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Ch. 10 – Planning

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This presentation outlines the processes involved in planning actions for goal-based agents within a block world environment. It covers essential concepts such as initial states, goals, and applicable actions, providing detailed definitions of preconditions and effects associated with actions like Move and MoveToTable. An example scenario illustrates how to achieve goals through state-space search methods, including forward and backward approaches. The planning graph approach highlights the problems and solutions for reaching the desired outcomes, underpinning the theoretical framework for efficient agent action planning.

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Ch. 10 – Planning

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  1. Ch. 10 – Planning Supplemental slides for CSE 327 Prof. Jeff Heflin

  2. Goal-Based Agent sensors State What the world is like now How the world evolves Environment What it will be like if I do action A What my actions do What action I should do now Goals actuators Agent From Fig. 2.13, p. 52

  3. Blocks World Example • initial state • On(A,Table)  On(B,Table)  Clear(A)  Clear(B)  Clear(Table)  Block(A)  Block(B) • goal • On(A,B) • actions Action(Move(b,x,y) , Precond: On(b,x)  Clear(b)  Clear(y)  Block(y), Effect: On(b,y)  Clear(x) On(b,x) Clear(y)) Action(MoveToTable(b,x), Precond: On(b,x)  Clear(b), Effect: On(b,Table)  Clear(x) On(b,x))

  4. Action(Move(b,x,y), Precond: On(b,x)  Clear(b)  Clear(y)  Block(y), Effect: On(b,y)  Clear(x) On(b,x) Clear(y)) Action(MoveToTable(b,x), Precond: On(b,x)  Clear(b), Effect: On(b,Table)  Clear(x) On(b,x)) an action a is applicable in any state that satisfies the precondition e.g., Move(A,Table,B) is applicable in initial state unify with action description apply substitution  ={b/A, x/Table, y/B} to the action’s Precondition initial state satisfies On(A,Table)  Clear(A)  Clear(B)  Block(B) Applicable Actions Initial State: On(A,Table)  On(B,Table)  Clear(A)  Clear(B)  Clear(Table)  Block(A)  Block(B)

  5. A Blocks World Problem • initial state • On(A,Table)  On(B,Table)  On(C,Table)  Clear(A)  Clear(B)  Clear(C)  Clear(Table)  Block(A)  Block(B)  Block(C) • goal state • On(B,C)  On(A,B)  On(C,Table) • actions • Action(Move(b,x,y) , Precond: On(b,x)  Clear(b)  Clear(y)  Block(y), Effect: On(b,y)  Clear(x) On(b,x) Clear(y)) • Action(MoveToTable(b,x), Precond: On(b,x)  Clear(b), Effect: On(b,Table)  Clear(x) On(b,x))

  6. Forward State-Space Search Move(A,T,B) MoveToTable(B,C) Move(A,T,C) Move(B,T,A) Move(B,C,A) On(A,T) ^ On(B,T) ^ On(C,T) ^ Clear(A) ^ Clear(B) ^ Clear(C) ^ Clear(T) On(A,T) ^ On(B,T) ^ On(C,T) ^ Clear(A) ^ Clear(B) ^ Clear(C) ^ Clear(T) ^ On(B,C) On(A,T) ^ On(C,T) ^ Clear(A) ^ Clear(B) ^ Clear(T) ^ On(B,C) ^ On(A,B) Move(B,T,C) Move(A,T,B) Move(A,T,A) Move(C,T,A) spurious actions Move(B,C,B) Move(C,T,B) MoveToTable(A,T) MoveToTable(A,T) MoveToTable(B,T) MoveToTable(C,T) spurious actions Move(A,T,A) Move(B,T,B) Move(C,T,C)

  7. Backward State-Space Search On(B,C) ^ On(A,B) ^ On(C,T) GOAL: MoveToTable(C,x) Move(B,x,C) xC Move(A,x,B) xB Move(C,x,T) On(A,B) ^ On(C,T) ^ On(B,x) ^ Clear(B) ^ Clear(C) On(B,C) ^ On(C,T) ^ On(A,x) ^ Clear(A) ^ Clear(B) ? ? Move(B,y,C) yC Move(A,y,B)? On(C,T) ^ On(A,x) ^ Clear(A) ^ Clear(B) ^ On(B,y) ^ Clear(C) INITIAL STATE: (if x=T and y= T) Not relevant:has effect delete Clear(B) bold – literal that was added to the predecessor underline – goal is not satisfied by initial state

  8. Planning Graph Example • Init(Have(Cake) • Goal(Have(Cake)  Eaten(Cake)) • Action(Eat(Cake) • PRECOND: Have(Cake) • EFFECT: Have(Cake)  Eaten(Cake)) • Action(Bake(Cake) • PRECOND: Have(Cake) • EFFECT: Have(Cake) Missing from book From Fig. 10.8, p. 380

  9. GraphPlan function GRAPHPLAN(problem) returns solution or failure graph  INITIAL-PLANNING-GRAPH(problem)goals  CONJUNCTS(problem.GOAL)nogoods an empty hash tablefort = 0 to doif goals all non-mutex in Stof graph thensolution  EXTRACT-SOLUTION(graph, goals, NUMLEVELS(graph),nogoods)ifgraph and nogoods have both leveled off then return failure graph  EXPAND-GRAPH(graph, problem) From Fig. 10.9, p. 383

  10. Spare Tire Problem Init(Tire(Flat)  Tire(Spare)  At(Flat,Axle)  At(Spare,Trunk)) Goal(At(Spare,Axle)) Action(Remove(obj,loc),PRECOND: At(obj,loc),EFFECT: At(obj,loc)  At(obj,Ground)) Action(PutOn(t, Axle),PRECOND: Tire(t)  At(t,Ground) At(Flat,Axle),EFFECT: At(t,Ground) At(t,Axle)) Action(LeaveOvernight,PRECOND: ,EFFECT: At(Spare,Ground) At(Spare,Axle) At(Spare,Trunk) At(Flat,Ground) At(Flat,Axle) At(Flat,Trunk)) From Fig. 10.2, p. 370

  11. Spare Tire Planning Graph From Fig. 10.10, p. 384

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