Yangsheng Xu, Yongsheng Ou. Control of Single Wheel Robots

Подождите немного. Документ загружается.

1345

rther

pics

Learning-based

Con

trol

0 200 400

−40

−20

[deg]

time(sec)

0 200 400

100

120

β [deg]

time(sec)

0 200 400

−4

−2

dba (deg/sec)

time(sec)

0 200 400

−200

−100

100

db [deg/sec]

time(sec)

0 200 400

−100

−50

da [deg/sec]

time(sec)

0 200 400

175

180

185

190

195

Tilt Command U

time(sec)

Fig. 5.3. SVMlearning control results.

Discussions and Remarks

Themost critical andtime-consuming part is the data selection andregroup-

ing. The data selection conditions need to be well controlled andparameters

needtobecarefullyselected.

If some of thesensor readings aretoo noisy to produce thedata selec-

tion andc

ollection,w

emay

usesmoothing tec

hnologies. Thereare man

proaches in digital signal processing.Animportantpractical pointthatneeds

to be kept in mind is thatthe state variablesinlearninghumancontrol are

usuallyverylow frequency signals.

As described in the signiﬁcance analysis section, if thereare only limited

groups, andtheir(X

− 1

do notexist, then remove these groups. If all

groups displaythe problemand it is because thereexist two or morevariables

with strong linear relations, remove oneorsome of them to avoid thelinear

relation andperform the signiﬁcance analysis again.

5.2

Imp

lemen

tationo

earning

Con

trol

135

Moreover, theinput variables X maymiss some importantvariables

and/oradd some almost irrelevantvariables. We do notconsider themissing

problemhere, as mentioned in the introduction section: i.e., we assume that

alreadyi

ncluded

imp

ortan

actors.

atter

pro

blems,

divide

X in

two

rts:

X =(

) ,

where X ∈ R

∈ R

and m = m

+ m

and

is not

relevantto Y .

Nowsuppose that thetrue model forEquation(5.15) becomes

δY =

δX

+ 



, (5.29)

but instead we ﬁt

δY =

δX

+ 



, (5.30)

to thedata, where

∈ R

and

∈ R

efer to Equation(

5.29) and

Equation (5.30) as thereduced and fullmodels respectively.Let

1 F

and

2 F

the least

squares estimates of

and

in ﬁttingmodel (5.30)tothe data.

Let

1 R

denote the least squares estimateswhen model(5.29) is ﬁtted to the

data.F

rom[

90], we

have

the following two

conclusions:

1 F

and

2 F

areu

iased estimates of

and

espectively.Thatis,

E (

1 F

and E (

2 F

)=0.

2. E (

¯σ

)=σ

This means in the latter case that it is still an ideal estimate forthe sensitivity

coeﬃcient

∂Y

∂x

Howt

hoose features is

another impo

rtant

aspect that will aﬀect the

learningaccuracy.Thus, in the next chapter, we willhandle this problem.

5.2 Implementation of LearningControl

In this chapter, we showthe implementation results of the CNN models

trained in theprevious chapter. First of all, we validate the CNN models

we obtained by applying aHidden Markov Modelbasedsimilaritymeasure.

Next, forthe experimental implementationsofthe CNN models, we evaluate

theperformance of these models by observingthe lean angleofthe robotand

the overall control on theﬂywheel. Later, we combinedthe two motionsinto

asingle motion. This combinedmotion ensures that therobot can be fully

recovered fromthe fall position backand balancedatits uprightposition.

1365

rther

pics

Learning-based

Con

trol

5.2.1Validation

In this subsection, we will evaluate eachofthe modelgenerated by thecas-

cade learningalgorithmfor diﬀerentbehaviors of the robot, includinglateral

stabilizationand tiltup motion.Weapply thesimilaritymeasure mentioned

in Section 3.2.4toquantify the level of similaritybetween the originalhuman

con

trol

l-generated

tra

ctories

thr

ough

sim

ations.

Since

noth

eap

sical

esek

ind

motionf

simulationsare done by feeding thecurrentand history state variablesand

control informationintothe cascadeneural network, to seeifitcan generate

similar control output in each time instant.

Basically,wehavetwo motions to learn: (1)Lateralbalancing ( i =1), and

(2) Tiltup ( i =2). Foreachmotion,wegivethree diﬀerent set of data forthe

simulation.For notation convenience,let X

i,j

, i ∈{1 , 2 } , j ∈{1 , 2 , 3 } ,denote

therun of diﬀerent motions i in trail # j .

VerticalBalancing

Figure 5.4,5.6 and5.8 show three diﬀerent verticalbalancedmotion by hu-

man control. Thegraph on theleft of eachﬁgure is theplot of leanangle

data ( β ), while the rightone plots the orientations of

theﬂywheel (

). The

correspondingh

uman con

trol data andC

NN model controldata for

(1, 1)

(1, 2)

and X

(1, 3)

areshown in Figure 5.5, 5.7 and5.9 respectively.Weperform

the similaritymeasure between the human control andCNN modelcontrol

trajectories foreachmotion,t

he resultsa

re summarized in Ta

ble 5.9. From

theperformance of this verticalbalancing CNN model,wecan observethat

the modelcan generate similarcontrol trajectories as human operator, with

an average similarityvalue of 0.5940.

similarity σ

(1, 1)

0.5885

(1, 2)

0.6235

(1, 3)

0.5700

average 0.5940

Table 5.9. Similaritymeasures for vertical balanced control between human and

CNN model

Tilt-up Motion

Figure 5.10, 5.12and 5.14 showthree diﬀerent tiltup motionbyhuman con-

trol. The correspondinghuman control data andCNN model controldata for

(2, 1)

, X

(2, 2)

and X

(2, 3)

areshown in Figure 5.11, 5.13 and5.15 respectively.

5.2

Imp

lemen

tationo

earning

Con

trol

137

0 20 40 60 80

−50

−40

−30

−20

−10

[deg]

time(sec)

tilt angle of flywheel

0 20 40 60 80

100

110

120

130

140

β [deg]

time(sec)

lean angle of Gyrover

Fig. 5.4. Vertical balanced motion by human control, X

(1, 1)

0 10 20 30 40 50 60 70 80

160

170

180

190

200

210

time

Tilt command

CNN model control trajectory

0 10 20 30 40 50 60 70 80

160

170

180

190

200

210

time

Tilt command

Human control trajectory

Fig. 5.5. Control trajectories comparison for X

(1, 1)

Again, we perform thesimilaritymeasure between the human control and

CNN modelcontrol trajectories foreachmotion,the results aresummarized

in Table 5.10. The CNN model canalso generate similar controltrajectories

as human operator,with an average similarityvalue of 0.7437.

1385

rther

pics

Learning-based

Con

trol

0 20 40 60 80 100

−30

−20

−10

[deg]

time(sec)

tilt angle of flywheel

0 20 40 60 80 100

100

110

120

130

β [deg]

time(sec)

lean angle of Gyrover

Fig. 5.6. Vertical balanced motion by human control, X

(1, 2)

0 10 20 30 40 50 60 70 80 90 100

160

170

180

190

200

time

Tilt command

CNN model control trajectory

0 10 20 30 40 50 60 70 80 90 100

160

170

180

190

200

time

Tilt command

Human control trajectory

Fig. 5.7. Control trajectories comparison for X

(1, 2)

Discussions

The simulations we have done in fact is the ﬁrst step to validate the CNN

models we obtained. By using the HMMsimilaritymeasure, we compare the

human controltrajectory with thecontrol trajectory generate fromthe CNN

model of aparticular motion.Ifthe similaritymeasure givesusarelatively

5.2

Imp

lemen

tationo

earning

Con

trol

139

0 20 40 60

−40

−20

[deg]

time(sec)

tilt angle of flywheel

0 20 40 60

100

110

120

130

β [deg]

time(sec)

lean angle of Gyrover

Fig. 5.8. Vertical balanced motion by human control, X

(1, 3)

0 10 20 30 40 50 60 70

150

160

170

180

190

200

time

Tilt command

CNN model control trajectory

0 10 20 30 40 50 60 70

150

160

170

180

190

200

time

Tilt command

Human control trajectory

Fig. 5.9. Control trajectories comparison for X

(1, 3)

high similarity value ( σ ≥ 0 5), which implies the particular CNN model

can produce ’similar’ control output as human control. From the simulation

results of the lateral balancing and tiltup motion, we can verify that the CNN

models for both motions are able to model the human control strategy. Later

on, in the next chapter, we will further verify the models by experimental

implementation.

1405

rther

pics

Learning-based

Con

trol

similarit

(2, 1)

0.7896

(2, 2)

0.7030

(2, 3)

0.7386

0.7437

ble

5.10.

Similarity

measures

for

tiltup

con

trol

twe

man

and

CNN

del

0 2 4 6

−40

−20

100

[deg]

time(sec)

tilt angle of flywheel

0 2 4 6

100

120

140

160

180

β [deg]

time(sec)

lean angle of Gyrover

Fig. 5.10. Tiltup motion by human control, X

(2, 1)

0 2 4 6

130

140

150

160

170

180

190

200

time

Tilt command

CNN model control trajectory

0 2 4 6

130

140

150

160

170

180

190

200

time

Tilt command

Human control trajectory

Fig. 5.11. Control trajectories comparison for X

(2, 1)

5.2

Imp

lemen

tationo

earning

Con

trol

141

0 2 4 6

−50

100

[deg]

time(sec)

tilt angle of flywheel

0 2 4 6

100

120

140

160

180

β [deg]

time(sec)

lean angle of Gyrover

Fig. 5.12. Tiltup motion by human control, X

(2, 2)

0 2 4 6

130

140

150

160

170

180

190

time

Tilt command

CNN model control trajectory

0 2 4 6

130

140

150

160

170

180

190

time

Tilt command

Human control trajectory

Fig. 5.13. Control

tra

jectories comparison for

(2, 2)

0 2 4 6 8 10

−100

−80

−60

−40

−20

[deg]

time(sec)

tilt angle of flywheel

0 2 4 6 8 10

100

150

β [deg]

time(sec)

lean angle of Gyrover

Fig. 5.14. Tiltup motion by human control, X

(2, 3)

1425

rther

pics

Learning-based

Con

trol

0 2 4 6 8

160

170

180

190

200

210

220

230

240

time

Tilt command

CNN model control trajectory

0 2 4 6 8

120

140

160

180

200

220

240

time

Tilt command

Human control trajectory

Fig. 5.15. Control trajectories comparison for X

(2, 3)

5.2.2 Implementation

VerticalBalanced Motion

umbe

xperiments have

been conducted to

verify theCNN mo

del

forvertical balancing, Figure5.16,5.17 and 5.18 shows the implementation

results. The human control strategyinbalancing the robotatthe vertical

sition is given

Figure5

.19.Asmentioned in

the

rviousc

hapter, we

evaluate the performance by the lean angleofthe robotand thedegree of

freedomremains forthe ﬂywheel. We

summarized

the ov

erall pe

rformance of

both CNN modeland human operator for the verticalstabilized motionin

Table 5.11.

average lean angle

β DOF

flywheel

CNN control#1 90. 24

0 . 9944

CNN control #2 88. 11

0 . 8756

CNN control #3 87. 57

0 . 8867

Human control 89. 41

0 . 9600

Table 5.11. Performance measures for vertical balancing.

When compared with human control, theCNN modelweobtainedfor

verticalbalancing behavesverysimilar to human. Forthe 3diﬀerenttrails,

the CNN model notonly able to stablize therobot at around 90

,but also

reserved ahigh level of degree of freedom for the internal ﬂywheel to oppose

anymotion that appearstomakethe robottofall down.

5.2

Imp

lemen

tationo

earning

Con

trol

143

0 10 20 30 40 50 60 70 80 90 100 110

100

110

120

β [deg]

time(sec)

lean angle of Gyrover

0 10 20 30 40 50 60 70 80 90 100 110

−40

−20

[deg]

time(sec)

tilt angle of flywheel

Fig. 5.16. Ve

rtical balancing by

CNN mo

del,

trail

#1.

0 10 20 30 40 50 60

100

110

120

β [deg]

time(sec)

lean angle of Gyrover

0 10 20 30 40 50 60

−40

−20

[deg]

time(sec)

tilt angle of flywheel

Fig. 5.17. Vertical balancing by CNN model, trail #2.

Tilt-up Motion

Next, we implementanotherCNN model whichistrainedbyhumantiltup

motiondata, theresults areshown in Figure 5.20 and5.21 for CNN model