Yangsheng Xu, Yongsheng Ou. Control of Single Wheel Robots

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6.5

rimen

tal

Study

165

STARTFINISH

44 f

eets

Fig. 6.8. Experimentontracking astraightpath under shared control.

6.5.3Circular Path

Similar to thestraightpath test,the experimentalsetup is showninFigure 6.9.

This time, theoperatorisrequired to control the robot travel acircular path.

In ordertomakethe robottoturn in place,the operator needstothe tilt the

internal ﬂywheel to makea“lean steering” precisely.Ifthe robotfailstofollow

the rightcommands, it

unable to

steer

ll. Figure 6.13indicatest

he desired

path andthe actualpath travelled by therobot respectively.Figure 6.14shows

the correspondingsensor data (trail #3)ofthe robotduring trav

ellingi

circular path.

START

FINISH

9 feets

7 feets

Fig. 6.9. Experimentontracking acurved path under shared control.

Theaverage oﬀset in thecircular path test is 0.51ft. Althoughthe robot

cannot trackthe circular path precisely,the operator can control therobot

to move back to the target location within 0.25 ft at nearly theend of the

experiments. Therefore, with adegree of shared controlwith the robot, the

operatorisstill able to control the robot to turn atightcorner.

6.5.4 Point-to-pointNavigation

In this experiment, we requirethe robottotravelfromone location to another

whichare separatedbyaright-hand corner andthey arefar apart(≈ 60 ft),

1666

Shared

Con

trol

Figure6.10.The operator needs to controlthe robottomovefromastarting

area to aspeciﬁc destination, whichisa2ft × 2ftregion(thedimension of

Gyroverisabout 1 . 5ft × 0 . 8ftasviewed fromthe top). This experimenthas

two

main

goals:

1. Therobot must reachthe destination within thespeciﬁc area.

2. Afterthe robothas reached the destination, it is required that the robot

can maintain its lateral balance even when the operator does notfurther

control it.

Theexperimental results are showninFigure 6.15and 6.16.

Although

aren

concerned

with

ether

ther

can

ccurately

trackthe path or not, the overall oﬀset fromthe path is 1.18 ft, whichisan

acceptable value for a60ftlongjourney.Moreover, forthe three trailsinthis

experiment, allthe trajectories of therobot areconverging to the destination

at theend of thepath.FromFigure 6.16, when t ≥ 14 (at thedestination),

the operator didnot commandthe robotanymore, however, the robotcan

balance itself at around 90

.Therefore, under ashared controlenvironment,

with the human operator responsible forthe na

vigation tasko

he robo

the robotisable to move fromone location to another location whichare

fara

part, andtobalance itself at

thev

ertical po

sition when the robotstops

moving (with no operator’s command).

6.6Discussions

From theresults we obtained fromthe previous experiments, we verify that our

proposed shared control

algorithm can let

the system ch

se be

twe

en hu

man

operator’s controlcommands or thecommands fromthe autonomousmodule

systematically.W

heneve

he operator hasc

hosena

highlevel

autonomy,

the system will execute the command from the the autonomous module unless

the operator hasgiven acommandwhichis’conﬁdent’ enough to overcome

thec

onﬂictb

ween the op

erator andthe mac

hine.O

he other hand, if al

degree of autnomyischosen, the system will follow theoperator’s command

unless a’signiﬁcant’ error/conﬂict is measured.The proposed shared control

algorithm is able to allow twoentities (human and machine) to exit in the

same system simultaneously.

Although Gyrov

nothav

eanautonomous module to

vigate it-

self to travelfromone location to another, this can be done by sharingthe

navigation task with the operator. Under shared control, therobot will main-

tain itslateralbalance when theoperatordoesnot commandit. On the other

hand, under adegree of sharing, the operator is still able to control therobot

to do some speciﬁc tasks(straightpath tracking, point-to-pointnavigation,

etc). It is believed that if an autonomous navigation module existsinthe sys-

tem, the operator canshare morenaviagtion controltothe machine using the

6.6

Dis

cussions1

START

FINISH

9 ft

51 ft

2 X 2

sq. ft

Fig. 6.10. Experimentonpoint-to-pointnavigationunder shared control.

proposed shared control algorithm, whichcan greatly reducethe dutyofthe

online human operator.

0 5 10 15 20 25 30 35 40 45

distance (ft)

path offset (ft)

Straight path test

Fig. 6.11. Tr

ectory tra

lled in

thestraightpath test.

1686 Shared Control

6.6

Dis

cussions1

0 1 2 3 4 5 6 7 8 9 10

100

120

β [deg]

time(sec)

lean angle of Gyrover

0 1 2 3 4 5 6 7 8 9 10

−20

−10

[deg]

time(sec)

tilt angle of flywheel

0 1 2 3 4 5 6 7 8 9 10

180

185

190

195

200

Drive Command

time(sec)

Drive command (Human)

0 1 2 3 4 5 6 7 8 9 10

175

180

185

190

Tilt Command

time(sec)

Tilt command (Human)

0 1 2 3 4 5 6 7 8 9 10

175

180

185

190

Tilt Command

time(sec)

Tilt command (robot)

Fig. 6.12. Sensor data acquired in the straightpath test.

1706

Shared

Con

trol

0 2 4 6 8 10 12 14

x (ft)

y (ft)

Circular path test

Fig. 6.13. Gyrove

rajectories in

the curved

path test.

6.6

Dis

cussions1

0 1 2 3 4 5 6 7 8 9

100

120

140

β [deg]

time(sec)

lean angle of Gyrover

0 1 2 3 4 5 6 7 8 9

[deg]

time(sec)

tilt angle of flywheel

0 1 2 3 4 5 6 7 8 9

Drive Command

time(sec)

Drive command (Human)

0 1 2 3 4 5 6 7 8 9

−30

−20

−10

Tilt Command

time(sec)

Tilt command (Human)

0 1 2 3 4 5 6 7 8 9

−30

−20

−10

Tilt Command

time(sec)

Final tilt command (robot)

Fig. 6.14. Sensor data acquired in the circular path test.

1726

Shared

Con

trol

0 2 4 6 8 10 12 14

x (ft)

y (ft)

Combined path test

Fig. 6.15. Gyrovertrajectories in the combined path test.

6.6

Dis

cussions1

0 2 4 6 8 10 12 14 16 18 20 22

100

120

140

β [deg]

time(sec)

lean angle of Gyrover

0 2 4 6 8 10 12 14 16 18 20 22

−40

−20

[deg]

time(sec)

tilt angle of flywheel

0 2 4 6 8 10 12 14 16 18 20 22

−5

Drive Command

time(sec)

Drive command (Human)

0 2 4 6 8 10 12 14 16 18 20 22

−20

−10

Tilt Command

time(sec)

Tilt command (Human)

0 2 4 6 8 10 12 14 16 18 20 22

−20

−10

Tilt Command

time(sec)

Final tilt command (robot)

Fig. 6.16. Sensor data acquired in the combined path test.

Conclusions

7.1 Concluding Remarks

7.1.1 Concept and Implementations

Gyroverisanovelconcept formobilitythathas distinct advantages over

conventional, statically stable ve

hicles. Theconcept hasb

een ve

riﬁedw

ith

three working models. Gyroverisparticularly suited foroperationsathigh

speed and roughterrain, andalso showspromise as amarine/amphibious

vehicle.The mechanismcan be completely enclosed, presenting avery clean,

protected enve

lope.

During the past severalyears,wehavemadesigniﬁcantadvances in the

technologies fora

gyroscopicallystabilized wheel. We

gained an

un-

derstanding of thebasics of gyro-stabilization,and have demonstrated the

feasibilityofthe Gyroverconcept.

7.1.2 Kinematics and Dynamics

We have developed thekinematic anddynamic models of Gyroverinahorizon-

tal plan.Inderivation of the model, we consider therobot as acombination of

three components: arollingdisk, an internal mechanism andaﬂywheel. They

are linked by atwo-link manipulator. We simpliﬁed the modelbydecoupling

the tilt angle of theﬂywheel from the dynamics. We veriﬁedthe model by

experimentand simulation. We demonstratedthatthe dynamics of therobot

is nonholonomicand underactuated. We demonstratedthe dynamics coupling

between the wheel and the ﬂywheel, through the stabilizationand tilting eﬀect

of theﬂywheel on the robot.

Based on theabove work, we have established thedynamics of arobot

rolling without slipping on an inclined plane. The pendulum swinging motion

is neglected andthe verticaloﬀset of theactuation mechanism from the axis

of the whole wheel is reduced from the dynamics. If we let

, l

and θ be zero,

thedynamics areexactly the same as Gyroveronahorizontal plan.

Y. Xu and Y. Ou: Control of Single Wheel Robots, STAR 20, pp. 175–177, 2005.