Topological Navigation in Configuration Space Applied to Soccer Robots Gonçalo Neto ISLab Presentation Hugo Costelha February 2003

2Gonçalo Neto and Hugo Costelha, 2003 Summary M OTIVATION Topological Map Topological Navigation Experimental Results Conclusions and Future Work

3Gonçalo Neto and Hugo Costelha, 2003 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.

4Gonçalo Neto and Hugo Costelha, 2003 Summary Motivation T OPOLOGICAL M AP Topological Navigation Experimental Results Conclusions and Future Work

5Gonçalo Neto and Hugo Costelha, 2003 Training Postures

6Gonçalo Neto and Hugo Costelha, 2003 Principal Components Analysis Extraction of  eigenimages  eigenvectors of the training images covariance matrix: R = X X T Use only the most significant components – higher eigenvalues.

7Gonçalo Neto and Hugo Costelha, 2003 Reconstruction Square Error Training Set Test Set

8Gonçalo Neto and Hugo Costelha, 2003 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).

9Gonçalo Neto and Hugo Costelha, 2003 Topological 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. 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.

10Gonçalo Neto and Hugo Costelha, 2003 Summary Motivation Topological Map T OPOLOGICAL N AVIGATION Experimental Results Conclusions and Future Work

11Gonçalo Neto and Hugo Costelha, 2003 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.

12Gonçalo Neto and Hugo Costelha, 2003 Localization: Simulated Images X and  variable Y = 1.1 (m)

13Gonçalo Neto and Hugo Costelha, 2003 Localization: Real Images X, Y and  variable

14Gonçalo Neto and Hugo Costelha, 2003 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.

15Gonçalo Neto and Hugo Costelha, 2003 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.

16Gonçalo Neto and Hugo Costelha, 2003 Summary Motivation Topological Map Topological Navigation E XPERIMENTAL R ESULTS Conclusions and Future Work

17Gonçalo Neto and Hugo Costelha, 2003 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.

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20Gonçalo Neto and Hugo Costelha, 2003 Summary Motivation Topological Map Topological navigation Experimental Results C ONCLUSIONS AND F UTURE W ORK

21Gonçalo Neto and Hugo Costelha, 2003 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.

22Gonçalo Neto and Hugo Costelha, 2003 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.

23Gonçalo Neto and Hugo Costelha, 2003 Thanks for your attention!!! Gonçalo Neto Hugo Costelha

24Gonçalo Neto and Hugo Costelha, 2003

25Gonçalo Neto and Hugo Costelha, 2003 Appendix

26Gonçalo Neto and Hugo Costelha, 2003 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.

27Gonçalo Neto and Hugo Costelha, 2003 Images: Real vs Simulated Simulated imageReal Image

28Gonçalo Neto and Hugo Costelha, 2003 ___________

29Gonçalo Neto and Hugo Costelha, 2003 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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31Gonçalo Neto and Hugo Costelha, 2003 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.

32Gonçalo Neto and Hugo Costelha, 2003 Nodes images association

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34Gonçalo Neto and Hugo Costelha, 2003 Computational Cost Reduction R decomposition too costly! However… The R = XX T non-zero eigenvalues are the same of A = X T X. The eigenvectors of R might be obtained from the A’s ones and from the training images (centred on the origin). v R = (  A ) -½ X v A 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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36Gonçalo Neto and Hugo Costelha, 2003 Parameterization Comparison KMetricMean Classification Time (s) 1Euclidian Weighed Euclidian Weighed Euclidian Weighed0.183

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38Gonçalo Neto and Hugo Costelha, 2003 Failure Percentage