Math in Robotic Motion (2)

8/8/2019 Math in Robotic Motion (2)

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MATHEMATICAL INEVERYDAY LIFE

(NATRAH,NURUL ATIQAH,AMELIA)



THE ROLE OF MATHEMATICS IN

MODERN TECHNOLOGIES(PARTICULAR ROBOTIC MOTION)



ROBO

T

Any machine that is

capable of intelligently

controlling its motionthrough space

Designed to perform avariety of tasks by moving

parts, tools or specialized

devices.

Types

Mobile Stationary

free to move around remain in 1 place but have

arms that move



ROBOTIC ARM

Hand

Base

Polar

Joints

Linear

Joint



ROLE OF

MATHEMATICS IN

ROBOTIC MOTION

(ARM)

Coordinate system

Degree of freedom

Algebraic and

differential topology

Combinatoric

Optimization algorithm

Differential algebraic







Algebraic and differential topology

had been used to understand configuration

spaces of many-particle or many-body systems



Optimization algorithm

a robotic system design and many problems in

robot task planning can be formulated as

optimization problems, though they are typically

``hard'' in terms of complexity and lack of readily

recognizable or standard mathematical structures.

Success stories include graph-theoretic and

calculus of variation based approaches to

determining optimal paths, randomized algorithms

for finding solutions in complex spaces, optimal

feedback control policies for a range of robotic

tasks, and saddle-point policies for solving

differential games of pursuit and evasion.



combinatoric

Relevant to discrete actuators which are

the smoothly actuated robotic arms and

other manipulators that can bereplaced by a cheaper network of

discrete actuators (devices that extend

or contract into only two positions).



Differential algebraic

The used of differential algebraic inequalities inthe modeling of multibody systems in contact,

which in turn are central to robot manipulation.



FRIEZES AND MOSAIC



INTRODUCTION

´ MATH

- widely spread in several fields even in

architecture and art.- commonly use to describe the systematically

classification of friezes and mosaic.

´ FRIEZES & M

OSAIC

-used in decoration forseveral millennia by ancient worlds· like

Sumerian,Egyption,an Mayan civilization.



EX AMPLE««



FRIEZES

´ Oxford English Dictionary

-and of painted or sculptured decoration.

´ Mathematical point of view

(i) constant and finite width and infinitely long inthe perpendicular (horizontal) direction,

(ii) It is periodic, exist some minimal distance

where L > 0 such that the translation of thefrieze by distance L along the direction willleave the frieze unchanged



FRIEZES



REFLECTION BY HORIZONT AL

MIRROR



REFLECTION BY VERTIC AL MIRROR



MOSAIC

´ pattern that can be repeated to fill the plane.

´ periodic along two linearly independent

directions.´ linear independent directions

- remain the pattern unchanged under

translation.



INVARI ANT (UNCHANGED) MOSAIC

´ Repeated pattern to fill the plane.

´ Periodic along two linearly independent

direction.-Vectors t1 and t2 along which may be translated

without change.

´ Can be classified by symmetry groups.

´ Any rotation must have one of the following

angles; , , , (60°,90°,120°,180°)



THE POINT O AND TWO OF ITS

IMAGES A,B



INVARI ANT MOSAIC



APERIODIC TILING

´ Tiling plane with Penrose Tiles( PenroseRhombs).

´ no translational symmetry involves to tile the

plane. (arrange manually)



APERIODIC PENROSE TILING



ARCHIMEDE AN TILING

´ regular polygons.

´ each vertex is on the same type.

´ Both vertices must be coincident with similarpolygons and must appear in the same order.

´ 11 families in Archimedean tiling.



ARCHIMEDE AN TILING



ARCHIMEDE AN TILING



ARCHIMEDE AN TILING



INVESTIGATE THE BASES FOR CONTEMPOR ARY MATHEMATICS.

DISCUSS IN PARTICULAR BASE 2



THE USAGE OF OTHER BASES IN RE AL

LIFE :´

Quinary (base-5

) ² language including Gumati,Nunggubuyu, Kuurn Kopan Noot andSaraveca.

1 - wanggany

2-marrma3 - lurrkun

4 - dambumiriw

5 - wanggany rulu

10 - marrma rulu15 - lurrkun rulu

20 - dambumiriw rulu



Octal ( base 8 )

´

By Native AmericansThe Yuki language in California and the

Pamean languages in Mexico have octal

systems because the speakers count using

the spaces between their fingers rather than

the fingers themselves.



Base 10

´ Decimal notation often refers to the base-10

positional notation such as the Hindu-Arabic

numeral system, however it can also be used

more generally to refer to non-positional

systems such as Roman or Chinese numerals

which are also based on powers of ten.



BINARY ?

´ In mathematics and computer science, thebinary (base-two) numeral system is arepresentation for numbers that uses onlyzeroes and ones as digits.

´ Every communication that takes place insideyour computer uses this binary system becauseThe computer's CPU need only recognise twostates, on or off .

´ Usually arithmetic with base-two is easier thanbase-ten but the numbers are longer, making then harder to read.



´ 2 to the power of 0 = 1 (2^0)

2 to the power of 1 = 2 (2^1)

2 to the power of 2 = 4 (2^2) or (2*2)

2 to the power of 3 = 8 (2^3) or (2*2*2)

2 to the power of 4 = 16 (2^4) or (etc.)

2 to the power of 5 = 32 (2^5)2 to the power of 6 = 64 (2^6)

2 to the power of 7 = 128 (2^7)

2 to the power of 8 = 256 (2^8)

«

2 to the power of x = (2^x)



0 1 0 0 1 0 1 0 ?



´Thank you !

Documents

Math in Robotic Motion (2)