1. Introduction to Topological Navigation prof: S.Shiry Presenter: Masoomeh Bahreini M.Sc Computer Science Department of Computer Eng. and IT Amirkabir Univ. of Technology (Tehran Polytechnic) winter1383

2. Objectives Definition of Navigation Fundemental functions of navigation Type of Navigation Topological Navigation  Vornoi Diagram Metric Navigation Summary Refrence AppendX

3. Definition of Navigation Robot navigation is one of the key issue in mobile robotics It consists in driving a robot throgh a given environment,using the information from sensors

4. Fundemental functions of navigation Primary functions of navigation:  Where am I? Localization:relative or absolute  Where am I going? Usually defied by human operator or mission planner  What’s the best way to get there? Path planning:qualitative & quantitative  Where have I been? Map making

5. Type of Navigation 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.

6. Type of Navigation metric map(quantitive) topologic map(qualitive)

7. Type of Navigation Navigation  Topological vs Metric methods  Metric methosd: Potential fields  Topological methods: Waypoints Visibility graphs Vornoi Diagrams

8. Topological Navigation Steps of topological navigation  Define topological map  Costruct a Global map  Sence Sensors:vision,sonar,laser  Construct Local map  Navigation

9. Topological Navigation Define &Construction global map The map should be useful to the application Amount of abstraction in modeling world 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).

10. Topological Navigation Global Map (world model)  Provided :user,robot(exploration)  User map:unaccurate,not detailed  the robots will have to be able to deal with inaccuracies and lack of details that comes with the maps provided by users.  It does not require accurate metric and geometric information, and details about obstacles inside the environment can be omitted.  map can be given as a bitmap image,

11. An Example of a Sketch Floor Map Scale is unknown Scale is not uniform across the map. Geometrical details are not available. Details exact shapes of the walls, shapes of intersections,… Obstacles are left out of the map. Topological Navigation

12. Vornoi diagram Let P = p1, p2,..., pn be a set of points in the 2 dimensional Euclidean plane. P is called the generators. partition the plane by assigning every point in the plane to its nearest point p.P. All those points assigned to pi form the Voronoi region V (pi), that is,V (pi) = {x : |pi - x| = |pj - x|.j = i}. note that some points do not have a unique nearest neighbor. The set of all points that have more than one nearest neighbor forms the Voronoi diagram V(P) A Voronoi vertex is a point p. V(P) that has more than 2 nearest neighbors and a Voronoi edge is a set of points that forms a boundary between Voronoi regions.

13. Vornoi diagram p1 p2 p3 p1

14. Vornoi diagram Vornoi diagram with 2 points

15. Vornoi diagram Vornoi diagram with 3 points

16. Vornoi diagram Vornoi diagram of floor map

17. Augmented Topological Map a traditional topological map is a graph that represents connectivity between landmarks, without containing any metric or geometrical information. +-intersection is a node connected with 4 arcs that extends approximately perpendicularly to each other. T-intersection is a node that is connected with 3 arcs, with two of them perpendicular to the other. Endpoint is a node that where the Voronoi diagram ends at a wall. Dead-end is a node that has 3 neighbors, and two of them are Endpoints. Corner is a node that has 3 neighbors, and one of them is an Endpoint. Generic node is a node that is not any of the above

18. Topological map

19. 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. current input map projection is compered to the projection of global map Make use of k-nearest neighbour method to localize the robot in a node/class.

20. Map Localization  Method of matching Iconic:  use raw (or near raw) sensor readings Feature-based:  use features extracted from raw data  Label and match corners, walls  Less features, so less computations Metric map-making relies on iconic localization Toplogical map-making relies on Feature-based localization

21. Map Localization Match between nodes Two nodes strictly match if  they have the same number of neighbors  have the same attributes, without considering diference of labels. For example, a Corner node v that has three neighbors v1, v2, v3 with v2 as the Endpoint matches with a Corner node w that has three neighbors w1,w2,w3 with w1 as the Endpoint.

22. Map Localization Two nodes match if they are strictly match or one of them is a generic node and they have the same number of neighbors A generic node match everything that has the same number of neighbors as itself.

23. Map Localization Robot Pose a directed arc ij in a topological map that the robot is moving on robot is somewhere between node i and j, and is heading to node j. Multiple Hypothesis Tracking.(MHT) Partially Observable Markov Process(POMP)  Given the last probality distribution and the current observation and action,calculate the probality of being in a state

24. POMDP It get states, actions, transitions,observations (a set of things that can be perceived by the agent ) An observation function maps each state (or sometimes state/action pair) to a probability distribution over observations there are unobservable state variables it is important to estimate missing information and to acquire better strategies that incorporate the prediction of environmental behaviors.

25. Path Generation Robot is aimed to sweep throgh all the reachable places of the terrain Nodes of the graph considered as goals Use of search algorithms, applied to the graph.  Large Graphs: Define an heuristic. use A*  Find the shortest path from start node to a goal node.  Small Graphs simple search, so it’s not worthy to use an heuristic. reduce A* or breadth-first search.

26. 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.

27. Topological Navigation using Occupancy Grid

28. Each cell of the occupancy grid contains a probality value which is an estimation that the representation position is occupied by some object Occupancy grid can be viewd as a 2-d grayscale image of the environment Digital image processing are valid approaches Skeletization Thinig Vornoi diagram

29. Topological Navigation using Occupancy Grid Steps of map building  Gloabal grid building  Sensor interpretation sonar  Integration over time Different sensors give different values for a grid cell because of noise and changing viewpoint it’s important to integrate the conditional probalities of distinct moments  Pose estimation Local map is match with a global map

30. Topological Navigation Using Landmark

31. Topological Maps Use Landmarks A landmark is one or more perceptually distinctive features of interest on an object or locale of interest Natural landmark: configuration of existing features that wasn’t put in the environment to aid with the robot’s navigation (ex. gas station on the corner) Artificial landmark: set of features added to the environment to support navigation (ex. highway sign) Roboticists avoid artificial landmarks!

32. Desirable Characteristics of Landmarks Recognizable (can see it when you need to)  Passive  Perceivable over the entire range of where the robot might need to view it  Distinctive features should be globally unique, or at least locally unique Perceivable for the task (can extract what you need from it)  ex. can extract relative orientation and depth Be perceivable from many different viewpoints

33. Global Map Construction without a predefiend map

34. Topologial Navigation Information required to represent each node must be gathered a set of images P of the space where the robot will navigate General enouph to represent all the areas of cs

35. Principal Components Analysis Use PCA (KL) to compress the information in P Extraction of  Eigenimages  eigenvectors of the training images covariance matrix: R = X X T Use only the most significant components – higher eigenvalues.

36. Construction Square Error The number of eigenvalue Choose to represent eigenspace These expressions provide a criteria to choose the number of eigenvectores

37. Map construction PCA compute principle images Space after computation :principle space project each image in the principle space, associating the projection with the node of graph

38. Introduction to Metric Navigation

39. Metric Navigation A geometric map represent objects according to their absolute geometric relationships. Localization  A sensor-drived geometric map must be matched against a global map of a large area

40. Metric Localization(iconic)

41. Summary Map-based navigation is limited to laboratory setting with well-structured environment Have not been tested extensively in real-world environment Require a significant amount of processing and sencing Higher level task can be performed by the robot after successful exploration.

42. Summary Localization and map making are intertwined  Localization requires good maps  Map making requires good localization

43. Summary

44. Future work Sensor selection and sensor fusion for specific applications and environments. Accurate and reliable algorithms for matching local maps to the stored map. Good error models of sensors and robot motion. Good algorithms for integrating local maps into a global map. Higher level task can be performed by the robot after successful exploration

45. Refrence Vachirasuk Setalaphruk Atsushi Ueno Izuru Kume Yasuyuki Kono ” Robot Navigation in Corridor Environments using a Sketch Floor Map” Gon¸calo Neto, Hugo Costelha, Pedro Lima “ Topological Navigation in Configuration Space Applied to Soccer Robots Szabo, R. / Topological Navigation of Simulated Robots using Occupancy Grid, pp. 201 - 206, International Journal of Advanced Robotic Systems, Volume 1, Number 3 (2004), ISSN 1729-8806 J. Borenstein, H. R. Everett, and L. Feng Contributing authors: S. W. Lee and R. H. Byrne “Where am I?Sensors and Methods for Mobile Robot Positioning”

46. Thanks for your Attention

47. Appendix

48. An example of vornoi

49. Measurement type in Navigation Relative  Odometry Absolute  Active Beacons  Landmark Recognition Artificial  Distinctive artificial landmarks are placed at known locations in the environment  3 or more landmarks must be ‘in view’ to allow pose estimation  Detection these landmarks are easier for knowing size and shape Natural  Distinctive features in the environment  Vertical edges :doors,wall junction  Environment must be known in advance

50. Measurement type in Navigation  Model Matching Information acquired from sensors is compared to a map or world model of the environment Geometric  Represent the world in a global coordinate system Toplogical  Represent the world as a network of nodes and arcs