Topological Navigation in Configuration Space Applied to Soccer Robots Gonçalo Neto [email protected] ISLab Presentation Hugo Costelha [email protected]

Topological Navigation in Configuration Space Applied to Soccer Robots

Gonçalo [email protected]

ISLab Presentation

Hugo [email protected]

February 2003

2 Gonçalo Neto and Hugo Costelha, 2003

Summary

MOTIVATION Topological Map Topological Navigation Experimental Results Conclusions and Future Work


Motivation

Metrical Navigation Needs a geometric model of the world. Assumes exact sensor information. Allows a more precise navigation.

Topological Navigation Leads to a qualitative description of the navigation goals. Uses a flexible, easy to define, map. Not suitable for very precise applications.

Ideal Solution Merge both navigation models.

Metrical: local, more precise, navigation. Topological: global, less precise, navigation.


Summary

Motivation

TOPOLOGICAL MAP Topological Navigation Experimental Results Conclusions and Future Work


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6 7

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xy

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Training Postures


Principal Components Analysis

Extraction of eigenimages

eigenvectors of the training images covariance matrix:

R = X XT

Use only the most significant components – higher eigenvalues.

x2

x1


Reconstruction Square Error

Training Set

Test Set

Number of Eigenvalues Usedto construct the Space

Mea

n S

quar

e E

rror

(pe

rcen

tage

)

10

20

30

40

50

60

70

80

90

00 10 20 30

40

50

60

Test SetTraining Set

sEigenValue All

used not sEigenvalueTr

sEigenvalue All

Error Square MeanTe


Topological Map Construction

The map should be useful to the application in question.

Can be represented as a directed graph where: Nodes: correspond to key-places in the map. Transitions: used to travel between key-places.

In robotic soccer, one could have: Nodes: field zones (half-field, penalty areas). Transitions: basic movements (turn left, move forward).


FYG

NYGR

NYGL

NOG3

FBG

NOG4NOG2NOG1

NBGR

NBGL

mfgr

mfgrTopological Map Description

rr: Rotate Right. rl: Rotate Left. mfgr: Move Forward (with) Goal (on

the) Right. mfgl: Move Forward (with) Goal (on

the) Left. mb: Move Backward.

FYG

NYGR

NYGL

rr rl

mfgr

NOG3

FBG

NOG4NOG2NOG1

NBGR

NBGLmfgl

mfgr

rl rr

rlrr

rlrr

rl

rl

rr

rr

rl rr

rr rl rl rr

rrrl

mb

mb

mb

mfgl

mb

mb

mb

mfgr

mfgl

mfgr

mfgl

NBGL: Near Blue Goal (with goal on the) Left.

NBGR: Near Blue Goal (with goal on the) Right.

FBG: Far Blue Goal. NYGL: Near Yellow Goal (with goal on

the) Left. NYGR: Near Yellow Goal (with goal on

the) Right. FYG: Far Yellow Goal. NOG: NO Goal.


Summary

Motivation Topological Map

TOPOLOGICAL NAVIGATION Experimental Results Conclusions and Future Work


Map Localization

Essential step for navigation (topological or metrical).

In the topological case, it’s equivalent to identify in which node (of the graph) the robot is.

Might be expressed as a classification problem. Projection of the image to be classified in the eigenspace. Comparison with the training images projection. Make use of k-nearest neighbour method to localize the robot

in a node/class. Several metrics can be used.


Localization: Simulated Images

X and variable

Y = 1.1 (m)

0

180

360

-5 0 5

x

NBGLNBGRFBGNYGLNYGRFYGNOG

x

y


Localization: Real Images

X, Y and variable

NBGLNBGRFBGNYGLNYGRFYGNOG

x

y-4 4-1-3 31-2 20

1

-1

-2

2

0


Path Generation

Use of search algorithms, applied to the graph. Large Graphs:

Define an heuristic. use A*.

Small Graphs (present case): simple search, so it’s not worthy to use an heuristic. reduce A* to uniform cost search or breadth-first search.


Path Following

Ideally, it corresponds to the sequential execution of the transitions defining the generated path.

Nevertheless…

Dynamic environment subject to sudden changes. Some transitions show more than 50% failures.

A failure detection and new path generation mechanism is needed.


Summary

Motivation Topological Map Topological Navigation

EXPERIMENTAL RESULTS Conclusions and Future Work


Experimental Results

Video 1 The border regions are in

the midfield zone.

Video 2 The border regions are

between the midfield area and the penalty area.




Summary

Motivation Topological Map Topological navigation Experimental Results

CONCLUSIONS AND FUTURE WORK


Conclusions

Presents promising results concerning navigation between key-places.

Allows a easy/quick learning of the world’s relevant characteristics, thus adapting itself easily to different environments.

Flexible to different topological maps. Makes possible to specify the goals using

qualitative languages. Assumes the use of a failure control mechanism.


Future Work

RoboCup Challenge 4 – Play with an arbitrary FIFA ball

A ball is presented to the robot for 60 seconds. The robot should search for the ball and score. Three different balls are used .

Solution: Principal Component Analysis to store a priori information

regarding the ball. Topological Navigation to drive the robot to the ball. Use implemented behaviours in the actual SocRob project to

lead the ball to the opponent’s goal.


Thanks for your attention!!!

Gonçalo [email protected]

Hugo [email protected]

http://b52.ist.utl.pt/costelha/socrob/index.htm



Appendix


Camera Simulator

Allows: Speedup of the development process. More flexible development, robot independent. Obtain results faster.

Implemented in VRML (Virtual Reality Modelling Language). Platform independent (Linux vs Windows©). Interaction with Matlab© and JAVA™. Makes possible the use various environment

conditions and textures.


Images: Real vs Simulated

Simulated image Real Image


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Discretization Model

Discretization Type: Uniform:

More flexible. No need of a priori knowledge. Allows the definition of various topological maps.

Non uniform: More precise. Specific application oriented.

Compromise in the images number: Low: might not correctly represent the field. High: might become too computationally costly.

Present case: Uniform Discretization. Discretization intervals: x=1m ; y=1m ; =45º


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Nodes images association

Based upon geometric characteristics, defined by the modes.

Use of a discretization grid.

Thus allowing: Changes in the key-place associated with each node (by

changing the images). Definition of various maps, using the same discretization

grid.


Nodes images association

FYG

NYGR

NYGL

rr rl

mfgr

NOG3

FBG

NOG4NOG2NOG1

NBGR

NBGLmfgl

mfgr

rl rr

rlrr

rlrr

rl

rl

rr

rr

rl rr

rr rl rl rr

rrrl

mb

mb

mb

mfgl

mb

mb

mb

mfgr

mfgl

mfgr

mfgl


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Computational Cost Reduction

R decomposition too costly! However… The R = XXT non-zero eigenvalues are the same of A = XTX. The eigenvectors of R might be obtained from the A’s ones

and from the training images (centred on the origin).

vR = (A)-½ X vA

It is still necessary to store all the training images. But… Only the most significant R’s eigenvectors. One can use an iterative procedure to compute them.


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Parameterization Comparison

K Metric Mean Classification Time (s)

1 Euclidian 0.129

1 Weighed 0.153

5 Euclidian 0.141

5 Weighed 0.169

10 Euclidian 0.160

10 Weighed 0.183


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Failure Percentage

Documents

Topological Navigation in Configuration Space Applied to Soccer Robots Gonçalo Neto [email protected] ISLab Presentation Hugo Costelha [email protected]