1. Motion Planning for Finding Evasive Targets in a Cluttered Environment + Map Building

2. Example robot cleared region robot’s visibility region hiding region 21 3 4 5 6

3. Problem A target is hiding in an environment cluttered with obstacles
A robot or multiple robots with vision sensor must find the target
Compute a motion strategy with minimal number of robot(s)

4. Assumptions Target is unpredictable and can move arbitrarily fast
Environment is polygonal
Both the target and robots are modeled as points
A robot finds the target when the straight line joining them intersects no obstacles (omni-directional vision)

5. Animated Target-Finding Strategy

6. Does a solution always exist for a single robot?
Easy to test: “Hole” in the workspace
No !
Hard to test:
No “hole” in the workspace

7. Effect of Geometry on the Number of Robots
Two robots
are needed

8. Effect of Number n of Edges
Minimal number of robots N = Q(log n)

9. Effect of Number h of Holes

10. Information State Example of an information state = (x,y,a=1,b=1,c=0)
a = 0 or 1
c = 0 or 1
b = 0 or 1
0  cleared region
1  contaminated region
visibility region
free edge
obstacle edge
Example of an information state = (x,y,a=1,b=1,c=0)
An initial state is of the form (x,y,a=1,b=1,...,u=1)
A goal state is any state of the form (x,y,a=0,b=0,..., u=0)

11. Critical Line (x,y,a=0,b=1) (x,y,a=0,b=1) (x,y,a=0,b=0) a=0 b=1 a=0
contaminated area
a=0
b=1
(x,y,a=0,b=1)
a=0
b=0
(x,y,a=0,b=0)
cleared area
Information state is unchanged
(x,y,a=0,b=1)
a=0
b=1
Critical line

12. Grid-Based Discretization
Ignores critical lines  Visits many “equivalent” states
Many information states per grid point
Potentially very inefficient

13. Discretization into Conservative Cells
In each conservative cell, the “topology” of the visibility region remains constant, i.e., the robot keeps seeing the same obstacle edges

14. Discretization into Conservative Cells
In each conservative cell, the “topology” of the visibility region remains constant, i.e., the robot keeps seeing the same obstacle edges

15. Discretization into Conservative Cells
In each conservative cell, the “topology” of the visibility region remains constant, i.e., the robot keeps seeing the same obstacle edges

17. Search Graph {Nodes} = {Conservative Cells} X {Information States}
Node (c,i) is connected to (c’,i’) iff:
Cells c and c’ share an edge (i.e., are adjacent)
Moving from c, with state i, into c’ yields state i’
Initial node (c,i) is such that:
c is the cell where the robot is initially located
i = (1, 1, …, 1)
Goal node is any node where the information state is (0, 0, …, 0)
Size is exponential in the number of edges

18. Example
(C,a=1,b=1) A B C D E
(D,a=1)
(B,b=1) a b

19. Example
(C,a=1,b=1) A B C D E
(D,a=1)
(B,b=1)
(E,a=1)
(C,a=1,b=0)

20. Example A B C D E (C,a=1,b=1) (D,a=1) (B,b=1) (E,a=1) (C,a=1,b=0)

21. Example A C D E B (C,a=1,b=1) (D,a=1) (B,b=1) (E,a=1) (C,a=1,b=0)
Much smaller search tree than
with grid-based discretization !

22. Example of Target-Finding Strategy
Visible
Cleared
Contaminated

23. More Complex Example 2 1 3

24. Example with Recontaminations3 1 2 6 4 5

25. Example with Linear Number of Recontaminations
Recontaminated area 1 2 3 4

26. Example with Two Robots
(Greedy algorithm)

27. Example with Two Robots

28. Example with Three Robots

29. Robot with Cone of Vision

30. Other Topics
Dimensioned targets and robots, three-dimensional environments
Non-guaranteed strategies
Concurrent model construction and target finding
Planning the escape strategy of the target

31. Map Building
Laser range finder

32. Sensing

33. Alignment of Contours

34. Merging of Four Partial Models

35. Dealing with Uncertainty
Simultaneous Localization and Mapping (SLAM)
Next-Best View (NBV) Planning

36. Next-Best View Planning

37. NBV Example 1

38. NBV Example 2

39. Map Building with NBV

40. 3D Mapping