1. 1 Planning Chapters 11 and 12 Thanks: Professor Dan Weld, University of Washington

2. 2 Planning Input Description of initial state of world (in some KR) Description of goal (in some KR) Description of available actions (in some KR) Output Sequence of actions Or, a partial order of actions

3. 3 Input Representation Description of initial state of world Set of propositions: ((block a) (block b) (block c) (on-table a) (on-table b) (clear a) (clear b) (clear c) (arm-empty)) Description of goal (i.e. set of desired worlds) Logical conjunction Any world that satisfies the conjunction is a goal (:and (on a b) (on b c))) Description of available actions

4. 4 How Represent Actions? Simplifying assumptions Atomic time Agent is omniscient (no sensing necessary). Agent is sole cause of change Actions have deterministic effects STRIPS representation World = set of true propositions Actions: Precondition: (conjunction of literals) Effects (conjunction of literals) a a a north11 north12 W0W0 W2W2 W1W1

5. 5 STRIPS Actions Action = a function from world-state to world-state Precondition says when function defined Effects 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)))

6. 6 Action Schemata (:operator pick-up :parameters ((block ?ob1)) :precondition (and (clear ?ob1) (on-table ?ob1) (arm-empty)) :effect (and (not (on-table ?ob1)) (not (clear ?ob1)) (not (arm-empty)) (holding ?ob1))) Instead of defining: pickup-A and pickup-B and … Variables: ?x. For example, ?ob1 Define a schema:

7. 7 STRIPS vs ADL Positive/Negative conditions Closed world assumption Negated Effects Quantified Effects Goals as conjunctions and disjunctions Conditional Effects (when … ) Equality Predicate Typing

8. 8 Examples Air Cargo Domain Spare Tire Problem The blocks world

9. 9 Planning as Search Nodes Arcs Initial State Goal State World states Actions The state satisfying the complete description of the initial conds Any state satisfying the goal propositions

10. 10 Forward-Chaining World-Space Search A C B C B A Initial State Goal State

11. 11 Backward-Chaining World-Space Search D C B A E D C B A E D C B A E * * * Problem: Many possible goal states are equally acceptable. From which one does one search? A C B Initial State is completely defined D E

12. 12 Backward Planning Try out http://www.cs.ubc.ca/labs/lci/CIspace/Versio n4/planning/ at UBC which shows goal- directed planning http://www.cs.ubc.ca/labs/lci/CIspace/Versio n4/planning/ Shows blocks world planning Idea: find a first subgoal Achieve it by selecting an action Regress to discover new subgoals from the action ’ s preconditions Continue

13. 13 Planning as Search 2 Nodes Arcs Initial State Goal State Partially specified plans Adding + deleting actions or constraints (e.g. <) to plan The empty plan A plan which when simulated achieves the goal

14. 14 Plan-Space Search and Partial Order Planning pick-from-table(C) pick-from-table(B) pick-from-table(C) put-on(C,B) How represent plans? How test if plan is a solution?

15. 15 Terminologies Partial Ordering Linearization Ordering constraints Causal Links Achieves Conflicts Open Preconditions Consistent Plans

16. 16 Planning as Search 3 Phase 1 - Graph Expansion Necessary (insufficient) conditions for plan existence Local consistency of plan-as-CSP Phase 2 - Solution Extraction Variables action execution at a time point Constraints goals, subgoals achieved no side-effects between actions

17. 17 Planning Graph Proposition Init State Action Time 1 Proposition Time 1 Action Time 2

18. 18 Constructing the planning graph … Initial proposition layer Just the initial conditions Action layer i If all of an action ’ s preconds are in i-1 Then add action to layer I Proposition layer i+1 For each action at layer i Add all its effects at layer i+1 Also allow propositions at layer i to persist to i+1

19. 19 Mutual Exclusion (or Mutex) Actions A,B exclusive (at a level) if A deletes B ’ s precond, or B deletes A ’ s precond, or A & B have inconsistent preconds (so they cannot be executed at the same time) Propositions P,Q inconsistent (at a level) if all ways to achieve P exclude all ways to achieve Q

20. 20 Graphplan Create level 0 in planning graph Loop If goal  contents of highest level (nonmutex) Then search graph for solution If find a solution then return and terminate Else Extend graph one more level A kind of double search: forward direction checks necessary (but insufficient) conditions for a solution,... Backward search verifies...

21. 21 Searching for a Solution For each goal G at time t For each action A making G true @t If A isn ’ t mutex with a previously chosen action, select it If no actions work, backup to last G (breadth first search) Recurse on preconditions of actions selected, t-1 Proposition Init State Action Time 1 Proposition Time 1 Action Time 2

22. 22 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))

23. 23 Planning Graph noGarb cleanH quiet dinner present carry dolly cook wrap cleanH quiet 0 Prop 1 Action 2 Prop 3 Action 4 Prop

24. 24 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

25. 25 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

26. 26 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

27. 27 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

28. 28 Planning Languages PDDL Tutorials FF Planner

29. 29 Robot Architectures (page787) Problem: low level action takes too long to reason about! Function Based Architecture: Task Planning and Learning Vision Inferencing Map based Navigation Sensors and Actuators

30. 30 Behavior-based Robotics (page 788) Rodney Brooks designed behavior-based robotics Agent design should not be function based (I.e., should not be based on learning, task planning, sensing, etc). Instead, it should be indepdent modules Each has own sensing, inferencing, and acting Higher level modules more intelligent, and can access sensors independently, and can modify outputs of lower-level modules sensors actuators explore wonder Avoid objects vision learn Plan ahead

31. 31 Robot Insect Video Rodney Brooks ’ robots in a video http://www.youtube.com/watch?v=C9p8B7-5MTI

32. 32 Summary Planning Reactive systems vs. planning Planners can handle medium to large-sized problems Relaxing assumptions Atomic time Agent is omniscient (no sensing necessary). Agent is sole cause of change Actions have deterministic effects Generating contingent plans Large time-scale Spacecraft control