Practical Planning: Scheduling and Hierarchical Task NetworksOutlineReal-world planning domainsPlanning vs. schedulingHierarchical decompositionHTN operator: ExampleHTN planning: exampleSIPE-2Slide 9Blocksworld in SIPE-2HTN operator representationTruth criterionTruth criterion in SIPE-2Increasing expressivityReasoning about resourcesOther real-world planning issuesPlanning summaryApplications of PlanningOil-Spill Response in SIPE-2Practical Planning:Practical Planning:Scheduling and Hierarchical Scheduling and Hierarchical Task NetworksTask NetworksChapter 12.1-12.2CS 63CS 63Adapted from slides byTim Finin andMarie desJardins.Outline•Intelligent scheduling•Hierarchical task network (HTN) planning•Increasing expressivityReal-world planning domains•Real-world domains are complex and don’t satisfy the assumptions of STRIPS or partial-order planning methods•Some of the characteristics we may need to deal with:–Modeling and reasoning about resources–Representing and reasoning about time–Planning at different levels of abstractions–Conditional outcomes of actions–Uncertain outcomes of actions–Exogenous events–Incremental plan development–Dynamic real-time replanning} a.k.a. scheduling!Planning vs. scheduling•Planning: given one or more goals, generate a sequence of actions to achieve the goal(s)•Scheduling: given a set of actions and constraints, allocate resources and assign times to the actions so that no constraints are violated•Traditionally, planning is done with specialized logical reasoning methods•Traditionally, scheduling is done with constraint satisfaction, linear programming, or OR methods•However, planning and scheduling are closely interrelated and can’t always be separatedHierarchical decomposition•Hierarchical decomposition, or hierarchical task network (HTN) planning, uses abstract operators to incrementally decompose a planning problem from a high-level goal statement to a primitive plan network•Primitive operators represent actions that are executable, and can appear in the final plan•Non-primitive operators represent goals (equivalently, abstract actions) that require further decomposition (or operationalization) to be executed•There is no “right” set of primitive actions: One agent’s goals are another agent’s actions!HTN operator: ExampleOPERATOR decomposePURPOSE: ConstructionCONSTRAINTS: Length (Frame) <= Length (Foundation), Strength (Foundation) > Wt(Frame) + Wt(Roof) + Wt(Walls) + Wt(Interior) + Wt(Contents)PLOT: Build (Foundation)Build (Frame) PARALLEL Build (Roof) Build (Walls) END PARALLEL Build (Interior)HTN planning: exampleSIPE-2•SIPE-2 is an HTN planner with many advanced features:–Plan critics–Resource reasoning–Constraint reasoning (complex numerical or symbolic variable and state constraints)–Interleaved planning and execution–Interactive plan development–Sophisticated truth criterion–Conditional effects–Parallel interactions in partially ordered plans–Replanning if failures occur during executionSIPE-2Image from: http://www.ai.sri.com/~sipe/architecture.htmlBlocksworld in SIPE-2;;some colored blocks for other problems(ON R1 B1)(ON B1 TABLE)(ON B2 TABLE)(ON R2 TABLE);true in all problems(CLEAR TABLE)END PREDICATESSTOPOPERATOR: PUTON1ARGUMENTS: BLOCK1, OBJECT1 IS NOT BLOCK1;PURPOSE: (ON BLOCK1 OBJECT1)PLOT:PARALLEL BRANCH 1:GOALS: (CLEAR OBJECT1) BRANCH 2:GOALS: (CLEAR BLOCK1)END PARALLELPROCESS ACTION: PUTON; ARGUMENTS: BLOCK1,OBJECT1 RESOURCES: BLOCK1 EFFECTS: (ON BLOCK1 OBJECT1)END PLOTEND OPERATORExcerpt taken from http://www.ai.sri.com/~sipe/blocks-sipe.txtImage taken from http://www.ai.sri.com/~sipe/sussman-derivation.htmlSussman AnomalyExcerpt from SIPE-2Blocksworld DefinitionHTN operator representation•Russell & Norvig explicitly represent causal links; these can also be computed dynamically by using a model of preconditions and effects (this is what SIPE-2 does)•Dynamically computing causal links means that actions from one operator can safely be interleaved with other operators, and subactions can safely be removed or replaced during plan repair•Russell & Norvig’s representation only includes variable bindings, but more generally we can introduce a wide array of variable constraintsTruth criterion•Determining whether a formula is true at a particular point in a partially ordered plan is, in the general case, NP-hard•Intuition: there are exponentially many ways to linearize a partially ordered plan•In the worst case, if there are N actions unordered with respect to each other, there are N! linearizations•Ensuring soundness of the truth criterion requires checking the formula under all possible linearizations•Use heuristic methods instead to make planning feasible•Check later to be sure no constraints have been violatedTruth criterion in SIPE-2•Heuristic: prove that there is one possible ordering of the actions that makes the formula true – but don’t insert ordering links to enforce that order•Such a proof is efficient–Suppose you have an action A1 with a precondition P–Find an action A2 that achieves P (A2 could be initial world state)–Make sure there is no action necessarily between A2 and A1 that negates P•Applying this heuristic for all preconditions in the plan can result in infeasible plansIncreasing expressivity•Conditional effects–Instead of having different operators for different conditions, use a single operator with conditional effects–Move (block1, from, to) and MoveToTable (block1, from) collapse into one Move (block1, from, to):•Op(ACTION: Move(block1, from, to),PRECOND: On (block1, from) ^ Clear (block1) ^ Clear (to)EFFECT: On (block1, to) ^ Clear (from) ^ ~On(block1, from) ^ ~Clear(to) when to≠Table•There’s a problem with this operator: can you spot what it is?•Negated and disjunctive goals•Universally quantified preconditions and effectsReasoning about resources•Introduce numeric variables that can be used as measures•These variables represent resource quantities, and change over the course of the plan•Certain actions may produce (increase the quantity of) resources•Other actions may consume (decrease the quantity of) resources•More generally, may want different types of resources–Continuous vs. discrete–Sharable vs. nonsharable–Reusable vs. consumable vs. self-replenishingOther real-world planning issues•Conditional planning•Partial