Wiimotes and Robots

David Lippman

Pierce College Ft Steilacoom

“Real World” What do we mean by this? Capturing data for analysis is cool, but Can we solve a problem, and see it in action?

Wiimotes Can connect over Bluetooth to computer 3-axis accelerometer Infrared camera with blob detection (4 pts)

Interacting with the Wiimote

Low LevelWiiuse / WiiuseJ (C / Java)Wiimotelib (C#)

High LevelGlovePIE

Problem #1

Prereq: AlgebraProblem: Wiimote returns dot values in the range x: 0-1023, y: 0-767 GlovePIE maps mouse position to a 0-1 scale in

the x and y How do we map Wiimote position to a mouse

position?

Prob #1 Soln

Wiimote pointing left puts dots on the right, so need to invert x. Don’t need to invert y since Mouse.y measures down from the top of the screen

Mouse.x = 1 - wiimote.dot1x/1023 Mouse.y = wiimote.dot1y/767

Problem #2

Prereq: TrigProblem: Wiimote returns dot values in the range x: 0-1023, y: 0-767, roll GlovePIE maps mouse position to a 0-1 scale in

the x and y How do we map Wiimote position to a mouse

position, compensating for roll?

Prob #2 Soln

Angle = asin(Wiimote.gx/1) or use atan2 Angle is off horiz Find xcamera, ycamera

Convert to polar Adjust for roll angle Convert back to Cartesian,

map to mouse

Problem #3

Prereq: Algebra

Problem:

How do we determine 3D position of Wiimote in space? (using triangles)

(Assume no roll for simplicity)

Prob #3 SolnCalculate distance between dots

Distance from camera = 264/dot dist

Dist at 1m = 0.1mreal / 132 pxcamera

X position:

1 m

200 px = 200*0.1/132 = 0.1515 m

4 m

0.1515 0.606

1 4

m m

m m

Problem #4

Prereq: TrigProblem: How do we determine 3D position of Wiimote in

space? (using trig) (Assume no roll for simplicity)

Could we have done this with 2 Wiimotes and one dot?

Prob #4 Soln Camera FOV = about 45 degrees Pixels/degree = 1024/45 = 22.8

200px → 8.8 deg1 m

4 m

4sin(8.8 ) 0.611x m

0.1dist

1dot separation

2tan22.8 pixels/degree

m

How different?Distance determination:

Dis

t (m

)

Dot separation (pixels)

Relative difference

X-location determination:

Pixel x

actual x

Relative difference

Johnny Lee's Youtube Video

Problem #5Prereq: Linear Algebra

Problem:

Mark 4 points on a projected plane (projector image) that correspond to 4 points of a unit square (screen coordinates). Find the transformation that maps points on the projected plane to the unit square.

u

v

x

y

Prob #5 SolnHomogenous Coordinates: , ,x y w

xx wyy w

u

v

x

y

, , , ,1

1

a d g

x y w u v b e h

c f

1

1

au bv cx

gu hv

du ev fy

gu hv

1

1

au bv cx

gu hv

du ev fy

gu hv

x au bv c xgu xhv

y du ev f ygu yhv

0 0 0 0 0 0

1 1 1 1 1 1

2 2 2 2 2 2

3 3 3 3 3 3

0 0 0 0 0 0

1 1 1 1 1 1

2 2 2 2 2 2

3 3 3 3 3 3

1 0 0 0

1 0 0 0

1 0 0 0

1 0 0 0

0 0 0 1

0 0 0 1

0 0 0 1

0 0 0 1

u v u x v x a

u v u x v x b

u v u x v x c

u v u x v x d

u v u x v x e

u v u x v x f

u v u x v x g

u v u x v x h

0

1

2

3

0

1

2

3

x

x

x

x

y

y

y

y

Using 4 corner points, this gives:

Reduces further using unit square for (u,v)

Solve using Gaussian Elimination.

To map back to (u,v), find inverse of the mapping matrix.

Problem #6

Prereq: Integral Calculus / DiffEq Problem:

Use the accelerometer readings to estimate distance the Wiimote moves.

Prob #6 Soln

Simplistic approach:s0 = 0, v0 = 0. Step: Δt = .05 secLoop: vn = vn-1 + .05a sn = sn-1 + .05vn

However, accelerometers are very noisy, so this is not very accurate. In fact, it’s so horrible I’m not even going to show it!

Arduino

Computer on a chip 14 digital I/O, w/ 6

pseudo analog out 6 analog inputs 16KB storage 1KB RAM Serial over USB Open hardware Open software

Problem #7

Prereq: Algebra

Problem: Create a car backup alarm using distance sensor and LED light.

Distance sensor can detect time (in microseconds) that a sound takes to echo back.

Prob #7 Soln

dist = rate*timerate = experimentally determined, or speed

of sound converted to appropriate unitsblink delay proportional to distance

Does direct proportionality look good? Should it be quadratic? Logarithmic?

Problem #8

Prereq: Algebra

Problem: Map Nunchuck joystick data (values -105 to 105) to PWM values (500 to 2500) for the Servos

Prob #8 Soln

Joystick Servo

-105 2500

-105 500

500 2500 200

105 ( 105) 21

200Servo (Joystick 105) 2500

21

m

Problem #9

Prereq: Trig

Problem: Use the Pan/Tilt laser pointer to draw a circle

Prob #9 Soln

Use parametric equations:t=0Loop: x = cos(t) y = sin(t) map (x, y) to Servos t = t + .1 delay(20)

Problem #10

Prereq: Pre-algebraProblem: In a robot with differential drive,

each wheel can turn at a different rate. If the wheels are 10cm apart and the outside wheel turns at full speed, at what fraction of full speed will the inside wheel need to turn to drive a circle with inner radius 50cm?

Prob #10 Soln

10cm 50cm

Cinside = 2π(50) cm

Coutside = 2π(50+10) cm

Speedinside = (2π(50) cm)/unit time

Speedoutside = (2π(50+10) cm)/unit time

Ratio of speeds = 50 / (50 + 10) = 5/6

Problem #11

Prereq: Trig

Problem: Ballistics trajectories. Experimentally determine initial velocity, then adjust launch angle to hit a target.

Have a class competition to see who can come closest!

Prob #11 Soln0

20 0

0

0 0

0 00 0

00

To determine :

4.9

assuming 0

sin( )

4.9horizontal hit dist

sin( )cos( )

4.9

9.8

sin(2 )

v

hit

v

s t v t s

s

vt

d

vd v

dv

0

0

00

20

12

0

To find launch angle:

again assuming 0

sin( )

4.9to achieve horizontal hit dist

sin( )cos( )

4.9

sin(2 )

9.8

1 9.8sin

2

hit

s

vt

d

vd v

vd

d

v

Advanced ideas

Kalman filters Gesture recognition (hidden Markov

model) Augmented Reality

Playtime

Wii Quizzer Wii Buzzer

Correlation doesn't imply causation, but it does waggle its eyebrows suggestively and gesture furtively while mouthing 'look over there'.