FragmentBased Conformant Planning - PowerPoint PPT Presentation

1 / 33
About This Presentation
Title:

FragmentBased Conformant Planning

Description:

The system must choose actions to respond to the failure ... Smith & Weld 1998. SAT encoding determines possible plans which must be checked ... – PowerPoint PPT presentation

Number of Views:21
Avg rating:3.0/5.0
Slides: 34
Provided by: jamesk67
Category:

less

Transcript and Presenter's Notes

Title: FragmentBased Conformant Planning


1
Fragment-Based Conformant Planning
  • James Kurien Palo Alto Research Center
  • Pandu Nayak Stratify, Inc.
  • David E. Smith NASA Ames Research Center

2
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

3
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

4
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

5
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)

6
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

7
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

8
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

9
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

10
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

11
Fragment-based Conformant Planning
Planning Process
12
Fragment-based Conformant Planning
Planning Process
13
Fragment-based Conformant Planning
Planning Process
14
Fragment-based Conformant Planning
Planning Process
15
Fragment-based Conformant Planning
Planning Process
16
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

17
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
18
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.

19
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

20
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

21
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

22
10 Package Bomb in the Toilet with Parallelism
  • Space of serialized plans explodes as parallelism
    increases
  • Parallelism renders fragments independent,
    yielding linear speedup

23
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

24
Handling Non-Deterministic Actions
  • Action A has n possible outcomes
  • Disjunction doesnt ensure conformance

25
Handling Non-Deterministic Actions
  • Action A has n possible outcomes
  • Disjunction doesnt ensure conformance

26
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

27
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

28
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
29
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?

30
SCOPE Safe, Conformant, Optimizing Planning
Engine
  • Approach Manipulate the scope of the problem

While (Time ? 0) select constraints from G ? S ?
Worlds FragPlan(constraints)
31
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
32
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

33
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
Write a Comment
User Comments (0)
About PowerShow.com