1. Mapping and Pursuit-Evasion Strategies For a Simple Wall-Following Robot Anna Yershova Duke University Algorithms Seminar April 20, 2010

2. The Main Theme: Planning in Information Spaces  Think about the devices we build that intermingle sensors, actuators, and computers.  They are completely blind to the world until we equip them with sensors.  All of their accomplishments rest on their ability to sift through sensor data and make appropriate decisions.

3. References IROS 2009 TUTORIAL The 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems Filtering and Planning in Information Spaces Date: 11 October 2009, Time: 8:45-5:30 The 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems By: Steve LaValle, University of Illinois Steve LaValle

4. References Mapping and Pursuit-Evasion Strategies For a Simple Wall-Following Robot Mapping and Pursuit-Evasion Strategies For a Simple Wall-Following Robot Anna Yershova, Benjamin Tovar, Max Katsev, Robert Ghrist, and Steven M. LaValle IEEE Transactions on Robotics, 2010, under review Bitbots: Simple Robots Solving Complex Tasks Bitbots: Simple Robots Solving Complex Tasks Anna Yershova, Benjamin Tovar, Robert Ghrist, and Steven M. LaValle, In Proc. The Twentieth National Conference on Artificial Intelligence (AAAI 2005) J. Barraquand and P. Ferbach. Motion planning with uncertainty: The information space approach. In Proceedings IEEE International Conference on Robotics & Automation, pages 1341–1348, 1995. A. Blum, P. Raghavan, and B. Schieber. Navigating in unfamiliar geometric terrains. In Proceedings ACM Symposium on Computational Geometry, pages 494–504, 1991. M. Blum and D. Kozen. On the power of the compass (or, why mazes are easier to search than graphs). In Proceedings Annual Symposium on Foundations of Computer Science, pages 132–142, 1978. B. R. Donald. On information invariants in robotics. Artificial Intelligence Journal, 72:217–304, 1995. M. A. Erdmann. On motion planning with uncertainty. Master’s thesis, Massachusetts Institute of Technology, Cambridge, MA, August 1984. S. L. Laubach and J. W. Burdick. An autonomous sensor-based pathplanning for planetary microrovers. In Proceedings IEEE International Conference on Robotics & Automation, 1999. S. Suri, E. Vicari, and P. Widmayer. Simple robots with minimal sensing: From local visibility to global geometry. International Journal of Robotics Research, 27(9):1055–1067, September 2008. S. Thrun, W. Burgard, and D. Fox. Probabilistic Robotics. MIT Press, Cambridge, MA, 2005.

5. Scenarios with Sensors Needed

7. Where are Sensors?

8. Classical vs. Sensor-Centric Computation

9. Definition of a Virtual Sensor

11. Simple Example Imagine trying to infer the location of a point on a planar graph while observing only a single coordinate. This simple example involves a point moving along a graph that has four edges.

12. Preimages

13. The Partition Induces by h

14. A Lattice of Partitions

15. The Sensor Lattice

16. The Main Theme: Planning in Information Spaces  It is tempting (and common) to introduce the most complete and accurate sensors possible to eliminate uncertainties and learn a detailed, complex model of the surrounding world.  In contrast, our theme is to start with sensing first and then understand what information is minimally needed to solve specific tasks.  If we can accomplish our mission without knowing certain details about the world, then the overall system may be more simple and robust.

17. Solving Complex Tasks with a Simple Wall-Following Robot  What kinds of global information can be learned and what kinds of tasks can be accomplished with as little sensing and actuation as possible.  Imagine designing motion strategies for a simple, low-cost, differential-drive robot.

18. The Robot Model Actions Sensor reading s

19. The Robot Implementation ($15 USD) Movies: http://www.cs.illinois.edu/homes/katsev1 /videos/

20. State, Action, and Observation Spaces  The state space:  Additional pebble sensor and actions {DROP, GRAB}:

21. Information Spaces  Although we assume that the state space is known, the particular state will be, in general, unknown to the robot.  We need to be precise about what information the robot has available.  Such information is called information space  History I-space:

22. More Information Spaces the total number of edges traversed by the robot. the distance traveled after eliminating all reversals. let a i = 1 if u i = LFOLLOW, a i = −1 if u i = RFOLLOW, and a i = 0 otherwise. let w i = 1 if the pebble is detected, and w i = 0 otherwise. the number of times the pebble has been contacted.

23. Simple Task: Determining the Winding Number

24. Simple Task: Counting Polygon Vertices

25. More Complex Task: Learning the Environment Structure The Cut Ordering:

26. Information Stored in Cut Ordering: The Cut Diagram

28. Learning the Environment Structure: The Cut Ordering

29.  The robot can learn the cut ordering associated with E using O(n 2 ) actions and O(n) space, in which n is the number of vertices in ∂E.  Without sensing a pebble, the robot cannot construct the cut ordering.  Once the cut ordering has been learned, no additional combinatorial information regarding the cut arrangement of E can be obtained.

30. More Complex Task: Pursuit-Evasion!  Detect all unpredictably moving targets in the polygonal environment.

31. State, Action, and Observation Spaces  The state space:  Additional detection sensor

32. Combinatorial Changes in Visibility Information

33. Cut Diagram Contains the Visibility Information

35. Conservative Approximation of Bitangents  let B(i, j) indicate whether there is a bitangent between v i and v j.  The proposition establishes a necessary (but not sufficient) condition for B(i, j) :  For any pair, v i, v j, (reflex vertices) let C(i, j) be a predicate indicating that they satisfy Proposition 11. If C(i, j), then v i and v j are called a bitangent candidate.

36. Conservative Approximation of Bitangents

37. Pursuit-Evasion Strategy  Any systematic search over the visibility polygon components using the bitangent approximations

38. Simulation Results  Movies: http://www.cs.duke.edu/~yershova/movies/t5.mpg http://www.cs.duke.edu/~yershova/movies/taz.mpg

39. Conclusions and Future Directions  Virtual sensors: The interface from physical sensor to filters  h : X → Y slices X into equivalence classes  All basic sensors embed into the sensor lattice  All planning problems live in an I-space  Design virtual sensors, filters, planning problems together around a task.  Particular examples are demonstrated on a simple wall-following robot, and strategies are developed for solving complex tasks  Localization and mapping  Pursuit-evasion

40. Conclusions and Future Directions Relationship to Theory of Computation:

41. Conclusions and Future Directions Relationship to Computational Geometry:

42. Foundation of Robotics: Where is our Theory?