1 Logistics z1 Handout yCopies of my slides zReading yRecent Advances in AI Planning, sections 1-2

2 2 Approaches to Agent Control zReactive Control ySet of situation-action rules yE.g. x1) if dog-is-behind-me then run-forward x2)if food-is-near then eat zPlanning yReason about effect of combinations of actions y“Planning ahead” yAvoiding “painting oneself into a corner”

3 Different Planning Approaches zGenerative Planning yReason from first principles (knowledge of actions) to generate plan yRequires formal model of actions zCase-Based Planning yRetrieve old plan which worked for similar problem yRevise retrieved plan for this problem zSee also yPolicy Iteration / Markov-Decision Processes yReinforcement Learning

4 Generative Planning zInput yDescription of initial state of world (in some KR) yDescription of goal (in some KR) yDescription of available actions (in some KR) zOutput ySequence of actions

5 Input Representation zDescription of initial state of world ySet of propositions:  ((block a) (block b) (block c) (on-table a) (on-table b) (clear a) (clear b) (clear c) (arm-empty)) zDescription of goal (i.e. set of desired worlds) yLogical conjunction yAny world that satisfies the conjunction is a goal  (and (on a b) (on b c))) zDescription of available actions

6 Representing Actions STRIPS UWL ADL SADL TractableExpressive Situation Calculus

7 How Represent Actions? zSimplifying assumptions yAtomic time yAgent is omniscient (no sensing necessary). yAgent is sole cause of change yActions have deterministic effects zSTRIPS representation yWorld = set of true propositions yActions: xPrecondition: (conjunction of literals) xEffects (conjunction of literals) a a a north11 north12 W0W0 W2W2 W1W1

8 STRIPS Actions zAction =function from world-state  world-state zPrecondition says where function defined zEffects say how to change set of propositions a a north11 W0W0 W1W1 precond: (and (agent-at 1 1) (agent-facing north)) effect: (and (agent-at 1 2) (not (agent-at 1 1))) Note: strips doesn’t allow derived effects; you must be complete!

9 Action Schemata (:operator pick-up :parameters ((block ?ob1)) :precondition (and (clear ?ob1) (on-table ?ob1) (arm-empty)) :effect (and (not (clear ?ob1)) (not (on-table ?ob1)) (not (arm-empty)) (holding ?ob1))) zInstead of defining: pickup-A and pickup-B and … zDefine a schema: Note: strips doesn’t allow derived effects; you must be complete! }

10 Planning as Search zNodes zArcs zInitial State zGoal State World states Actions The state satisfying the complete description of the initial conds Any state satisfying the goal propositions

11 Forward-Chaining World-Space Search A C B C B A Initial State Goal State

12 Backward-Chaining Search Thru Space of Partial World-States D C B A E D C B A E D C B A E * * * zProblem: Many possible goal states are equally acceptable. zFrom which one does one search? A C B Initial State is completely defined D E

13 “Causal Link” Planning zNodes zArcs zInitial State zGoal State Partially specified plans Adding + deleting actions or constraints (e.g. <) to plan The empty plan (Actually two dummy actions…) A plan which when simulated achieves the goal Need efficient way to evaluate quality (percentage of preconditions satisfied) of partial plan … Hence causal link datastructures

14 Plan-Space Search pick-from-table(C) pick-from-table(B) pick-from-table(C) put-on(C,B) zHow represent plans? zHow test if plan is a solution?

15 Planning as Search 3 Graphplan zPhase 1 - Graph Expansion yNecessary (insufficient) conditions for plan existence yLocal consistency of plan-as-CSP zPhase 2 - Solution Extraction yVariables xaction execution at a time point yConstraints xgoals, subgoals achieved xno side-effects between actions

16 Planning Graph Proposition Init State Action Time 1 Proposition Time 1 Action Time 2

17 Constructing the planning graph… zInitial proposition layer yJust the initial conditions zAction layer i yIf all of an action’s preconds are in i-1 yThen add action to layer I zProposition layer i+1 yFor each action at layer i yAdd all its effects at layer i+1

18 Mutual Exclusion zActions A,B exclusive (at a level) if yA deletes B’s precond, or yB deletes A’s precond, or yA & B have inconsistent preconds zPropositions P,Q inconsistent (at a level) if yall ways to achieve P exclude all ways to achieve Q

19 Graphplan zCreate level 0 in planning graph zLoop yIf goal  contents of highest level (nonmutex) yThen search graph for solution xIf find a solution then return and terminate yElse Extend graph one more level A kind of double search: forward direction checks necessary (but insufficient) conditions for a solution,... Backward search verifies...

20 Searching for a Solution zFor each goal G at time t yFor each action A making G xIf A isn’t mutex with a previously chosen action, select it xIf no actions work, backup to last G (breadth first search) zRecurse on preconditions of actions selected, t- 1 Proposition Init State Action Time 1 Proposition Time 1 Action Time 2

21 Dinner Date Initial Conditions: (:and (cleanHands) (quiet)) Goal: (:and (noGarbage) (dinner) (present)) Actions: (:operator carry :precondition :effect (:and (noGarbage) (:not (cleanHands))) (:operator dolly :precondition :effect (:and (noGarbage) (:not (quiet))) (:operator cook :precondition (cleanHands) :effect (dinner)) (:operator wrap :precondition (quiet) :effect (present))

22 Planning Graph noGarb cleanH quiet dinner present carry dolly cook wrap cleanH quiet 0 Prop 1 Action 2 Prop 3 Action 4 Prop

23 Are there any exclusions? noGarb cleanH quiet dinner present carry dolly cook wrap cleanH quiet 0 Prop 1 Action 2 Prop 3 Action 4 Prop

24 Do we have a solution? noGarb cleanH quiet dinner present carry dolly cook wrap cleanH quiet 0 Prop 1 Action 2 Prop 3 Action 4 Prop

25 Extend the Planning Graph noGarb cleanH quiet dinner present carry dolly cook wrap carry dolly cook wrap cleanH quiet noGarb cleanH quiet dinner present 0 Prop 1 Action 2 Prop 3 Action 4 Prop

26 One (of 4) possibilities noGarb cleanH quiet dinner present carry dolly cook wrap carry dolly cook wrap cleanH quiet noGarb cleanH quiet dinner present 0 Prop 1 Action 2 Prop 3 Action 4 Prop