1. Simple set-membership methods and control algorithms applied to robots for exploration Fabrice LE BARS

2. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 2 Outline  Introduction  A simple localization example  Interval analysis  Other localization scenarios  Line following  Additional common problems and possible methods  Conclusion

3. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 3 Introduction

4. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 4 Robotics at ENSTA Bretagne  Main research areas : Autonomous marine and submarine robotics using interval methods Swarm of robots

5. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 5  Facts Autonomous robotics rise new and difficult problems There are few demonstrations of cheap autonomous robots able to do survey, cartography, localization tasks, especially in marine and submarine environments Current methods : mainly probabilistics Robotics at ENSTA Bretagne

6. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 6  Goals Develop observation, control methods for submarine, marine, ground and aerial robotics Demonstrate the use of interval methods through new applications in autonomous robotics Build real and convincing demonstrators Copyright Ifremer Robotics at ENSTA Bretagne

7. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 7 A simple localization example

8. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 8 A simple localization example  Context : An underwater robot must follow a wall (not necessarily straight) The environment (walls to follow) is known The robot has a good compass and a sonar

9. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 9 A simple localization example  Assumptions : The wall to follow is on the right of the robot We can approximate it as a line y=ax+b

10. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 10 A simple localization example  Assumptions : The wall to follow is on the right of the robot We can approximate it as a line y=ax+b

11. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 11 A simple localization example  Assumptions : The wall to follow is on the right of the robot We can approximate it as a line y=ax+b

12. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 12 A simple localization example  Assumptions : The wall to follow is on the right of the robot We can approximate it as a line y=ax+b

13. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 13 A simple localization example  Assumptions : The wall to follow is on the right of the robot We can approximate it as a line y=ax+b

14. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 14 A simple localization example  The robot needs to find : Its distance to the line Its angle to the line (-> angle of the line)

15. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 15 A simple localization example  Available data : The angle of the robot thanks to the compass Sonar data

16. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 16 A simple localization example  Methods : Linear regression using least squares What if we want to localize in a pool, a lake…?

17. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 17  Uncertainty representations : Probabilistics Gaussians Particles => We try to get a probability density Sets Zonotopes Ellipsoids Intervals => We try to enclose all possible solutions A simple localization example

18. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 18 Interval analysis

19. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 19 ,, are examples of intervals  Operations smallest interval containing the set of possible values for  Multiplication by a number, intersection, union  Image by a function Interval analysis

20. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 20 Interval analysis  Real intervals can be generalized Vectors intervals (boxes) Sets intervals Functions intervals (tubes) Any set with a lattice structure

21. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 21  Contraction If and,,, then Interval analysis

22. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 22  Contraction and propagation We call contractor an operator that reduce the domain of variables A propagation is a repeated call to contractors We can repeat contractions until a fix point Interval analysis

23. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 23  Other techniques such as bisections can also be done Interval analysis

24. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 24  Handling outliers : relaxed intersection (q-intersection) Interval analysis

25. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 25 Other localization scenarios

26. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 26 State Measurements For each k Other localization scenarios  Dynamic localization

27. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 27  EURATHLON 2013 Task "Search and rescue in a smoke-filled underground structure“ Other localization scenarios Controller Robot Observer (implemented as an interval simulator)

28. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 28  Localization of a swarm of robots with acoustic communication Other localization scenarios

29. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 29 Line following

30. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 30  Purpose Cover autonomously an area as accurately as possible Line following

31. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 31  From waypoints following to line following Primitive heading control loop Existing approaches : basic waypoint following The robot follows a heading in direction of its waypoint Waypoint reached when in a predefined radius Problem : nothing prevent the drift between waypoints (because of currents...) => Line following (use the distance to the line) Line following

32. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 32 Line following Primitive heading regulator Robot

33. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 33 Init GetSensorsData NavigationManager Supervisor PrimitiveHeadingController SetActuators Line following

34. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 34  Line following Primitive controller stage for heading control Rudder control Navigation manager sends lines to supervisor and validates lines Validation condition Line following

35. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 35  Line following Desired heading is the line made by the 2 current waypoints with an attractiveness angle to the line depending on the distance to the line Line following

36. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 36 Additional common problems and possible methods

37. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 37 Additional common problems and possible methods  Evaluate the guaranteed covered area depending on localization accuracy  Obstacle avoidance using vector fields

38. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 38 Conclusion

39. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 39 Conclusion Interval methods can be efficient for parameters and state estimation problems Advantages : can give an estimation of the error together with the state, parameters Can also be used when there are outliers Line following can improve easily the accuracy of a trajectory following especially in marine environment Vector fields are interesting for obstacle avoidance or other higher level trajectory planning

40. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 40 Questions?  Contact fabrice.le_bars@ensta-bretagne.fr

41. Simple set-membership methods and control algorithms applied to robots for exploration 12/08/2015- 41