1. PLANNING Partial order regression planning Temporal representation 1 Deductive planning in Logic Temporal representation 2

2. 2 The task of planning  Given:  a description of an initial state of the world  a description of a desired state of the world  a set of actions:  with their preconditions that should hold in the world  with their effects on the world  Find:  a sequence of actions that transform the initial state into the final one.

3. Partial order regression planning The STRIPS approach

4. 4 State descriptions in STRIPS  Only ground facts are used.  Example: the blocks world:  States of the world are represented individually in logic:  Meaning: there is NO representation of how one state relates to the next  Nor any representation of time!

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6. 6 Action description in STRIPS  Effects:  two sets of ground facts:  Preconditions:  a set of ground facts that need to be true in the state for the action to be applicable.  the delete list: –need to be removed from the previous state  the add list: –need to be added to the previous state

7. 7 Example: Some operator patterns:  Action1: “move block x from block y to block z” Preconditions If on(x,y) clear(x) clear(x) clear(z) clear(z) Add list Add on(x,z) clear(y) clear(y) Delete list Delete on(x,y) clear(z) clear(z)

8. 8 Example: Operator patterns (2):  Action2: “move block x from block y to Table” If on(x,y) clear(x) clear(x) Add on(x,Table) clear(y) clear(y) Delete on(x,y)

9. 9 Example: Operator patterns (3):  Action3: “move block x from Table to block z”  Note: actual operators are ground instances of these! If on(x,Table) clear(x) clear(x) clear(z) clear(z) Add on(x,z) Delete on(x,Table) clear(z) clear(z)

10. 10 What about using search in forward chaining on this?  This is similar to Automated Reasoning: bottom-up inference is not goal directed, top-down reasoning is!  See example:  Such search is NOT goal directed!  No information on what state to reach

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12. 12 Backward chaining:  Forward chaining would be progression:  move from initial state to goal state  Example: limited to 1 goal fact!  and only 1 possible path explored  Planning as regression:  start from the goal state and reason backwards to the initial state

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20. 20 Regression planning: goal reduction.  Select an atomic goal that still needs to be established  Find an operator that establishes it (  add list)  Add the operator to the plan and add an ESTABLISH link between operator and goal.  In general: complex goals are decomposed into atomic ones that themselves are reduced to new goals.  Is somewhat similar to ‘top-down’ goal-directed reasoning in AR.

21. 21 Principle of least commitment (1)  Establish links only impose a partial order:  they do NOT impose that first operator needs to occur EXACTLY before second operator  BUT they are protected links:  NO operator may be scheduled between them that UNDOES the established property !  Clue: do not decide on a choice before it is necessary!

22. 22 High-level algorithm Initialize: operators: = empty; operators: = empty; establishes:= empty; establishes:= empty; before:= empty; before:= empty; complete:= false; blocked:= false; Case: before has loop: blocked:= true; Case: before has loop: blocked:= true; While not(complete) and not(blocked) do Case: O  operators threatens Case: O  operators threatens E(O1,O2)  establishes: E(O1,O2)  establishes: add B(O,O1) OR add B(O2,O) add B(O,O1) OR add B(O2,O) to before; to before; … … … … … …

23. 23 … … … … … … End-While End-While Case: O  operators has unsatisfied Case: O  operators has unsatisfied condition: condition: find O’  operators find O’  operators OR add O’ to operators OR add O’ to operators AND install establishes and AND install establishes and before links before links Otherwise: complete:= true; Otherwise: complete:= true; High-level algorithm (continued)

24. 24 Some comments:  The algorithm is imprecise:  The Case for threatens links can be activated infinitely often for the same link  should test whether it has been dealt with

25. 25 High-level algorithm Initialize: operators: = empty; operators: = empty; establishes:= empty; establishes:= empty; before:= empty; before:= empty; complete:= false; blocked:= false; Case: before has loop: blocked:= true; Case: before has loop: blocked:= true; While not(complete) and not(blocked) do Case: O  operators threatens Case: O  operators threatens E(O1,O2)  establishes: E(O1,O2)  establishes: add B(O,O1) OR add B(O2,O) add B(O,O1) OR add B(O2,O) to before; to before; … … … … … …

26. 26 Some comments:  The algorithm is imprecise:  The Case for threatens links can be activated infinitely often for the same link  should test whether it has been dealt with  The initial situation and goal situation are not explicitly present  and, the initial situation is not considered for unsatisfied conditions  add the initial and goal situation to operators in the Initialization –initial operator has no conditions, just adds initial situation –final operator adds/deletes nothing, just has a condition part.

27. 27 Blocks example:  Initial operator: If Add on(A,C) on(C,Table) clear(A) on(D,B) on(B,Table) clear(D) on(D,B) on(B,Table) clear(D)Delete  Final operator: If on(A,B) on(B,C) on(B,C)AddDelete

28. 28 Further refinement: backtracking:  When it exits the While loop because blocked = true (there is a before loop), then don’t terminate, but backtrack over operator choices.

29. 29 High-level algorithm Initialize: operators: = empty; operators: = empty; establishes:= empty; establishes:= empty; before:= empty; before:= empty; complete:= false; blocked:= false; Case: before has loop: blocked:= true; Case: before has loop: blocked:= true; While not(complete) and not(blocked) do Case: O  operators threatens Case: O  operators threatens E(O1,O2)  establishes: E(O1,O2)  establishes: add B(O,O1) OR add B(O2,O) add B(O,O1) OR add B(O2,O) to before; to before; … … … … … …

30. 30 … … … … … … End-While End-While Case: O  operators has unsatisfied Case: O  operators has unsatisfied condition: condition: find O’  operators find O’  operators OR add O’ to operators OR add O’ to operators AND install establishes and AND install establishes and before links before links Otherwise: complete:= true; Otherwise: complete:= true; High-level algorithm (continued)

31. 31 Further refinement: backtracking:  When it exits the While loop because blocked = true (there is a before loop), then don’t terminate, but backtrack over operator choices.  Note: no point in backtracking over selection of unsatisfied pre-conditions:  they ALL need to be satisfied anyway at the end

32. 32 … … … … … … End-While End-While Case: O  operators has unsatisfied Case: O  operators has unsatisfied condition: condition: find O’  operators find O’  operators OR add O’ to operators OR add O’ to operators AND install establishes and AND install establishes and before links before links Otherwise: complete:= true; Otherwise: complete:= true; High-level algorithm (continued)

33. 33 Further refinement: backtracking:  When it exits the While loop because blocked = true (there is a before loop), then don’t terminate, but backtrack over operator choices.  Note: no point in backtracking over selection of unsatisfied pre-conditions:  they ALL need to be satisfied anyway at the end  PS: note how this is similar to the ‘top-down’ automated reasoning techniques.  (backtrack over previous clause selections, not over previous atom selections).

34. 34 Least commitment(2): plan with operator patterns  Key point:  Use operator patterns:  move x from y to Table  move x from Table to y  move x from y to z  instead of explicit operators:  move A from B to Table  move A from Table to B  move A from B to C  Avoids to make choices when the information to decide upon various alternatives is not yet there!

35. 35 Blocks example: on(A,Table) goal on(A,B)clear(A)on(B,Table) initial on(A,B)clear(A)on(B,Table)on(A,Table) if on(A,y) clear(A) clear(A) add clear(y) on(A,Table) on(A,Table) delete on(A,y) on(A,B)clear(A)on(B,Table) on(A,Table) establishes unification: {x/A) if on(x,y) clear(x) clear(x) add clear(y) on(x,Table) on(x,Table) delete on(x,y) move x from y to Table establishes unification: {y/B)

36. 36 Change in the algorithm: Case: O  operators has unsatisfied condition: condition: find O’  operators find O’  operators OR add O’ to operators OR add O’ to operators AND install establishes and AND install establishes and before links before links  O and O’ are (partially instantiated) operator patterns now  The unsatisfied needs to be unifiable with an element of the add list of O’ now (not be identical)  The unifier needs to be applied on the entire set of operators constructed so far!

37. 37 When is there a threat?  Example: on(A,B)on(B,D)clear(A)clear(B) clear(C)on(B,Table) if on(A,C) clear(A) clear(A) add clear(C) on(A,y) on(A,y) delete on(A,C) clear(y) clear(y) move A from C to y establishes if on(B,z) clear(B) clear(B) add clear(z) on(B,Table) on(B,Table) delete on(B,z) move B from z to Table establishes establishes threat? establishes

38. 38 Dealing with possible threats 1) Ignore them, until they become instantiated to real threats.  Example: only if ‘delete clear(y)’ becomes ‘delete clear(B)’ we consider it a threat  Optimization: at least check whether there is still a consistent value for the variables (Ex.: y can still be assigned value D) 2) Introduce inequality constraints and replace unification by constraint solving  Example: constraint y  B + unification must now also respect the inequalities 3) Choose a value for y  Ex.: assign y = D.