1. Agent-Centered Search
Mitja Luštrek
Jožef Stefan Institute
Department of Intelligent Systems

2. Introduction
Setting: mobile agent (robot) in an known/unknown environment (labyrinth with/without map)
Objective: to reach the goal from the starting position in as short time as possible
Two phases:
Planning of the path
Execution of the plan
Traditional search: first planning of the whole path, then execution of the plan
Agent-centered search: planning of the beginning of the path from the starting position, execution of the partial plan, planning from the new starting position...

3. Why Agent-Centered Search
Planning long in comparison to execution:
Environment very large
Environment not wholly known
Environment changing
Agent must act in real time
Results:
Shorter planning
Longer execution (path not optimal)
Shorter sum

4. Traditional Search – A*
Multiple paths from the starting position
Agent keeps expanding the most promising path until the goal is reached
Evaluation function for path ending in position n:
f (n) = g (n) + h (n)
g (n) ... the length of the shortest path found so far from the starting position to n
h (n) ... heuristic evaluation of the length of the shortest path from n to the goal
If h (n) is admissible (optimistic – always smaller or equal to the length of the shortest path from n to the goal), A* finds the shortest path

5. A* – Example
The agent’s environment is divided into squares, some of them impassable
The agent can move up, down, left and right
The distance between adjacent squares is 1
h (n) is the Manhattan distance from n to the goal

6. A* – Example 4 3 2 1
GOAL 5
START 6 7 8

7. A* – Example
4+1 3 2 1
GOAL 5
START 4
6+1 7 6 8

8. A* – Example
4+1
3+2 2 1
GOAL 5
START 4 3
6+1 7 6 8

9. A* – Example
4+1
3+2
2+3 1
GOAL 5
START 4 3 2
6+1 7 6 8

10. A* – Example
4+1
3+2
2+3 1
GOAL 5
START 4
3+4 2
6+1 3 7 6 8

11. A* – Example
4+1
3+2
2+3 1
GOAL 5
START 4
3+4 2
6+1
4+5 3 7 6 8

12. A* – Example
4+1
3+2
2+3 1
GOAL 5
START 4
3+4 2
6+1
4+5 3
7+2 6 8 7

13. A* – Example
4+1
3+2
2+3 1
GOAL 5
START 4
3+4 2
6+1
4+5 3
7+2 6
8+3 7

14. A* – Example 4+1 3+2 2+3 1 GOAL 5 START 4 3+4 2 6+1 4+5 3+6 7+2 6 5+6
GOAL 5
START 4
3+4 2
6+1
4+5
3+6
7+2 6
5+6 3
8+3 7

15. A* – Example 4+1 3+2 2+3 1 GOAL 5 START 4 3+4 2 6+1 4+5 3+6 2+7 7+2 6
GOAL 5
START 4
3+4 2
6+1
4+5
3+6
2+7
7+2 6
5+6
4+7 3
8+3 7

16. A* – Example 4+1 3+2 2+3 1 GOAL 5 START 4 3+4 2 1+8 6+1 4+5 3+6 2+7
GOAL 5
START 4
3+4 2
1+8
6+1
4+5
3+6
2+7
7+2 6
5+6
4+7
3+8
8+3 7

17. A* – Example 4+1 3+2 2+3 1 0+9 GOAL 5 START 4 3+4 2 1+8 6+1 4+5 3+6
2+7
7+2 6
5+6
4+7
3+8
8+3 7

18. A* – Example 4+1 3+2 2+3 1 0+9 GOAL 5 START 4 3+4 2 1+8 6+1 4+5 3+6
2+7
7+2 6
5+6
4+7
3+8
8+3 7

19. A* – Example 4+1 3+2 2+3 1 0+9 GOAL 5 START 4 3+4 2 1+8 6+1 4+5 3+6
2+7
7+2 6
5+6
4+7
3+8
8+3 7

20. Agent-Centered Search
Agent searches local search space, which is a part of the whole space centered on the agent
Makes some steps in the most promising direction
Repeats until it reaches the goal
In game playing (chess), the search is performed around the current position:
The whole game tree is too large (environment very large)
The opponent’s moves are not known in advance (environment not wholly known)
This is an example of two-agent search, we focus on single-agent search.

21. LRTA* Learning real-time A*
Agent updates h (l) for every point l in the local search space: h (l) = min (d (l, n) + h (n))
d (l, n) ... the length of the shortest path from l to a point n just outside the local search space
h (n) ... heuristic evaluation of the length of the shortest path from n to the goal
Moves to the adjacent position l with the lowest h (l).
Repeats until the goal is reached.
Updated h (l) can be used in later searches.

22. LRTA* – Example Same setting as for A*.
The local search space is 3 x 3 squares centered on the agent.

23. LRTA* – Example 4
START 3 2 1
GOAL 5 6 7 8

24. LRTA* – Example 4
START 3 2 1
GOAL 5 6 7 8

25. LRTA* – Example 8
START 7 6 1
GOAL 5 2 4 3

26. LRTA* – Example 10
START 11 12 1
GOAL 9 2 8 3 7 6 5 4

27. LRTA* – Example 10
START 11 12 1
GOAL 9 2 8 3 7 6 5 4

28. LRTA* – Example 10
START 11 12 1
GOAL 2 3 9 6 5 4 8 7

29. LRTA* – Example 10
START 11 12 1
GOAL 2 3 9 6 5 4 8 7

30. LRTA* – Example 10
START 11 12 1
GOAL 2 3 9 6 5 4 8 7

31. LRTA* – Example 10
START 11 12 1
GOAL 2 3 9 6 5 4 8 7

32. LRTA* – Example 10
START 11 12 1
GOAL 2 3 9 6 5 4 8 7

33. LRTA* – Example 10
START 11 12 1
GOAL 2 3 9 6 5 4 8 7

34. LRTA* – Example 10
START 11 12 1
GOAL 2 3 9 6 5 4 8 7

35. LRTA* – Example 10
START 11 12 1
GOAL 2 3 9 6 5 4 8 7

36. LRTA* – Example 10
START 11 12 1
GOAL 2 3 9 6 5 4 8 7

37. LRTA* – Example 10
START 11 12 1
GOAL 2 3 9 6 5 4 8 7

38. LRTA* – Example 10
START 11 12 1
GOAL 2 3 9 6 5 4 8 7

39. LRTA* – Example, search restarted10
START 11 12 1
GOAL 2 3 9 6 5 4 8 7

40. LRTA* – Example, search restarted10
START 13 12 1
GOAL 11 2 3 9 6 5 4 8 7

41. LRTA* – Example, search restarted10
START 13 12 1
GOAL 11 2 3 9 6 5 4 8 7

42. LRTA* – Example, search restarted10
START 13 12 1
GOAL 11 2 3 9 6 5 4 8 7

43. LRTA* – Example, search restarted10
START 13 12 1
GOAL 11 2 3 9 6 5 4 8 7

44. LRTA* – Example, search restarted10
START 13 12 1
GOAL 11 2 3 9 6 5 4 8 7

45. LRTA* – Example, search restarted10
START 13 12 1
GOAL 11 2 3 9 6 5 4 8 7

46. LRTA* – Example, search restarted10
START 13 12 1
GOAL 11 2 3 9 6 5 4 8 7

47. LRTA* – Example, search restarted10
START 13 12 1
GOAL 11 2 3 9 6 5 4 8 7

48. LRTA* – Example, search restarted10
START 13 12 1
GOAL 11 2 3 9 6 5 4 8 7

49. LRTA* – Example, search restarted10
START 13 12 1
GOAL 11 2 3 9 6 5 4 8 7

50. LRTA* – Example, search restarted10
START 13 12 1
GOAL 11 2 3 9 6 5 4 8 7

51. LRTA* – Example, search restarted10
START 13 12 1
GOAL 11 2 3 9 6 5 4 8 7

52. LRTA* – Example, search restarted10
START 13 12 1
GOAL 11 2 3 9 6 5 4 8 7