LMHanoi - Tower of Hanoi with Lego Software Mindstorms - - PowerPoint PPT Presentation

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LMHanoi - Tower of Hanoi with Lego Software Mindstorms - - PowerPoint PPT Presentation

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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot LMHanoi - Tower of Hanoi with Lego Software Mindstorms Inter-thread communication Application logic Robot controller Music Experiment Markus Flatz, Peter Palfrader,

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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

LMHanoi - Tower of Hanoi with Lego Mindstorms

Markus Flatz, Peter Palfrader, Andreas Rottmann 25.01.2011

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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Overview

1 Basics 2 The robot 3 Software

Inter-thread communication Application logic Robot controller Music

4 Experiment

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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

The puzzle

  • Move a set of disks from one rod to another
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

The puzzle

  • Move a set of disks from one rod to another
  • With moving only ever one disk
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

The puzzle

  • Move a set of disks from one rod to another
  • With moving only ever one disk
  • No larger disk may rest on a smaller one
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Lego Mindstorms

  • Extends Lego with new building blocks:
  • Sensors
  • Motors
  • Programmable computer
  • NXT 2.0: 32-bit ARM7 microprocessor, 64 kB RAM and

256 kB Flash memory

  • 4 input, 3 output ports
  • Bluetooth, USB
  • Sound
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

ABuNQEUC1 NXC Not eXactly C

  • Free compiler to build Lego Mindstorms executables from

something similar to C

  • Somewhat documented
  • Several limitations, e.g., no recursion, no passing of

mutexes as parameters

  • Workarounds require abusing the preprocessor

1almost, but not quite, entirely unlike C

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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

The robot: Klaus

  • Forklift
  • Can move along three axes
  • Movement limited by

sensors for two of them

  • Using touch and color

sensors

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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Software

  • App. Logic

Controller Music

MBox Global Variable

Robot

Three threads

  • Application logic (Tower of Hanoi algorithm)
  • Robot controller
  • Music playback
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Inter-thread communication

NXC Primitives

  • Mutex

Mailbox

6 5 4 3 2 1

front fill

  • Circular buffer
  • Mutex (protects fill count and front pointer)
  • Two counting semaphores (full, empty)[1]
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Application logic

  • Determine movement sequence
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Recursive algorithm

void hanoi ( i n t n , rod source , rod help , rod dest ) { i f ( n > 0) { hanoi ( n − 1 , source , dest , help ) ; move disk ( source , dest ) ; hanoi ( n − 1 , help , source , dest ) ; } }

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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Recursive algorithm

void hanoi ( i n t n , rod source , rod help , rod dest ) { i f ( n > 0) { hanoi ( n − 1 , source , dest , help ) ; move disk ( source , dest ) ; hanoi ( n − 1 , help , source , dest ) ; } }

  • 2n − 1 moves
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Recursive algorithm

void hanoi ( i n t n , rod source , rod help , rod dest ) { i f ( n > 0) { hanoi ( n − 1 , source , dest , help ) ; move disk ( source , dest ) ; hanoi ( n − 1 , help , source , dest ) ; } }

  • 2n − 1 moves
  • Optimal movement sequence
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Iterative algorithm [2],[3]

  • Rods source, help and destination on a circle
  • Even number of disks: ordered clockwise
  • Odd number of disks: ordered counterclockwise
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Iterative algorithm [2],[3]

  • Rods source, help and destination on a circle
  • Even number of disks: ordered clockwise
  • Odd number of disks: ordered counterclockwise

while ( not a l l d i s k s

  • n

d e s t i n a t i o n rod ) { move the s m a l l e s t d i s k

  • ne

rod c l o c k w i s e ; i f ( a d i s k

  • ther

than the s m a l l e s t can be moved ) { move t h i s d i s k ; } }

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SLIDE 18

LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Iterative algorithm [2],[3]

  • Rods source, help and destination on a circle
  • Even number of disks: ordered clockwise
  • Odd number of disks: ordered counterclockwise

while ( not a l l d i s k s

  • n

d e s t i n a t i o n rod ) { move the s m a l l e s t d i s k

  • ne

rod c l o c k w i s e ; i f ( a d i s k

  • ther

than the s m a l l e s t can be moved ) { move t h i s d i s k ; } }

  • Same movement sequence
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Implementation

  • No support for recursion
  • Choose iterative algorithm
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Na¨ ıve implementation

help dest. source . . . dest. disk 1 2 3 . . . n

  • Store the current location of each disk
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Na¨ ıve implementation

help dest. source . . . dest. disk 1 2 3 . . . n

  • Store the current location of each disk
  • Space complexity: O(n)
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Na¨ ıve implementation

help dest. source . . . dest. disk 1 2 3 . . . n

  • Store the current location of each disk
  • Space complexity: O(n)
  • Time complexity per move: O(n)
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Refined implementation

source 3 help 4 1 destination 5 2 height: 1 2 2 source help dest.

  • Store the disks on each rod
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Refined implementation

source 3 help 4 1 destination 5 2 height: 1 2 2 source help dest.

  • Store the disks on each rod
  • Store the height of each rod’s stack
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Refined implementation

source 3 help 4 1 destination 5 2 height: 1 2 2 source help dest.

  • Store the disks on each rod
  • Store the height of each rod’s stack
  • Approximately three times as much memory
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Refined implementation

source 3 help 4 1 destination 5 2 height: 1 2 2 source help dest.

  • Store the disks on each rod
  • Store the height of each rod’s stack
  • Approximately three times as much memory
  • Space complexity: O(n)
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SLIDE 27

LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Refined implementation

source 3 help 4 1 destination 5 2 height: 1 2 2 source help dest.

  • Store the disks on each rod
  • Store the height of each rod’s stack
  • Approximately three times as much memory
  • Space complexity: O(n)
  • Time complexity per move: O(1)
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Robot controller (1)

General structure

  • Get movements from mailbox and execute them
  • Maintains current position
  • Wagon position stops on color sensor readings
  • Fork vertical movement stops on touch sensor
  • Fork moves horizontally by fixed amount
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Robot controller (2)

Specialties

  • Overshoot

T arget Position Sensor Path

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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Robot controller (2)

Specialties

  • Overshoot

T arget Position Sensor Path

  • Use raw mode of color sensor to detect blue
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Music

  • Additional concurrency
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Music

  • Additional concurrency
  • Situational
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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Experiment

duration(n) = (2n − 1) · d + c

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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Experiment

duration(n) = (2n − 1) · d + c

100 200 300 400 500 1 2 3 4 5 duration [s] number of disks ’lmhanoi.dat’ expreg(x)

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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Experiment

duration(n) = (2n − 1) · d + c

100 200 300 400 500 1 2 3 4 5 duration [s] number of disks ’lmhanoi.dat’ expreg(x)

expreg(x) = (e0.693·x − 1) · 23.2 + 12.7

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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

References

John A. Trono and William E. Taylor. Further comments on “a correct and unrestrictive implementation of general semaphores”. SIGOPS Oper. Syst. Rev., 34:5–10, July 2000. Wikipedia. Tower of Hanoi – Wikipedia, The Free Encyclopedia, 2011. https://secure.wikimedia.org/wikipedia/en/w/ index.php?title=Tower_of_Hanoi&oldid=407310252. Wikipedia. T¨ urme von Hanoi – Wikipedia, Die freie Enzyklop¨ adie, 2011. https: //secure.wikimedia.org/wikipedia/de/w/index. php?title=T%C3%BCrme_von_Hanoi&oldid=83701385.

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LMHanoi - Tower of Hanoi with Lego Mindstorms Basics The robot Software

Inter-thread communication Application logic Robot controller Music

Experiment

Thank you for your attention.