4 Odometry Final

8/3/2019 4 Odometry Final

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DOMETRY MOTION MODELMOTION AND MAPS

Nguyn Th L Linh

Nguyn ng KhoaNguyn Thi Ha

Nguyn Vn Tun

on Xun TrngV Th T ThanhTrn Vit Quc

Slide 1


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Odometry Motion Model

Closed-form Calculation

Sampling Algorithm

Maps

Outline

2

Slide 2


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ODOMETRY MOTION MODEL

Odometry is the estimation of distance and direction

from a previous location using wheel encoder

information of robot instead of commanded velocity

(Robots with wheel encoders)

3

higher accuracy than velocity

good for short term, relative position estimation

measurements only available retrospectively

unusable for accurate motion planning and control

Slide 3


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Example Wheel Encoders

These modules require

+5V and GND to powerthem, and provide a 0 to5V output. They provide+5V output when they"see" white, and a 0V

output when they "see"black.

These disks aremanufactured out of highquality laminated colorplastic to offer a very crispblack to white transition.This enables a wheelencoder sensor to easilysee the transitions.

Source: http://www.active-robots.com/ 4

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Closed-form calculation

In the time interval ( t-1, t ] :

Robot moves from to

Odometrymotion information:

yxxt 1 ''' yxxt

5

T

tttxxu

1

T

rottransrottu 21

Transform into

Slide 5


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6

22 )'()'( yyxxtrans

)','(atan21 xxyyrot

12

'rotrot


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Here are the true values of the rotationand translation from the measured ones

with independent noise (with zero

mean) and variance b:

||||11 211

transrotrotrot

||||22 221

transrotrotrot

|||| 2143

rotrottranstranstrans


b

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22 )'()'( yyxxtrans

)','(atan21 xxyyrot

12' rotrot

22 )'()'( yyxxtrans

)','(atan2 1 xxyyrot

12' rotrot

)

|

|,

(prob trans21rot11rot1rot1 p|))||(|,(prob rot2rot14trans3transtrans2 p

)||,(prob trans22rot12rot2rot3 p

odometry values (u)

values of interest (xt-1, xt)

T

t yxx )(1 T

t yxx )(

),( baprob

),( 1ttt xuxp 8

Closed-form calculationAlgorithm

: Tttt xxu 1

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9

Closed-form calculationGraphs :

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)||sample( 21111 transrotrotrot

|))||(|sample( 2143 rotrottranstranstrans

)||sample( 22122 transrotrotrot

)cos(' 1rottransxx

)sin(' 1rottransyy

21' rotrot

Tt yxx ',',' sample_normal_distribution

10

Sampling algorithm

22 )'()'( yyxxtrans

)','(atan21 xxyyrot

12 ' rotrot

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11

Sampling algorithmGraphs :

Slide 11


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Start

Sampling from the motion model

12Slide 12


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13

Maps

If robot has a map of the environment, ....

Such an opportunity gives us more information,

and also makes the model more complex. Model is

represented as p(x(t)|u(t),x(t-1),m) instead of

p(x(t)|u(t),x(t-1))

This model is called as map-based motion model

Most important problem is that there is a

probability of an unoccupied path between x(t)

and x(t-1)

This model can be calculated by:

)',|()|(),',|( xuxpmxpmxuxp 13Slide 13


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14

Maps (Algorithms)

Algorithm motion_model_with_map ( x(t), u(t), x(t-1), m );

return p(x(t)|u(t), x(t-1))*p(x(t)|m)

Algorithm sample_motion_model_with_map ( u(t), x(t-1), m );

do

x(t) = sample_motion_model(u(t), x(t-1))

= p(x(t)|m)

Until >0 Return

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5.4.3


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5.4.3


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MOTION AND MAPS

Slide 16


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MOTION AND MAPS

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y l chun ha thng thng

Thut ton cho m mnh di chuyn da trn bn

Slide 18


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Slide 19


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Nhm 3 v 4

Slide 20

4 Odometry Final

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