Nick Hawes

Robot Programming

Lecture 16: A Sensitive Soul

sensor modelthe probability of sensing

returning a particular value given what the sensor is pointed at

action modelthe probability of ending up in a

given cell given the robot’s previous position and action

Markov Localisation

sensor modelthe probability of sensing a

colour given what the sensor is pointed at

P(pink | “actually pink”) = 1 P(pink | “actually yellow”) = 0

P(yellow | “actually pink”) = 0 P(yellow | “actually yellow”) = 1

a perfect sensor

a perfect sensorthe distance the sensor reports is always the correct distance between the robot and the wall

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0

c1 c2 c3 c4

a perfect sensorthe distance the sensor reports is always the correct distance between the robot and the wall

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1

00.25 0.25 0.25 0.25

c1 c2 c3 c4

probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...

0 1 2 3 4 5 6

sensor

reading

0sensor

reading

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sensor

reading

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sensor

reading

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sensor

reading

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sensor

reading

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sensor

reading 6

1 0 0 0 0 0 0

0 1 0 0 0 0 0

0 0 1 0 0 0 0

0 0 0 1 0 0 0

0 0 0 0 1 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

sens

or.g

etRa

nge(

)

6

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2

1

00.25 0.25 0.25 0.25

c1 c2 c3 c4

sensor.getRange() == 3

P(c1 | 3) = α P(3 | c1) P(c1)

what’s the probability of getting a reading of 3 from cell c1

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5

4

3

2

1

00.25 0.25 0.25 0.25

c1 c2 c3 c4

sensor.getRange() == 3

P(c1 | 3) = α P(3 | c1) P(c1)

what’s the probability of getting a reading of 3 from cell c1

our map says that the robot should

measure 1 from c1

1

what’s the probability of the distance really

being 1 when the sensor returns 3?

our map says that the robot should

measure 1 from c1

6

5

4

3

2

1

00.25 0.25 0.25 0.25

c1 c2 c3 c4

sensor.getRange() == 3

P(c1 | 3) = α P(3 | c1) P(c1)

1

what’s the probability of the distance really

being 1 when the sensor returns 3?

3

0 1 2 3 4 5 6

0 0 0 1 0 0 0

P(c1 | 3) = α 0 * 0.25

6

5

4

3

2

1

00.25 0.25 0.25 0.25

c1 c2 c3 c4

sensor.getRange() == 3

our map says that the robot should

measure 1 from c1

1

3

0 1 2 3 4 5 6

0 0 0 1 0 0 0

what’s the probability of the distance really

being 1 when the sensor returns 3?

6

5

4

3

2

1

00.25 0.25 0.25 0.25

c1 c2 c3 c4

sensor.getRange() == 3

our map says that the robot should

measure 1 from c1

1

P(c1 | 3) = α 0 * 0.25 P(c2 | 3) = α 1 * 0.25 P(c3 | 3) = α 0 * 0.25 P(c4 | 3) = α 1 * 0.25

6

5

4

3

2

1

00.25 0.25 0.25 0.25

c1 c2 c3 c4

sensor.getRange() == 3

our map says that the robot should

measure 1 from c1

1

P(c1 | 3) = α 0 * 0.25 = α 0 P(c2 | 3) = α 1 * 0.25 = α 0.25 P(c3 | 3) = α 0 * 0.25 = α 0 P(c4 | 3) = α 1 * 0.25 = α 0.25

6

5

4

3

2

1

00.25 0.25 0.25 0.25

c1 c2 c3 c4

sensor.getRange() == 3

our map says that the robot should

measure 1 from c1

1

P(c1 | 3) = α 0 * 0.25 = α 0 = 0 P(c2 | 3) = α 1 * 0.25 = α 0.25 = 0.5 P(c3 | 3) = α 0 * 0.25 = α 0 = 0 P(c4 | 3) = α 1 * 0.25 = α 0.25 = 0.5

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00 0.5 0 0.5c1 c2 c3 c4

P(c1 | 3) = α 0 * 0.25 = α 0 = 0 P(c2 | 3) = α 1 * 0.25 = α 0.25 = 0.5 P(c3 | 3) = α 0 * 0.25 = α 0 = 0 P(c4 | 3) = α 1 * 0.25 = α 0.25 = 0.5

probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...

0 1 2 3 4 5 6

sensor

reading

0sensor

reading

1

sensor

reading

2

sensor

reading

3

sensor

reading

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sensor

reading

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sensor

reading 6

1 0 0 0 0 0 0

0 1 0 0 0 0 0

0 0 1 0 0 0 0

0 0 0 1 0 0 0

0 0 0 0 1 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

sens

or.g

etRa

nge(

)

probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...

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sensor

reading

0sensor

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sensor

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0.7 0.2 0.1 0 0 0 0

0.1 0.7 0.1 0.1 0 0 0

0.05 0.1 0.7 0.1 0.05 0 0

0 0.05 0.1 0.7 0.1 0.05 0

0 0 0.05 0.1 0.7 0.1 0.05

0 0 0 0.1 0.1 0.7 0.1

0 0 0 0 0.1 0.2 0.7

sens

or.g

etRa

nge(

)

6

5

4

3

2

1

00.25 0.25 0.25 0.25

c1 c2 c3 c4

sensor.getRange() == 3

P(c1 | 3) = α P(3 | c1) P(c1)

what’s the probability of getting a reading of 3 from cell c1

our map says that the robot should

measure 1 from c1

1

what’s the probability of the distance really

being 1 when the sensor returns 3?

6

5

4

3

2

1

00.25 0.25 0.25 0.25

c1 c2 c3 c4

sensor.getRange() == 3

P(c1 | 3) = α P(3 | c1) P(c1)

our map says that the robot should

measure 1 from c1

1

3

0 1 2 3 4 5 6

0 0.05 0.1 0.7 0.1 0.05 0

what’s the probability of the distance really

being 1 when the sensor returns 3?

6

5

4

3

2

1

00.25 0.25 0.25 0.25

c1 c2 c3 c4

sensor.getRange() == 3

our map says that the robot should

measure 1 from c1

1

3

0 1 2 3 4 5 6

0 0.05 0.1 0.7 0.1 0.05 0

P(c1 | 3) = α 0.05 * 0.25 what’s the probability of the distance really

being 1 when the sensor returns 3?

6

5

4

3

2

1

00.25 0.25 0.25 0.25

c1 c2 c3 c4

sensor.getRange() == 3

our map says that the robot should

measure 1 from c1

1

P(c1 | 3) = α 0.05 * 0.25P(c2 | 3) = α 0.70 * 0.25P(c3 | 3) = α 0.05 * 0.25P(c4 | 3) = α 0.70 * 0.25

6

5

4

3

2

1

00.25 0.25 0.25 0.25

c1 c2 c3 c4

sensor.getRange() == 3

our map says that the robot should

measure 1 from c1

1

P(c1 | 3) = α 0.05 * 0.25 = α 0.0125P(c2 | 3) = α 0.70 * 0.25 = α 0.175P(c3 | 3) = α 0.05 * 0.25 = α 0.0125P(c4 | 3) = α 0.70 * 0.25 = α 0.175

6

5

4

3

2

1

00.25 0.25 0.25 0.25

c1 c2 c3 c4

sensor.getRange() == 3

our map says that the robot should

measure 1 from c1

1

P(c1 | 3) = α 0.05 * 0.25 = α 0.0125 = 0.033P(c2 | 3) = α 0.70 * 0.25 = α 0.1750 = 0.467P(c3 | 3) = α 0.05 * 0.25 = α 0.0125 = 0.033P(c4 | 3) = α 0.70 * 0.25 = α 0.1750 = 0.467

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00.033 0.467 0.033 0.467

c1 c2 c3 c4

sensor.getRange() == 3

P(c1 | 3) = α 0.05 * 0.25 = α 0.0125 = 0.033P(c2 | 3) = α 0.70 * 0.25 = α 0.1750 = 0.467P(c3 | 3) = α 0.05 * 0.25 = α 0.0125 = 0.033P(c4 | 3) = α 0.70 * 0.25 = α 0.1750 = 0.467

sensor modelthe probability of sensing

returning a particular value given what the sensor is pointed at

action modelthe probability of ending up in a

given cell given the robot’s previous position and action

Markov Localisation

probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...

0 1 2 3 4 5 6

sensor

reading

0sensor

reading

1

sensor

reading

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sensor

reading

3

sensor

reading

4

sensor

reading

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sensor

reading 6

0.7 0.2 0.1 0 0 0 0

0.1 0.7 0.1 0.1 0 0 0

0.05 0.1 0.7 0.1 0.05 0 0

0 0.05 0.1 0.7 0.1 0.05 0

0 0 0.05 0.1 0.7 0.1 0.05

0 0 0 0.1 0.1 0.7 0.1

0 0 0 0 0.1 0.2 0.7

sens

or.g

etRa

nge(

)

Ultrasonic Sensor

Measures distance in cm using reflected ultrasound

http://www.cs.bham.ac.uk/internal/courses/robot-prog/nxt/lejos/nxt/UltrasonicSensor.html

Noisy! Range 0cm to 255cm, +/- 3cm

probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...

0 1 2 3 4 5 6

sensor

reading

0sensor

reading

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sensor

reading

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sensor

reading

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sensor

reading

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sensor

reading

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sensor

reading 6

0.7 0.2 0.1 0 0 0 0

0.1 0.7 0.1 0.1 0 0 0

0.05 0.1 0.7 0.1 0.05 0 0

0 0.05 0.1 0.7 0.1 0.05 0

0 0 0.05 0.1 0.7 0.1 0.05

0 0 0 0.1 0.1 0.7 0.1

0 0 0 0 0.1 0.2 0.7

sens

or.g

etRa

nge(

)

probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...probability of the distance to the obstacle really being...

0 1 2 3 4 5 6

sensor

reading

0sensor

reading

1

sensor

reading

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sensor

reading

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sensor

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0.7 0.2 0.1 0 0 0 0

0.1 0.7 0.1 0.1 0 0 0

0.05 0.1 0.7 0.1 0.05 0 0

0 0.05 0.1 0.7 0.1 0.05 0

0 0 0.05 0.1 0.7 0.1 0.05

0 0 0 0.1 0.1 0.7 0.1

0 0 0 0 0.1 0.2 0.7

sens

or.g

etRa

nge(

)

probability of the distance to the obstacle really being...

probability of the distance to the obstacle really being...

probability of the distance to the obstacle really being...

0 - 2 3 - 4 5 - 6

sensor

reading

0sensor

reading

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sensor

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1 0 0

0.9 0.1 0

0.85 0.15 0

0.15 0.8 0.05

0.05 0.8 0.15

0 0.2 0.8

0 0.1 0.9

sens

or.g

etRa

nge(

)

Build your sensor model in real conditions

The best approach would be to let the robot move to a junction then check the

actual and measured distances

You could also just move the robot gradually away from an obstacle