Practical Planning: Scheduling and Hierarchical Task Networks

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Practical PlanningScheduling and Hierarchical
Task Networks
CS 63

• Chapter 12.1-12.2

Adapted from slides by Tim Finin and Marie
desJardins.
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Outline

• Intelligent scheduling
• Hierarchical task network (HTN) planning
• Increasing expressivity

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Real-world planning domains

• Real-world domains are complex and dont 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!
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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 cant always be separated

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Hierarchical 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
  agents goals are another agents actions!

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HTN operator Example

• OPERATOR decompose
• PURPOSE Construction
• CONSTRAINTS
• Length (Frame) lt Length (Foundation),
• Strength (Foundation) gt Wt(Frame) Wt(Roof)
• Wt(Walls) Wt(Interior) Wt(Contents)
• PLOT Build (Foundation)
• Build (Frame)
• PARALLEL
• Build (Roof)
• Build (Walls)
• END PARALLEL
• Build (Interior)

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HTN planning example
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SIPE-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 execution

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SIPE-2
Image from http//www.ai.sri.com/sipe/architectu
re.html
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Blocksworld in SIPE-2
Excerpt from SIPE-2 Blocksworld Definition
Sussman Anomaly

• 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 PREDICATES
• STOP
• OPERATOR PUTON1
• ARGUMENTS BLOCK1, OBJECT1 IS NOT BLOCK1
• PURPOSE (ON BLOCK1 OBJECT1)
• PLOT
• PARALLEL
• BRANCH 1

Excerpt taken from http//www.ai.sri.com/sipe/blo
cks-sipe.txt Image taken from http//www.ai.sri.co
m/sipe/sussman-derivation.html
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HTN 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 Norvigs representation only includes
  variable bindings, but more generally we can
  introduce a wide array of variable constraints

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Truth 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
  violated

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Truth criterion in SIPE-2

• Heuristic prove that there is one possible
  ordering of the actions that makes the formula
  true but dont 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 plans

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Increasing 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
• Theres a problem with this operator can you
  spot what it is?
• Negated and disjunctive goals
• Universally quantified preconditions and effects

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Reasoning 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-replenishing

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Other real-world planning issues

• Conditional planning
• Partial observability
• Information gathering actions
• Execution monitoring and replanning
• Continuous planning
• Multi-agent (cooperative or adversarial) planning

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SATPlan
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SATPlan

• Formulate the planning problem as a CSP
• Assume that the plan has k actions
• Create a binary variable for each possible action
  a
• Action(a,i) (TRUE if action a is used at step i)
• Create variables for each proposition that can
  hold at different points in time
• Proposition(p,i) (TRUE if proposition p holds at
  step i)

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Constraints

• Only one action can be executed at each time step
  (XOR constraints)
• Constraints describing effects of actions
• Persistence if an action does not change a
  proposition p, then ps value remains unchanged
• A proposition is true at step i only if some
  action (possibly a maintain action) made it true
• Constraints for initial state and goal state

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Now apply our favorite CSP solver!
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Planning summary

• Planning representations
• Situation calculus
• STRIPS representation Preconditions and effects
• Planning approaches
• State-space search (STRIPS, forward chaining, .)
• Plan-space search (partial-order planning, HTN,
  )
• Constraint-based search (GraphPlan, SATplan, )
• Search strategies
• Forward planning
• Goal regression
• Backward planning
• Least-commitment
• Nonlinear planning

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Applications of Planning

• Military operations
• Autonomous space operations
• Construction tasks
• Machining tasks
• Mechanical assembly
• Design of experiments in genetics
• Command sequences for satellite

Most applied systems use extended representation
languages, nonlinear planning techniques, and
domain-specificheuristics
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Oil-Spill Response in SIPE-2
Image taken from http//www.ai.sri.com/sipe/oil.h
tml