Automated Planning Dr. Héctor Muñoz-Avila

What is Planning? Classical Definition Domain Independent: symbolic descriptions of the problems and the domain. The plan generation algorithm remains the same Domain Specific: The plan generation algorithm depends on the particular domain Advantage: - opportunity to have clear semantics Disadvantage: - symbolic description requirement Advantage: - can be very efficient Disadvantage: - lack of clear semantics - knowledge-engineering for adaptation Planning: finding a sequence of actions to achieve a goal Domain-configurable Planning Domain independent planning algorithm Add domain-specific search control Examples:  SHOP  TLPlan Domain-configurable Planning Domain independent planning algorithm Add domain-specific search control Examples:  SHOP  TLPlan

Classical Assumptions (I) A0: Finite system  finitely many states, actions, and events A1: Fully observable  the controller always knows what state  is in A2: Deterministic  each action or event has only one possible outcome A3: Static  No exogenous events: no changes except those performed by the controller Plan adaptation

Classical Assumptions (II) A4: Attainment goals  a set of goal states S g A5: Sequential plans  a plan is a linearly ordered sequence of actions (a 1, a 2, … a n ) A6 :Implicit time  no time durations  linear sequence of instantaneous states A7: Off-line planning  planner doesn’t know the execution status Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: Plan space planning TLPlan HTN planning

Plan Representation Classical representation  Predicates, variables, constants  Most of our systems used it Set-theoretic representation  Predicates and constants (no variables!)  Useful in algorithms that manipulate ground atoms directly Used in internal representations: planning graphs (Chapter 6), satisfiability (Chapters 7) State-variable representation  Keeps track of the value of each variable: loc(truck) = l1

Expressive Power Any problem that can be represented in one representation can also be represented in the other two Can convert in linear time and space, except when converting to set-theoretic (where we get an exponential blowup) Classical representation State-variable representation Set-theoretic representation trivial P(x 1,…,x n ) becomes f P (x 1,…,x n )=1 write all of the ground instances f(x 1,…,x n )=y becomes P f (x 1,…,x n,y) Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License:

Classical Planning

State-Space Planning A C B ABC AC B C B A B A C B A C BC A C A B A C B B C A AB C A B C A B C State space V: set of states E: set of transitions (s,  (s,a)) But: computed graph is a subset of state space Search modes: Forward Backward Sussman Anomaly Generally thought to be slow But: Fastforward, TLPlan, SHOP are state-space planners How come?

Plan-Space Planning Initial plan complete plan for goals Plan space V: set of plans E: plan refinement transitions As before: computed graph is a subset of plan space Least commitment: Does not commit on action ordering  Threats  Open conditions Solves the Sussman anomaly Also thought to be slow But: VHPOP

Plan Adaptation Transformational analogy: transforms an input plan Derivational analogy: reuses the derivational trace that led to a plan  Therefore requires more knowledge to be provided Both forms of adaptation have been developed for state-space, plan-space, hierarchical (HTN) planning All can be subsumed in the Universal Classical Planning framework Interesting: some authors have proposed using planning graphs during adaptation (is this derivational? Transformational?)

Neo-Classical Planning

Planning Graphs Move(B,C,table) Move(A,table,B) Move(B,C,A) Clear(B) On(B, C) Clear(A) On(A, table) On(C,table) P0P0 BCA B C A B CA B CA Clear(C) On(B, table) On(B, C) On(A, B) On(A,table) Clear(B) On(B, A) Clear(A) On(C,table) A1A1 P1P1 Planning graphs encode an inclusive disjunction of actions Since some actions in a disjunction may interfere with one another (mutex), it keeps track of incompatible propositions Solution extracted via backward chaining in the planning graph  Must consider mutex Can improve performance More crucially: used for defining heuristics (FF,…)

Planning as Satisfiability Encodes the planning problem as a logical formula For example:  The initial state is represented as:  Applicability of Actions as: Davis-Putnam procedure: finds truth assignments that make the formula true Blackbox: encodes the planning graph rather than the planning problem  Trial and error process

Heuristics in Planning A C B ABC AC B C B A B A C B A C BC A C A B A C B B C A AB C A B C A B C State space V: set of states E: set of transitions (s,  (s,a))  (s,G): estimates how far is s from achieving G This estimate is made by constructing the goal graph… …on a relaxation of the problem: domain with no negative effects A greedy strategy is selected (pick the one with highest value) after performing breadth-first search

Domain-configurable Planning

Search Control Rules in Planning A C B ABC AC B C B A B A C B A C BC A C A B A C B B C A AB C A B C A B C State space V: set of states E: set of transitions (s,  (s,a)) Uses temporal logic to prune potential actions / states υ (until), □ (always), ◊ (eventually), ○ (next), GOAL Example rule: “Don’t move container if position is consistent with goal” Formula progress(Φ,s i ) is true in s i+1 iff Φ is true in s i.

Reasoning with Time in Planning Extends search control rules representation as in TLPlan  After all this representation is based on temporal logics Example: ( def-adl-operator (drive ?t ?l ?l’) (pre (?t) (truck ?t) (?l) (loc ?l) (?l’) (loc ?l’) (at ?t ?l)) (del (at ?t ?l)) (delayed-effect (/ (dist ?l ?l’) (speed ?t) (add (at ?t ?l’)))) It associates a time stamp with every state  Transformations between states with same time stamp are instantaneous  Crucial: each state has an associated event queue (future updates)

Hierarchical Planning Non-primitive task precond method instance s0s0 precondeffectsprecondeffects s1s1 s2s2 primitive task operator instance Non-primitive task Order in which subtasks are fulfilled Distinguishes between primitive and non- primitive tasks Primitive tasks: concrete actions (instances of operators) Compound task: high- level goals (decomposed by methods) Operators: standard STRIPS knowledge Methods: domain- configurable constructs

Final Summary Classical Planning  State-space  Plan-Space  Plan adaptation Neo Classical planning  Planning graphs  Planning as Satisfiability  Heuristics in Planning Domain-configurable planners Search control rules Reasoning with time Hierarchical Planning Complexity of Planning