LEGO MINDSTORMS Simulink Support Package

Development of Educational Contents for Control Engineering

Using LEGO MINDSTORMS and Simulink Support Package

∗M. Kawata (National Institute of Technology, Maizuru College)

Abstract– This paper discusses the development of a rotary inverted pendulum using the new LEGOMINESTORMS EV3 for control engineering education. We use Power Functions XL motor with GlideWheel-M (rotary encoder) instead of EV3 motors, and we use GlideWheel-M for detection of a pendulum angle.As a software in order to implement Simulink model, we use “ Simulink Support Package for LEGO MIND-STORMS EV3 Hardware ” which is provided free of charge. We verify whether it is possible to use ourproposed inverted pendulum in order to study the basis of control system analysis/design.

Key Words: LEGO MINDSTORMS, Simulink support package, Inverted pendulum, Education

1

LEGO MINDSTORMS LEGO MIT

LEGO

1) PBL

LEGO MINDSTORMS NXT

LEGO

2)–4) NXTLEGO Power Functions

Table 1: NXT and EV3 intelligent brick

NXT EV3

Main processor ARM7 48MHz ARM9 300MHzOperating system Proprietary Linux-based

Main memory 256KB flash64KB RAM

16MB flash64MB RAM

Motor ports 3 (with encoders) 4 (with encoders)

Sensor ports 4 4USB communication 12 Mbit/s 480 Mbit/s

USB host —Wi-Fi dongle,Ethernet adaptor,USB storage

SD card — Micro SD card(up to 32 GB)

Communication USB, BluetoothUSB, Bluetooth,Wi-Fi (Ethernet)

User interface 4 Buttons6 Buttons withbacklight

5),6)

PID( )

5),6)

MATLAB Simulink Support Package(MathWorks ) Simulink

NXT

LEGOMINDSTORMS EV3

2 LEGO MINDSTORMS Simulink

Support Package

2.1 LEGO MINDSTORMS

2.1.1

LEGO MINDSTORMS

NXT EV3Table 1

NXT OSOS (starting) (shutting down)

Simulink Support PackageSimulink

( 1)

OFF EV3OS Linux OS

30 [s] 50 [s]Simulink ON

MATLAB

for i = 1:5

set_param(’hoge’, ’SimulationCommand’, ’start’)

pause(10)

end

( 1) SimulinkSimulink

SimulinkScope, Display ToWorkspace MATLAB

1D07-1第57回自動制御連合講演会2014年11月10日ー12日 群馬伊香保 ホテル天坊

14PR0002/14/0000-0598 ￥400 © 2014 SICE598

Simulink hoge.slx

NXT Simulink SupportPackage 3

EV3USB

microSD( ) NXT

A∼C 3 EV3 A∼D4 ( )

NXT, EV3 1∼ 4 4

NXT, EV3 USB Bluetooth( 2)

EV3USB Wi-Fi ( )

Ethernet ( ) LAN( 3)

2.1.2

NXT

• 2

• 1

• 1

• 1

EV3

• 2

• 1

• 1

• 1

EV3NXT

( 4)

2.1.3

Fig. 1 (a) NXT EV3

NXT

• NXT 3

EV3

• EV3 L 2

• EV3 M 1

1180 A, B

Simulink Support PackageA, B 2 1360 1 [deg]

NXT EV3 L

EV3 M

(3.1 )

( 2) Bluetooth Bluetooth

( 3) LAN Wi-Fi Ethernet

( 4)

EV3

L servo motor

EV3

M servo motor

NXT

servo motor

(a) LEGO MINDSTORMS

PF

XL motor

PF

L motor

PF

M motor

PF

E motor

(b) LEGO Power Functions

Fig. 1: LEGO motors

PF XL motor GlideWheel-M(rotary encoder)

Servo motor

Fig. 2: PF XL motor with GlideWheel-M

3.1Fig. 1 (b) LEGO Power Functions

(PF E/M/L/XL )DC

Fig. 2 mindsen-sors.com GlideWheel-M( 5)

GlideWheel-M1 180 A, B

21 [deg]

2.2 Simulink Support Package

2.2.1

LEGO MINDSTORMSNXT/EV3

C ROBOTC

• NXT/EV3

• ROBOTC

MATLAB/SimulinkWindows R2012a

( 5) TechShare (http://store.techshare.jp/)ROBO Product (http://www.roboproduct.com/)

599

( )Simulink Support Pack-

age R2014aArduino (Uno/Nano/Mega2560 7) Due)

LEGO MINDSTORMS (NXT 5) EV3) Bea-gleBoard, Gumstix Overo, PandaBoard, RaspberryPi, Samsung GALAXY Android

Simulink

2.2.2 Simulink Support Package for LEGOMINDSTORMS NXT Hardware

NXT Simulink Support Package R2012bFig. 3

LEGOHiTechnic (

)

✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿

Bluetooth

✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿

NXTBluetooth

COM5)

Fig. 4 PI–D ( PID) Simulink hoge NXT.slx

“ ”“ ode1 (Euler) ” ( ) “

( ) ” 0.01( 6)

• Simulink Encoder int32double

Simulink Data Type Conversion

double ( )

• Simulink Encoder “ Sampletime ” 0.1

0.01

• MATLAB

0 [s] 1∼ 2[s]

2.2.3 Simulink Support Package for LEGOMINDSTORMS EV3 Hardware

EV3 Simulink Support Package R2014a(R2013b

)✿✿✿✿

USB✿✿✿✿✿✿✿✿✿✿✿✿✿

Bluetooth✿✿✿✿✿✿✿✿✿✿✿✿✿✿

✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿

Wi-Fi✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿

Ethernet✿✿✿✿

✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿

LAN✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿

MAT-LAB

Windows/ /

( )( ) MATLAB

( 6) 10 [ms]

LEGO MINDSTORMS NXT

Copyright 2011-2013 The MathWorks, Inc.

Freq

Vol

LEGO

Speaker

Port A

LEGO

Motor

Line 1

LEGO

LCD

Mailbox 1

Data

Size

LEGO

Receive via Bluetooth(R) Connection

Port 1

X

Y

Z

LEGO

Acceleration Sensor

LEGO

Timer

Port 1

LEGO

Gyro Sensor

Port 1

LEGO

Sound Sensor

Mailbox 1

LEGO

Send via Bluetooth(R) Connection

Port A

LEGO

Encoder

Port 1

R

G

B

LEGO

Color Sensor

Port 1

LEGO

Ultrasonic Sensor

LEGO

Battery

LEGO

Button

Port 1

LEGO

Touch Sensor

Port 1

LEGO

Light Sensor

Port 1

LEGO

Compass Sensor

Port 1

LEGORed

Blue

IR Receiver Sensor

Examples forLEGO MINDSTORMS

NXT

[Examples]

Port 1

Lat

Lon

LEGO

GPS Sensor

Fig. 3: Simulink Support Package for LEGO MIND-STORMS NXT Hardware (R2014a)

In1 Out1

Subsystem

(Motor)

In1

In2

Out1

Subsystem

(PI-D Controller)

Step

Clock

t

To Workspace

y

To Workspace1

Scope

Line 1

LEGO

LCD

(a) hoge NXT.slx

Port A

LEGO

Encoder

Port A

LEGO

Motor

Saturation

double

Data Type Conversion

1

In1

1

Out1

(b) Subsystem (Motor)

1

In1

1

Out1

2

In2

kP

Gain

kI

Gain1

1s

Integrator

du/dt

Derivative

1

0.025s+1

Transfer Fcn

kD

Gain2

(c) Subsystem (PI-D Controller)

Fig. 4: Example of Simulink model (NXT Hardware)

Fig. 6 PI–D Simulinkhoge EV3.slx

Subsystem (PI-D Controller) Fig. 6 (c)NXT

GlideWheel-M SimulinkEncoder Encoder “ Resetmode ” No reset GlideWheel-M No reset

600

LEGO MINDSTORMS EV3

Copyright 2013 The MathWorks, Inc.

Freq

Vol

LEGO EV3

Speaker

Port 1

LEGO EV3

Touch Sensor

Port 1

LEGO EV3

Ultrasonic Sensor

Port 1

LEGO EV3

Gyro Sensor

Port 1

LEGO EV3

Color Sensor

Port A

LEGO EV3

Motor

Port A

LEGO EV3

Encoder

Up

LEGO EV3

Button

Line 1

LEGO EV3

Display

Port 1

LEGO EV3

Infrared Sensor

LEGO EV3

Status Light

Examples forLEGO MINDSTORMS

EV3

[Examples]

Fig. 5: Simulink Support Package for LEGO MIND-STORMS EV3 Hardware (R2014a)

In1 Out1

Subsystem

(Motor)

In1

In2

Out1

Subsystem

(PI-D Controller)

Step

Clock

t

To Workspace

y

To Workspace1

Scope

Line 1

LEGO EV3

Display

(a) hoge EV3.slx

Saturation

double

Data Type Conversion

1

In1

1

Out1Port A

LEGO EV3

Encoder

Port A

LEGO EV3

Motor

Clock

> 0

Switch

1

Constant1

0

Constant

int8

Data Type Conversion1

(b) Subsystem (Motor)

Fig. 6: Example of Simulink model (EV3 Hardware)

OFF“ Reset

mode ” Reset by external signal

Fig. 6 (b)Encoder 0

3

3.1

Fig. 1 (a) NXTEV3 L/M Fig. 1 (b) PFXL/L/M/E

GlideWheel-MLEGO 8)

LEGO (NXT, EV3)

Table 2: Comparison of LEGO motors (no load)

(a) NXT intelligent brickMotor Dead zone ymax [deg/s] α β

NXT |u(t)| ≤ 3 942 9.5 −12.6

EV3 L |u(t)| ≤ 4 977 9.8 −16.3

EV3 M |u(t)| ≤ 19 1,434 16.0 −133.4

PF XL |u(t)| ≤ 6 1,250 12.7 −33.9

PF L |u(t)| ≤ 12 2,142 23.6 −213.4

PF M |u(t)| ≤ 16 2,268 23.4 −101.4

PF E |u(t)| ≤ 4 4,298 43.7 −82.7

(b) EV3 intelligent brickMotor Dead zone ymax [deg/s] α β

NXT — 950 9.1 23.8

EV3 L — 974 9.4 21.1

EV3 M — 1,458 13.1 174.7

PF XL |u(t)| ≤ 3 1,250 12.3 8.5

PF L |u(t)| ≤ 6 2,087 21.7 −104.2

PF M |u(t)| ≤ 16 2,288 23.2 −89.0

PF E |u(t)| ≤ 2 4,234 41.7 74.9

1000

--100

Dead zone

1000

--100

(a) NXT intelligent brick (b) EV3 intelligent brick

Fig. 7: Motor velocity

u(t) = uc (uc 1 ∼ 100 )h = 0.01 [s] y(t) [deg]

Table 2ymax [deg/s] (uc = 100

)y∞ [deg/s] 1

y∞ = αuc + β (1)

α, β

NXT Table 2 (a)β

(Fig. 7 (a)) β NXT, EV3L PF XL/E

y(s) = P (s)u(s), P (s) =b

s(s + a)(2)

NXT, EV3 L

PF ENXT

PF XL

EV3 Table 2 (b)NXT ymax

601

Pendulum

Arm

GlideWheel-Mfor pendulum

PF XL motorwith

GlideWheel-M

NXT intelligentbrick

Pendulum

PF XL motorwith

GlideWheel-M

EV3 intelligentbrick

Arm

GlideWheel-Mfor pendulum

Wi-Fidongle

(a) NXT version5) (b) EV3 version

Fig. 8: LEGO rotary inverted pendulum

βFig. 7

(b) PF XLβ 0

EV3 Mβ ( )

3.2

GlideWheel-M ( 7)

3.1GlideWheel-M PF XLFig. 8 NXT EV3

90 GlideWheel-M GlideWheel-M

3

3.3

3.3.1

J2 = J2 + m2l22

θ1 = − aθ1 − asgnsgn θ1 + bv (3)

m2L1l2 cos θ2 · θ1 + J2θ2

= J2θ21 sin θ2 cos θ2 + m2gl2 sin θ2 − c2θ2 (4)

5) θ1 [rad]θ2 [rad] ( ) v

(−100 ∼ 100)L1 = 7.10×10−2 [m]

m2 = 4.00×10−3 [kg] l2 = 7.10×10−2

[m] g = 9.81 [m/s2]a, asgn, b

J2 [kg·m2]

( 7) GlideWheel-MTechShare

c2 [kg·m2/s]

3.3.2

(a) NXT

(3)asgnsgn θ1 (2)

u = v, y = θ1 P

u(s) = kPe(s), e(s) = r(s) − y(s) (5)

y rr y G(s) 2

G(s) =ω2

n1

s2 + 2ζ1ωn1s + ω2n1

,

{ω2

n1 = bkP

2ζ1ωn1 = a(6)

Amax

kP, r Amax

Tp ζ1, ωn1

a, b Fig. 9 (a)NXT a, b

NXTFig. 9

(a)

NXTasgnsgn θ1

M f1(t)p1 = Nf1(t) (7)

M f1(t) = Gf1(s)M1(t), Nf1(t) = Gf1(s)N1(t),

M1 =[−θ1 −sgnθ1 v

], p⊤

1 =[a asgn b

], N1 = θ1

( 8)

J = ‖M fs1p1 − Nfs1‖ (8)

p1

p1 = (M⊤

fs1M fs1)−1M⊤

fs1Nfs1 (9)

( )5) Gf1(s) =1/(1+Tf1s)

3 3t = t1, . . . , tk

M fs1 =

M f1(t1)

...M f1(tk)

, Nfs1 =

Nf1(t1)

...Nf1(tk)

0 0.2 0.4 0.6 0.8 10

30

60

t [s]

θ1(t)[deg]

ExperimentSimulation

0 0.2 0.4 0.6 0.8 10

30

60

t [s]

θ1(t)[deg]

ExperimentSimulation

(a) NXT version (b) EV3 version

Fig. 9: Arm parameter identification (2nd order lagsystem)

( 8) θ1 θ1 θ1

602

0 0.2 0.4 0.6 0.8 10

30

60

t [s]

θ1(t)[deg]

ExperimentNonlinearSimulation

Fig. 10: Arm parameter identification using NXTversion (least square method)

Table 3: Identification result of armNXT version EV3 version

Method 1 Method 2 Method 1

a 1.32 × 101 1.28 × 101 1.42 × 101

asgn 0 6.96 × 100 0

b 2.97 × 100 3.14 × 100 3.45 × 100

„

Method 1: identification based on 2nd lag system responseMethod 2: identification based on least square method

«

Fig. 10 asgnsgn θ1

NXT asgn

NXTTable 3

(b) EV3

Fig. 9 (b) EV3 2a, b

EV3

Fig. 9 (b)0

EV3

2

EV3Table 3

3.3.3

NXT EV3

(θ2 = φ2 + π)(4)

J2φ2 + c2φ2 + m2gl2 sinφ2 = 0 (10)

sin φ2 ≃ φ2 (10) 2

φ2 + 2ζ2ωn2φ2 + ω2n2φ2 = 0,

{ω2

n2 = c2/J2

2ζ2ωn2 = m2gl2/J2

(11)

Tλ

Ti λi T , λ

1 2 3 4 5 60

0.25

0.5

0.75

1

i

TiandT

[s]

1 2 3 4 5 60

0.25

0.5

0.75

1

i

λiandλ

(a) Ti and T (b) λi and λ

0 1 2 3 4 5

−90

−45

0

45

90

t [s]

φ2(t)[deg]

ExperimentLinear Simulation

0 1 2 3 4 5

−90

−45

0

45

90

t [s]

φ2(t)[deg]

ExperimentNonlinear Simulation

(c) Linear simulation (d) Nonlinear simulation

Fig. 11: Pendulum parameter identification (2nd or-der lag system)

0 1 2 3 4 5

−90

−45

0

45

90

t [s]φ2(t)[deg]

ExperimentNonlinear Simulation

Fig. 12: Pendulum parameter identification (leastsquare method)

Table 4: Identification result of pendulum

Method 1 Method 2

J2 1.33 × 10−5 9.27 × 10−6

c2 1.58 × 10−5 1.33 × 10−5

„

Method 1: identification based on 2nd lag system responseMethod 2: identification based on least square method

«

ζ2, ωn2

J2, c25) Fig. 11

Fig. 11 (a), (b)Ti, λi

Fig. 11 (c), (d)sinφ2 ≃ φ2

sinφ2

NXT

M f2(t)p2 = Nf2(t) (12)

M f2(t) = Gf2(s)M2(t), Nf2(t) = Gf2(s)N2(t),

M2 =[φ2 φ2

], p⊤

2 =[J2 c2

], N2 = −m2gl2 sinφ2

sinφ25) Fig. 12

Table 4

603

3.3.4

(a) NXT

NXT asgnsgn θ1

v = u +asgn

bsgn θ1 (13)

(3)

θ1 = − aθ1 + bu (14)

cos θ2 ≃ 1, sin θ2 ≃ θ2

(4)

m2L1l2θ1 + J2θ2 = m2gl2θ2 − c2θ2 (15)

x =[x1 x2 x3 x4

]⊤ =

[θ1 θ2 θ1 θ2

]⊤ (16)

x = Ax + Bu (17)

(b) EV3

EV3 asgnsgn θ1

asgn = 0 u = v(14) NXT

(4) x

(16) (17)

3.4 ( )

(a) NXT

(17)

J =

∫∞

0

(x⊤Qx + Ru2

)dt (18)

u = Kx (19)

Q = diag{50, 2000, 0.01, 0.01

}, R = 1 K

h = 0.01[s]

ωi(s) =s

1 + Tisθi(s) (Ti = 0.06, i = 1, 2) (20)

1 ωi(t) = θi(t)

0 2 4 6 8−60

−30

0

30

60

t [s]

θ1(t)[deg]

withnonlinear

compensator

withoutnonlinear

compensator

0 2 4 6 8−10

−5

0

5

10

t [s]

θ2(t)[deg]

Fig. 13: State feedback control using NXT version(effectiveness of nonlinear compensator)

0 1 2 3 4 5 6−90

−45

0

45

90

t [s]

θ1(t)[deg]

0 1 2 3 4 5 0−20

−10

0

10

20

t [s]

θ2(t)[deg]

(a) NXT version

0 1 2 3 4 5 6−90

−45

0

45

90

t [s]

θ1(t)[deg]

0 1 2 3 4 5 0−20

−10

0

10

20

t [s]

θ2(t)[deg]

(b) EV3 version

Fig. 14: State feedback control (impression of im-pulse disturbance to pendulum at t = 3 [s])

(13) t =4 [s] v = u Fig. 13

(13)Fig. 14 (a)

t = 3 [s]

(b) EV3

NXT Q, R(17) (18)

(19)Fig. 14 (b) t = 3 [s]

NXT EV3

EV3

3.5

(a) NXT

ωi(t) = θi(t)

˙x = Ax + Bu − L(y − Cx

)(21)

x =[x1 x2 x3 x4

]⊤ x

y

y =[θ1 θ2

]⊤ = Cx, C =

[1 0 0 00 1 0 0

](22)

(21) x3

(13)

v = u +asgn

bsgn x3 (23)

x (19)

{˙x = Ax + By

u = Cx,

{A = A + BK + LC

B = −L, C = K(24)

604

0 2 4 6 8−60

−30

0

30

60

t [s]

θ1[deg]

withnonlinear

compensator

withoutnonlinear

compensator

0 2 4 6 8−10

−5

0

5

10

t [s]

θ2[deg]

Fig. 15: Observer based output feedback control us-ing NXT version (effectiveness of nonlinearcompensator)

(24)1

h = 0.01 [s]{

x[k + 1] = Adx[k] + Bdy[k]

u[k] = Cdx[k] + Ddy[k](25)

f [k] := f(kh) (k = 0, 1, 2, . . .)

K

L A+BK

−16± 8j, −4, −1.5 A + LC

5 K, L

t = 4 [s] (23) v = uFig. 15 Fig. 15

(23)NXT

t = 3 [s]Fig. 16 (a) θ1,

θ2 (20)

(b) EV3

EV3 NXT(23) v = u

NXTA+BK −16±8j, −4, −1.5 A+LC

5 K, L

(25)Fig. 16 (b) t = 3

[s] Fig. 16 (b)EV3

4

LEGO MINDSTORMSEV3Simulink Support Package

GlideWheel-MLEGO NXT EV3

NXT EV3 PF XLNXT

0 1 2 3 4 5 6−90

−45

0

45

t [s]

θ1andx1[deg]

θ1x1

0 1 2 3 4 5 6−10

0

10

20

t [s]

θ2andx2[deg]

θ2x2

0 1 2 3 4 5 6−600

−300

0

300

t [s]

θ1andx3[deg/s]

θ1x3

0 1 2 3 4 5 6−100

0

100

200

t [s]

θ2andx4[deg/s]

θ2x4

(a) NXT version

0 1 2 3 4 5 6−90

−45

0

45

t [s]

θ1andx1[deg]

θ1x1

0 1 2 3 4 5 6−10

0

10

20

t [s]

θ2andx2[deg]

θ2x2

0 1 2 3 4 5 6−600

−300

0

300

t [s]

θ1andx3[deg/s]

θ1x3

0 1 2 3 4 5 6−100

0

100

200

t [s]

θ2andx4[deg/s]

θ2x4

(b) EV3 version

Fig. 16: Observer based output feedback control(impression of impulse disturbance to pen-dulum at t = 3 [s])

EV3

EV3

1) Mindstorms Vol. 21,No. 5, pp. 517–559 (2006)

2) P. J. Gawthrop and E. W. McGookin: A LEGO-BasedControl Experiment, IEEE Control Systems Magazine,Vol. 24, No. 5, pp. 43–56 (2004)

3) NXTway (LEGO Segway) —LEGO Mind-storms NXT — 7 SICE

63–1–4 (2007)4) S. S. Prieto, T. A. Navarro, M. G. Plaza and O. R. Polo: A

Monoball Robot Based on LEGO Mindstorms, IEEE Con-trol Systems Magazine, Vol. 32, No. 2, pp. 71–83 (2012)

5) MATLAB/Simulink —PID— TechShare (2013)

6) LEGO MINDSTORMS NXT MATLAB/Simulink—

13 SICE 7D4–4(2013)

7) Arduino MATLAB !TechShare (2012)

8) Philo’s Home Page: http://www.philohome.com/motors/motorcomp.htm

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