Modelling the world Knowledge, Mission Data Base Commands - - PowerPoint PPT Presentation

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Modelling the world

Raw data Environment Model Local Map "Position" Global Map Actuator Commands Sensing Acting Information Extraction Path Execution Cognition Path Planning Knowledge, Data Base Mission Commands Path Real World Environment Localization Map Building

Motion Control Perception

• 1. R. Siegwart, I. Nourbakhsh, "Introduction to Autonomous Mobile Robots", The MIT Press,2004

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World models

• Represent the environment. The models

have to be:

• Compact to be used efficiently
• Adapted to the task and the enviromment
• Usable in case of sensor and position

uncertainty

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Representation of the Environment

– Continuos Metric → x,y,θ – Discrete Metric → metric grid – Discrete Topological → topological grid

5.5

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Environment modelling

• Raw sensor data, e.g. laser range data, grayscale images

– large volume of data, low distinctiveness on the level of individual values – makes use of all acquired information

• Low level features, e.g. line other geometric features

– medium volume of data, average distinctiveness – filters out the useful information, still ambiguities

• High level features, e.g. doors, a car, the Eiffel tower

– low volume of data, high distinctiveness – filters out the useful information, few/no ambiguities, not enough information

5.5

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Representation of the Environment

• Environment Representation

– Continuos Metric → x,y,θ – Discrete Metric → metric grid – Discrete Topological → topological grid 5.5

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Topological maps

~ 400 m ~ 1 km ~ 200 m ~ 50 m ~ 10 m

• 1. R. Siegwart, I. Nourbakhsh, "Introduction to Autonomous Mobile Robots", The MIT Press,2004

www.biorobotics.ttu.ee

Topological decomposition

• 1. R. Siegwart, I. Nourbakhsh, "Introduction to Autonomous Mobile Robots", The MIT Press,2004

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Topological decomposition

• 1. R. Siegwart, I. Nourbakhsh, "Introduction to Autonomous Mobile Robots", The MIT Press,2004

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Exact cell decomposition

• 1. R. Siegwart, I. Nourbakhsh, "Introduction to Autonomous Mobile Robots", The MIT Press,2004

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Voronoi diagrams

• Sets of points which

are equidistant from

• bject boundaries
• Following the lines

keeps the robot possibly far from

• bject boundaries

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Voronoi diagrams

• http://www.cs.columbia.edu/~pblaer/project

s/path_planner/

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Grid maps

• 1. R. Siegwart, I. Nourbakhsh, "Introduction to Autonomous Mobile Robots", The MIT Press,2004

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Adaptive grid maps

• 1. R. Siegwart, I. Nourbakhsh, "Introduction to Autonomous Mobile Robots", The MIT Press,2004

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Quatrees

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Hybrid maps

Pär Buschka and Alessandro Saffiotti, “Some Notes on the Use of Hybrid Maps for Mobile Robots”, Proc. of the 8th Int. Conf. on Intelligent Autonomous Systems. Amsterdam, The Netherlands, March 2004

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Elevation maps

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Why are maps innacurate?

• Odometry errors. Not knowing the exact

position makes map updating inacurate

• Sensor noise
• Sensor data interpretation

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Odometry error propagation

• Growth of Pose

uncertainty for Straight Line Movement

• Errors perpendicular

to the direction of movement are growing much faster

• 1. R. Siegwart, I. Nourbakhsh, "Introduction to Autonomous Mobile Robots", The MIT Press,2004

www.biorobotics.ttu.ee

Odometry error propagation

• Growth of Pose

uncertainty for Movement on a Circle

• Errors ellipse in does

not remain perpendicular to the direction of movement

• 1. R. Siegwart, I. Nourbakhsh, "Introduction to Autonomous Mobile Robots", The MIT Press,2004

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Representing sensor uncertainty

• Occupancy grid maps
• Assume that the pose of the robot is known
• Assume that the map is static
• Generating maps from noisy and uncertain

sensor measurement data

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Occupancy grid maps

• Grid-based maps
• Each grid cell is assigned a probability that

this grid is occupied

• Can combine different sensor readings (e.g.

sonar, laser rangefinder, stereo vision)

• The probabilities of the cells are

independent from each other

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Occupancy grid maps

Obstacle could be anywhere on the arc at distance D

• The space closer

than D is likely to be free.

• A Useful Heuristic

The shortest sonar returns are reliable. – They are likely to be perpendicular reflections.

http://www.cs.utexas.edu/~kuipers/

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Occupancy grid maps

• Use Bayes rules to update occupancy values

http://www.cs.utexas.edu/~kuipers/

) ( log ) | ( log ) | ( log A

• A

B B A

• +

= λ

)) , ( ( log ) , ( | ( log ) | ) , ( ( log j i

• cc
• j

i

• cc

D r D r j i

• cc
• +

= = = λ

sensor model Conditional probability that the cell i,j is occupied, given the sensor reading

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Occupancy grid maps

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Home assignment

• Drive around in the virtual Center of

Biorobotics, passing through all rooms.

• Use the map generating utility to create an
• ccupancy grid map.