37

Rotary Inverted Pendulum

Failure：Reuse the last received value

：Success ：Failure

：Success

Success：Input the transmitted signal

：Failure

Controller TRx Plant TRx

In wireless channels, packet errors may occur.

Plant

:Control information (torque) :State information

38

Cooperative Motion Model

A example of synchronized motion

Top view

Controller1 Plant 1

Plant 2

Plant 3 Controller2

Controller3

(The pendulum maintains an upright position.)

39

System Model

Controller 1

TRx 1

Plant 1

Wireless channel

TRx 1

Controller 2

TRx 2

Plant 2

TRx 2

Controller 3

TRx 3

Plant 3

TRx 3

:Control information (torque) :State information

40

Independent Transmission Scheme

Failure :Reuse the last received value

:Success :Failure

:Success

Success :Input the transmitted signal

Controller 1

TRx 1

Plant 1

Wireless channel

TRx 1

Controller 2

TRx 2

Plant 2

TRx 2

Controller 3

TRx 3

Plant 3

TRx 3

:Failure

41

Proposed Transmission Scheme (signal input)

TRx 1

TRx 1

TRx 2

TRx 3

TRx 2

TRx 3

Plant 2

Plant 3

Rx 2 3

Rx 1 3

Rx 1 2

Plant 1

Each plant receives each other’s control information.

42

Proposed Scheme (selection of the signal)

TRx 1

TRx 1

TRx 2

TRx 3

TRx 2

TRx 3

plant 2

plant 3

Rx 2 3

Rx 1 3

Rx 1 2

Plant 1

e.g. Feedback loop No.1

43

:If 1 success =

TRx 1

TRx 1

TRx 2

TRx 3

Plant 1

Rx 2 3

Proposed Scheme (selection of the signal)

TRx 2

TRx 3

plant 2

plant 3

Rx 1 3

Rx 1 2

44

:If 1 fail or signal is used

signal is used

TRx 1

TRx 1

TRx 2

TRx 3

Plant 1

Rx 2 3

Proposed Scheme (selection of the signal)

TRx 2

TRx 3

plant 2

plant 3

Rx 1 3

Rx 1 2 -

-

Select the most

similar signal

=

45

:If 1and3 fail signal is used

TRx 1

TRx 1

TRx 2

TRx 3

Rx 2 3

Plant 1

Proposed Scheme (selection of the signal)

TRx 2

TRx 3

plant 2

plant 3

Rx 1 3

Rx 1 2

= 46

:If 1and2 fail

TRx 1

TRx 1

TRx 2

TRx 3

Rx 2 3

Plant 1

signal is used

TRx 2

TRx 3

plant 2

plant 3

Rx 1 3

Rx 1 2

Proposed Scheme (selection of the signal)

=

47

:If all fail

TRx 1

TRx 1

TRx 2

TRx 3

Rx 2 3

Plant 1

TRx 2

TRx 3

plant 2

plant 3

Rx 1 3

Rx 1 2

Proposed Scheme (selection of the signal)

= 48

Proposed Transmission Scheme (input)

Controller 1

TRx 1

Main controller

Controller 2

TRx 2

Controller 3

TRx 3

The state information of each controller is available to every other controller.

TRx 1

TRx 2

TRx 3

49

e.g. Feedback loop No.1

Controller 1

TRx 1

Main controller

controller 2

TRx 2

controller 3

TRx 3

TRx 1

TRx 2

TRx 3

Proposed Scheme (selection of the signal)

50

:If 1 success

Main controller

Controller 1

TRx 1

controller 2

TRx 2

controller 3

TRx 3

TRx 1

TRx 2

TRx 3

Proposed Scheme (selection of the signal)

=

51

or -

-

signal is used

signal is used

Main controller

Select the most

similar signal

Controller 1

TRx 1

controller 2

TRx 2

controller 3

TRx 3

TRx 1

TRx 2

TRx 3

Proposed Scheme (selection of the signal)

= 52

:If 1and3 fail signal is used

Main controller

Controller 1

TRx 1

controller 2

TRx 2

controller 3

TRx 3

TRx 1

TRx 2

TRx 3

Proposed Scheme (selection of the signal)

=

53

:If 1and2 fail signal is used

Main controller

Controller 1

TRx 1

controller 2

TRx 2

controller 3

TRx 3

TRx 1

TRx 2

TRx 3

Proposed Scheme (selection of the signal)

= 54

:If all fail

Main controller

Controller 1

TRx 1

controller 2

TRx 2

controller 3

TRx 3

TRx 1

TRx 2

TRx 3

Proposed Scheme (selection of the signal)

=

55

Simulation

Pendulum angle( ) Arm angle( ) Arm angle( )

0 [rad] 0 [rad] 0 [rad]

Period of arm motion (T) 10 [s] Precision level 10-3[rad]

Falling down range of pendulum /6[rad]

Every 5 seconds, the desired values are flipped.

Packet loss :Random

Desired value

The motion of plants 1and3 is equal

Plant 1 Plant 2 Plant 3 Top view

2. Synchronization performance :The difference among arm angles

1. Control performance :The rate at which the pendulum collapses

56

Simulation

Pendulum angle( ) Arm angle( ) Arm angle( )

0 [rad] 0 [rad] 0 [rad]

Period of arm motion (T) 10 [s] Precision level 10-3[rad]

Falling down range of pendulum /6[rad]

Every 5 seconds, the desired values are flipped.

Desired value

The motion of plants 1and3 is equal

Plant 1 Plant 2 Plant 3 Top view

2. Synchronization performance :The difference among arm angles

1. Control performance :The rate at which the pendulum collapses

Packet loss :Random

57

Rotary Inverted Pendulum

Failure：Reuse the last received value

:Success :Failure

:Success

Success：Input the transmitted signal

:Failure

Controller TRx Plant TRx

In wireless channels, packet errors may occur.

Plant

:Control information (torque) :State information

58

Pendulum Angle

Low packet loss (p=0.01)

Transmission Success Transmission Failure

：Packet transmission rate (20Hz)

Plant Controller

The pendulum can maintain its upright position.

Pen

dulu

m a

ngle

[ra

d]

Time [s]

59

High packet loss (p=0.2)

Time [s]

The pendulum falls down.

Plant Controller

Pendulum Angle

Pen

dulu

m a

ngle

[ra

d]

The pendulum is considered to fall down when its angle goes over /6 or below - /6 rad

Packet errors occur before the pendulum can restore its upright position.

Transmission Success Transmission Failure

：Packet transmission rate (20Hz)

60

Pendulum Angle

High packet loss (p=0.2)

Plant Controller

Pen

dulu

m a

ngle

[ra

d]

Time [s]

If packet transmission rate is high, the pendulum can maintain its upright position.

Transmission Success Transmission Failure

：Packet transmission rate (50Hz)

61

Transmission Rate / Loss Rate

Plant

Trade-off between the packet transmission rate and the packet loss rate [1]

[1] R.Kohinata,T.Yamazato and M.Katayama, “Influence of channel errors on a wireless-controlled rotary inverted pendulum”

in 1

00s

Controller TRx Plant TRx

62

Transmission Rate vs Loss Rate Each point :At least one of the pendulums falls down in a simulation of 1000 runs of 1000[s]

0.1

0.15

0.2

0.25

0.3

Pac

ket

loss

rat

e

0.05

Packet period [s] 0.1 0.02 0.04 0.06 0.08 0.12 0

（25Hz） (10Hz)

The proposed scheme is especially effective when packet transmission rates are low.

Proposed

Independent

63

Simulation

Pendulum angle( ) Arm angle( ) Arm angle( )

0 [rad] 0 [rad] 0 [rad]

Period of arm motion (T) 10 [s] Precision level 10-3[rad]

Falling down range of pendulum /6[rad]

Every 5 seconds, the desired values are flipped.

Desired value

The motion of plants 1and3 is equal

Plant 1 Plant 2 Plant 3 Top view

2. Synchronization performance :The difference among arm angles

1. Control performance :The rate at which the pendulum collapses

Packet loss :Random

64

Arm Angle (no packet loss)

Time [s]

Arm

ang

le [

rad]

Desired value 1 Output 1

Desired value 2 Output 2

Time [s]

Every 5 seconds, the desired values are flipped.

65

Arm Angle (Independent) A

rm a

ngle

[ra

d]

Arm

ang

le [

rad]

Arm

ang

le [

rad]

Time（s）

Output 1(　　)

Output 2(　　) Output 3(　　)

Packet loss rate :0.05

66

Arm Angle (Proposed)

Arm

ang

le [

rad]

Arm

ang

le [

rad]

Arm

ang

le [

rad]

Time（s）

Output 1(　　)

Output 2(　　) Output 3(　　)

Packet loss rate :0.05

67

Synchronization Error of Arm Angle

Arm

ang

le [

rad]

Time [s] Time [s]

Synchronization error: The difference between the two arm angles

Sync

hron

izat

ion

erro

r of

arm

ang

le [

rad]

Output 1

Output 2

68

Synchronization Error of Arm Angle Independent Proposed

Synchronization error between output 1 and output 2

The proposed scheme reduces the synchronization error.

Time [s]

Sync

hron

izat

ion

erro

r of

arm

ang

le [

rad]

Sync

hron

izat

ion

erro

r of

arm

ang

le [

rad]

Time [s]

69

Distribution of Worst Synchronization Error The distribution of worst synchronization errors in a simulation run of 1000[s] (number of trials :1000)

600

400

200

0 ～0.05 ～0.1 ～0.15 ～0.2 ～0.25 ～0.3 ～0.35

Num

ber

of t

imes

Synchronization error range [rad]

Proposed Independent

Average and variance of the synchronization error of the proposed scheme are smaller than independent scheme.

～0.4 ～0.45

Packet loss rate :0.05

～0.45 ～0.5 ～0.55 ～0.6 over

70

Synchronization Error for Packet Transmission Rate

Proposed

Independent

Packet transmission rate [Hz]

Ave

rage

of

wor

st

sync

hron

izat

ion

erro

r

[rad

]

20 30 40 10

10-1

10-2

10-3

1

The average of worst synchronization errors in a simulation run of 1000[s] (number of trials :1000)

Packet loss rate :0.05

The proposed scheme reduces the synchronization error for whole packet transmission rate.

71

Synchronization Error for Packet Loss Rate

Proposed

Independent

Packet loss rate 0 0.05 0.1 0.075

10-1

10-2

Packet transmission rate :20Hz

0.025

The average of worst synchronization errors in a simulation run of 1000[s] (number of trials :1000)

10-3

Ave

rage

of

wor

st

sync

hron

izat

ion

erro

r

[rad

]

The proposed scheme reduces the synchronization error for whole packet loss rate.

72

Conclusions

The control performance of each machine is improved.

The synchronization performance of machines is improved.

Proposal

New measurement of the machine synchronization

For wireless cooperative motion of machines

Mutual use of control signals