical and

environmental abuse,and provides an enclosure that is resilient, although less

rugged than hoped. Therobot contains avarietyofsensors to monitor motor

currents, positions andspeeds, tire and vacuumpressure,wheel/body orien-

tation, andgyro temperature. Gyrov

hasb

een assembled anddriven by

manualremote control on asmoothﬂoor, andhas shown the abilitytoﬂoat

andbecontrollable on water.

Thethird version,GyroverIII,(Figure 1.6)was designed on alarger scale

to permitittocarry numerous inertial sensors andacomputer(486 PC) for

data acquisitionand/or control. This machine utilizes alightweight, 40 cm

bicycle tire andrim, and apair of transparentdomesattachedtothe axle.

Overall weightisabout 7

kg.Heavy-duty R/Cmotorsand servoare usedto

spin the gyro,drivethe wheel forwardand controlgyro tilt. GyroverIII trav-