1. AI Automated Planning In A Nutshell Vitaly Mirkis March 4, 2013 Netanya Academic College Acknowledgments: Some slides are based slides of Prof. Carmel Domshlak and of Dr. Michael Katz Technion – Israel Institute of Technology Industrial Engineering & Management

2. Abstract During the past two decades the focus on AI Domain Independent Planning (planning) research has led to a noticeable theoretical progress and planning systems started demonstrating leading performance. A practical impact are the planning systems growing use in different industrial areas and the worldwide increasing popularity of planning academic courses. The lecture will present the basic principles of modern planning.

3. Planning “Adventure is just bad planning” Roald Amundsen “Planning is the art and practice of thinking before acting: of reviewing the courses of action one has available and predicting their expected (and unexpected) results to be able to choose the most beneficial course of action, with respect to ones goals.” Patrik Haslum

4. Planning in today’s industry Planning in today’s Industry: NASA’s mars rover, Hubble Space Telescope etc.

5. UAV Cooperative Mission x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 y1y2y3y4 y5y6y1y2y3y4 y5y6 An UAV is able to move to some of its neighbor cells. An UAV is able to photograph a object in current cell. The goal is to photograph all colored objects and return to its initial position.

6. UAV Cooperative Mission x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 y1y2y3y4 y5y6y1y2y3y4 y5y6

7. Planning software principle A Planning software (planner) execution flow description: – A given task is translated (compiled) to a planning problem . – Planning problem  supplied to a solver (planner). – The solution λ is also a solution for the task (or can be easily translated to such). TranslatorTranslatorPlannerPlanner task  λ

8. Planning software principle A Planning software (planner) execution flow description: – A given task is translated (compiled) to a planning problem . – Planning problem  supplied to a solver (planner). – A solution λ is also a solution for the task (or can be easily translated to such). – Hence, it is sufficient to consider any convenient task, for planning principles introduction. TranslatorTranslatorPlannerPlanner task  λ x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 y1y2y3y4 y5y6y1y2y3y4 y5y6 ’’ ’’ Solution λ ’

9. Planning in blocks world Initial state Goal state Game rules: -No two blocks can be on top of the same block -Block can’t be on top of two blocks -Exact location on table or on block doesn’t matter ? ? B YG YG B

10. Planning in blocks world Initial state on-table(Y), clear(Y), on-table(G), on(R, G), on(B, R), clear(B) Goal state on-table(G), clear(G), on-table(Y), clear(Y), clear(R), on(R, B), on-table(B) on(i,j), on-table(i), clear(i)

11. Planning in blocks world Initial state Goal state Actions defined with: Move-Block( i )-from-Block(j)-to-Table Move-Block( i )-from-Table-to-Block(j) Move-Block( i )-from-Block(j)-to-Block(k) ? ?

12. Planning in blocks world B

13. Initial state Goal state Planning in blocks world B B G G Y Y R R G G Y Y R R B B G G R R

14. G R B Y GBY R

15. Optimal plan as shortest graph path: Optimal plan as shortest graph path: Planning in blocks world: states space How to solve (= find a plan) the described problem? G R YB G R B Y G R Y B GRYB G R B Y GYB R YB R G G R B Y Partial transition graph for 4 blocks: Plan as graph path: Plan as graph path:

16. How to find an optimal solution? – Use Dijkstra’s to find optimal solution. – The problem has 73 states For the general case? The traversing time for all problem’s states is growing very fast with problem size (planning is hard, both satisficing and optimal) – State space of 100 blocks problem have more states than number of atoms in the universe (> 10 87 )  visiting all states is infeasible approach. Yet, these problems are solved somehow. How? How hard Planning is? G R B Y G R YB G R B Y G R Y B GRYB G R B Y GYB R GYB R YB R G G R B Y

17. Planning Evolution

19. Heuristic search Since the beginning of the century, heuristic search planning solvers outperformed all other approaches. Thus, during the last decade, planning via heuristic search had a massive research focus and played one of the major roles in the vast progress of the entire field. Important property of a heuristic search is the practical ability to solve large problems, i.e., problems unsolvable using other algorithms.

20. The intuition behind heuristic search h : An oracle estimation of the coast of reaching the goal from a given state. Partial transition graph for 4 blocks: h = 2? ? ? h = 3 h = 1 G R YB G R B Y G R Y B GRYB G R B Y GYB R YB R G G R B Y h = 2

21. Heuristic search basic model Heuristic search composed of two major, (usually) independent, parts: I.State search algorithm II.Heuristic evaluation function ( h ) – Search dynamics: The search algorithm uses a heuristic function to evaluate state to decide which state visit next. Each part developed independently.

22. Heuristic function Heuristic function ( h )

23. The intuition behind heuristic search h : The coast of reaching the goal from the current state is no less than h ( h  real cost). G R YB G R B Y G R Y B GRYB G R B Y GYB R YB R G G R B Y Partial transition graph for 4 blocks: h = 2? ? ? h = 3 h = 1

25. Constructing a heuristic function The most common method to find a “good” heuristic is via a solution to an “easier” version of the problem. Such easier problem can be obtained from the given problem, via two common techniques: 1.Relaxation: ignoring some constrains of the given problem. The outcome often called relaxed problem. 2.Abstraction: use a smaller version of the given problem, small enough to traverse all its states. Practically, an “easy to compute” heuristics are preferable.

26. Relaxed Planning in blocks world B B

27. Initial state Goal state Game rules: -No two blocks can be on top of the same block -Block can’t be on top of two blocks -Exact location on table or on block doesn’t matter ? ? B YG YG B

28. Delete free (relaxation) One such relaxation technique named delete free. – Once fact achieved, it can’t be deleted: Initial state Goal G R Y R B RR B R B  Satisficing / parallel plan can be found in polynomial time (finding an optimal plan is still hard)

29. Ignore all but the goals (abstraction) One method can be to achieve an abstraction by choosing only the goal blocks: – Initial state: – Goal state:  But, how can it be utilized? R B

30. State of the art heuristics

31. Beyond classical planning Planning variations: Oversubscription planning – Given a plan cost limitation, achieve the most valuable goals. Probabilistic planning – Some of the action’s effects are stochastic. Planning with partial observability – The initial state is non-deterministic.

32. Summary Planning is a model-based approach to a machine autonomous behavior, Task independent problem solver, Wide researchers interest, Continue grow in usage in industrial applications.

33. The end Thank you Thank you

34. Appendix Appendix

35. Planning Model

36. STRIPS: A Formal Planning Language

37. From Language to Model