FragmentBased Conformant Planning

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Fragment-Based Conformant Planning

• James Kurien Palo Alto Research Center
• Pandu Nayak Stratify, Inc.
• David E. Smith NASA Ames Research Center

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Motivation Planning for Spacecraft Recovery
Closed
Open
Stuck
Valve

• System failures lead to uncertainty
• Internal actions are fairly reliable but do fail
• System interactions are complex
• Observability is limited
• Diagnosis yields multiple states ranked by
  magnitude of probability
• The system must choose actions to respond to the
  failure
• Under certain conditions an action may be
  damaging or disallowed

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Conformant Planning

• Problem Instance
• Let Domain be a description of a planning domain
• Let Worlds be a set of initial states of the
  domain, w1, w2, wn
• Let G be a goal description
• There are no sensing actions
• Task Find plan P that applied to any wi results
  in a state entailing G
• P is a conformant plan
• Challenge Actions chosen in wi may have
  undesirable effects in wj

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Existing Approaches to Conformant Planning

• Select actions for P by considering all Worlds
  simultaneously

• Generate a plan in wi and test if it achieves G
  in all Worlds

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An Observation on Conformant Plans
Bomb in the Toilet 6 packages, 1 toilet

• Example Domain Bomb in the Toilet
• Set of N packages, p1 through pN
• Packages may have bombs (1, many, a subset)
• Bombs defused by dunking the package in the
  toilet
• The toilet must be flushed before dunking again

• Example Problem
• 1 toilet
• 6 packages
• A bomb is in p1, p2, p3, p5 or (p4 p6)

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An Observation on Conformant Plans
Bomb in the Toilet 6 packages, 1 toilet

• Example Domain Bomb in the Toilet
• Set of N packages, p1 through pN
• Packages may have bombs (1, many, a subset)
• Bombs defused by dunking the package in the
  toilet
• The toilet must be flushed before dunking again

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An Observation on Conformant Plans
Bomb in the Toilet 6 packages, 1 toilet

• Example Domain Bomb in the Toilet
• Set of N packages, p1 through pN
• Packages may have bombs (1, many, a subset)
• Bombs defused by dunking the package in the
  toilet
• The toilet must be flushed before dunking again

• Fragment if bomb in p1

• Fragment if bombs in p6 and p4

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An Observation on Conformant Plans
Bomb in the Toilet 6 packages, 1 toilet

• Example Domain Bomb in the Toilet
• Set of N packages, p1 through pN
• Packages may have bombs (1, many, a subset)
• Bombs defused by dunking the package in the
  toilet
• The toilet must be flushed before dunking again

• Fragment if bomb in p1

• Repair action to unify fragments

• Fragment if bombs in p6 and p4

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An Observation on Conformant Plans
Bomb in the Toilet 6 packages, 1 toilet

• Example Domain Bomb in the Toilet
• Set of N packages, p1 through pN
• Packages may have bombs (1, many, a subset)
• Bombs defused by dunking the package in the
  toilet
• The toilet must be flushed before dunking again

• Every conformant plan P must contain a fragment
  that achieves the goal in each world
• Each world has plans that are fragments of some P
• Approach
• Grow a set of fragments into a conformant plan

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Fragment-based Conformant Planning

• Intuition

• For each wi in Worlds
• Generate a plan for Domain to achieve G in wi
• Add the planned actions to Domain

• Step 2 ensures the plan for wi1 includes the
  actions that achieved G in w1 wi

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Fragment-based Conformant Planning
Planning Process
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Fragment-based Conformant Planning
Planning Process
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Fragment-based Conformant Planning
Planning Process
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Fragment-based Conformant Planning
Planning Process
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Fragment-based Conformant Planning
Planning Process
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Fragment-based Conformant Planning
Planning Process

• Search will be required
• The fragment chosen for w1 may not allow a plan
  for w2
• The fragment chosen for w2 may disrupt the plan
  for w1

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The FragPlan Algorithm
completed? While (Worlds ? ?) select and remove
world wi from Worlds Choose a plan Pi for
Domain that achieves G in wi Fail if Pi doesnt
achieve G for all w ?completed Extract fragment
Fi from Pi Domain Domain Fi add wi to
completed Return Pi
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Search Strategies

• Chronological Backtracking
• Probing
• Extend fragments to as many worlds as possible,
  then restart
• On failure, discard all fragments and empty
  completed
• Effective even when a small subset of worlds are
  very difficult
• Fits well with deterministic planner we use to
  choose Pi for wi
• Bubbling
• Find difficult worlds. Solve first by moving them
  up the stack.

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Implementation

• Essentially conformant BlackBox (Kautz Selman
  99)

FragPlan
Worlds Specification
Conformant Plan
wi
Fragments
Plan Pi
Planning Domain
PDDL

• No actions with conditional outcomes in current
  implementation
• Planning graph cannot represent conditional
  outcome
• Conditional extension (Gazen Knoblock 1997) not
  applicable
• No non-deterministic actions

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Experimental Setup

• FragPlan tested on a number of domains
• Several variations of the bomb in the toilet
  problem
• Modified ringworld with no uncertain outcomes
• Logistics domain with uncertainty
• Compared to performance quoted in the literature
• CMBP, C-Plan, GTP from (Castellini, Giunchiglia,
  Tacchella 2001)
• HSCP from (Bertoli, Cimatti, Roveri 2001)
• FragPlan performance averaged over 30 probing
  runs

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Performance on Bomb in the Toilet Problems

• HSCP dominates on serial instances
• FragPlan is balanced
• HSCP, CMBP, GPT do not produce parallel plans
• C-Plan does poorly on serial instances of this
  problem

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10 Package Bomb in the Toilet with Parallelism

• Space of serialized plans explodes as parallelism
  increases
• Parallelism renders fragments independent,
  yielding linear speedup

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FragPlan Performance on Many Worlds

• Independent sources of uncertainty yield many
  worlds

• K bombs in N packages ? worlds

• N rooms with window open, closed or locked ? 3n
  worlds

• Less planning, more checking
• Fragment for n independent events is often a plan
  for each
• If n is high, a few fragments yield a conformant
  plan.
• In effect the plan is only checked on the
  remaining worlds
• Constant space usage, except for fragments

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Handling Non-Deterministic Actions

• Action A has n possible outcomes
• Disjunction doesnt ensure conformance

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Handling Non-Deterministic Actions

• Action A has n possible outcomes
• Disjunction doesnt ensure conformance

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Handling Non-Deterministic Actions

• Action A has n possible outcomes
• Disjunction doesnt ensure conformance

• Algorithm changes
• Implement conditional effects
• Generate plan Pi for one execution in wi using A
• Substitute A/A in Pi .
• Split completed worlds and wi
• Check Pi in all worlds, as before

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Message

• Performs well on both serial and parallel
  problems
• More scalable than other possible worlds
  approaches
• Memory usage is constant as the number of worlds
  increases
• Computation is less susceptible to explosive
  growth
• Probing is effective
• Constructive approach
• Always have a plan
• Conformance increases in an anytime manner
• Can delete and add worlds and re-use partial
  results

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Motivation Planning for Spacecraft Recovery

• Complex Plan Utility Function
• No safe, conformant plan may exist
• Safety always desired, often dominates
• Certain goals dominate at critical junctures
• A failure may force all actions to be unsafe
• Time for planning not known a priori
• We must have some plan

Given Utility function on goals, safety, and
worlds Return Best plan the available time
allows
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Safe, Conformant Planning with Optimization

• Problem Instance
• Let Domain be a description of a planning domain
• Let Worlds be a set of initial states of the
  domain, w1, w2, wn
• Let G be a set of goals
• Let S be a set of safety constraints
• Let U be a function from (world x goal x safety)
  -gt ?
• Task
• Find a plan P with highest U (in available time)
• Challenge
• Which subsets of G ? S ? Worlds admit a plan?
• Will we have a plan when time runs out?

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SCOPE Safe, Conformant, Optimizing Planning
Engine

• Approach Manipulate the scope of the problem

While (Time ? 0) select constraints from G ? S ?
Worlds FragPlan(constraints)
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SCOPE Safe, Conformant, Optimizing Planning
Engine

• Approach Manipulate the scope of the problem

While (Time ? 0) select constraints from G ? S ?
Worlds FragPlan(constraints) for some time
Balance solving current constraints vs.
exploration
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SCOPE Safe, Conformant, Optimizing Planning
Engine

• Approach Manipulate the scope of the problem

While (Time ? 0) select constraints from G ? S ?
Worlds FragPlan(constraints) for some time

• Strategy Start small and grow
• On success, add constraints guided by U(world x
  goal x safety)
• Anytime

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SCOPE Safe, Conformant, Optimizing Planning
Engine

• Approach Manipulate the scope of the problem

While (Time ? 0) select constraints from G ? S ?
Worlds FragPlan(constraints) for some time

• Strategy Start small and grow
• On success, add constraints guided by U(world x
  goal x safety)
• Anytime

• Strategy Start big, shrink
• Failures reveal difficult constraint combinations
• On failure, remove constraints guided by U,
  difficulty