Fragment-Based Conformant Planning James Kurien Palo Alto Research Center Pandu NayakStratify, Inc. David E. SmithNASA Ames Research Center

Motivation: Planning for Spacecraft Recovery ClosedOpen 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

Conformant Planning Problem Instance –Let Domain be a description of a planning domain –Let Worlds be a set of initial states of the domain, {w 1, w 2, … w n } –Let G be a goal description –There are no sensing actions Task: Find plan P that applied to any w i results in a state entailing G P is a conformant plan Challenge: Actions chosen in w i may have undesirable effects in w j P w1,w2,…wnw1,w2,…wn G

Existing Approaches to Conformant Planning Generate a plan in w i and test if it achieves G in all Worlds CGPSmith & Weld 1998Graphplan over multiple plan graphs CMBPCimatti & Roveri 1999BDD representation of belief state GPTBonet & Geffner 2001Heuristic search in space of belief states HSCPBertoli, Cimatti & Roveri 2001BDD + heuristic search CPlanCastellini, Giunchiglia & Tachella 2001 SAT encoding determines possible plans which must be checked Select actions for P by considering all Worlds simultaneously

An Observation on Conformant Plans Plan Step Action 1Dunk p3 2Flush 3Dunk p2 4Flush 5Dunk p1 6Flush 7Dunk p6 8Flush 9Dunk p4 10Flush 11Dunk p5 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)

An Observation on Conformant Plans 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 Plan Step Action 1Dunk p3 2Flush 3Dunk p2 4Flush 5Dunk p1 6Flush 7Dunk p6 8Flush 9Dunk p4 10Flush 11Dunk p5 Bomb in the Toilet 6 packages, 1 toilet Fragment if bomb in p1

An Observation on Conformant Plans 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 Plan Step Action 1Dunk p3 2Flush 3Dunk p2 4Flush 5Dunk p1 6Flush 7Dunk p6 8Flush 9Dunk p4 10Flush 11Dunk p5 Bomb in the Toilet 6 packages, 1 toilet Fragment if bomb in p1 Fragment if bombs in p6 and p4

An Observation on Conformant Plans 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 Plan Step Action 1Dunk p3 2Flush 3Dunk p2 4Flush 5Dunk p1 6Flush 7Dunk p6 8Flush 9Dunk p4 10Flush 11Dunk p5 Bomb in the Toilet 6 packages, 1 toilet Fragment if bombs in p6 and p4 Fragment if bomb in p1 Repair action to unify fragments

An Observation on Conformant Plans 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 Plan Step Action 1Dunk p3 2Flush 3Dunk p2 4Flush 5Dunk p1 6Flush 7Dunk p6 8Flush 9Dunk p4 10Flush 11Dunk p5 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-based Conformant Planning Intuition For each w i in Worlds 1. Generate a plan for Domain to achieve G in w i 2. Add the planned actions to Domain Step 2 ensures the plan for w i+1 includes the actions that achieved G in {w 1 … w i }

Fragment-based Conformant Planning Plan Step Plan for p1 1Dunk p Planning Process

Fragment-based Conformant Planning Plan Step Plan for p1 Fragments for p2 plan 1Dunk p Planning Process

Fragment-based Conformant Planning Plan Step Plan for p1 Fragments for p2 plan Plan for {p1,p2} 1Dunk p1 2 3Flush 4 5Dunk p2 Planning Process

Fragment-based Conformant Planning Plan Step Plan for p1 Fragments for p2 plan Plan for {p1,p2} Extracted fragment 1Dunk p1 2 3Flush 4 5Dunk p2 Planning Process

Fragment-based Conformant Planning Plan Step Plan for p1 Fragments for p2 plan Plan for {p1,p2} Extracted fragment Fragments for p3 plan 1Dunk p1 2 3Flush 4 5Dunk p2 Planning Process

Fragment-based Conformant Planning Plan Step Plan for p1 Fragments for p2 plan Plan for {p1,p2} Extracted fragment Fragments for p3 plan Plan for {p1,p2,p3} 1Dunk p1 2Flush 3 Dunk p3 4Flush 5Dunk p2 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

The FragPlan Algorithm completed=  While (Worlds   ) select and remove world w i from Worlds Choose a plan P i for Domain that achieves G in w i Fail if P i doesn’t achieve G for all w  completed Extract fragment F i from P i Domain = Domain + F i add w i to completed Return P i

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 P i for w i Bubbling –Find difficult worlds. Solve first by moving them up the stack. w1w1 F1F2F3 w3w3 F1F2F3 w2w2 F1F2F3 W 1 fragments First world selected

Implementation 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 Essentially conformant BlackBox (Kautz & Selman 99) Graph Builder Graph to WFF SAT (satz) WFF Plan Graph BlackBox Planning Domain Plan P i Fragments wiwi PDDL Worlds Specification Fragment Extraction Search Control FragPlan Conformant Plan

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

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

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

FragPlan Performance on Many Worlds Independent sources of uncertainty yield many 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 – N rooms with window open, closed or locked  3 n worlds ( NKNK ) – K bombs in N packages  worlds

Handling Non-Deterministic Actions Action A has n possible outcomes Disjunction doesn’t ensure conformance A Effect 1 Effect 2 or Worlds {w 1 w 2 }

Handling Non-Deterministic Actions Action A has n possible outcomes Disjunction doesn’t ensure conformance A Effect 1 Effect 2 or Worlds {w 1 w 2 } Worlds {w 1,P w 1,P w 2,P w 2,P } A’ Effect 1 Effect 2 P P

Handling Non-Deterministic Actions Action A has n possible outcomes Disjunction doesn’t ensure conformance A Effect 1 Effect 2 or Worlds {w 1 w 2 } Worlds {w 1,P w 1,P w 2,P w 2,P } A’ Effect 1 Effect 2 P P Algorithm changes –Implement conditional effects –Generate plan P i for one execution in w i using A –Substitute A’/A in P i. –Split completed worlds and w i –Check P i in all worlds, as before

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

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 Initial State Uncertainty Internal actions are fairly reliable Systems are complex Observability is limited Failures yield multiple diagnoses ClosedOpen Stuck Valve

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, {w 1, w 2, … w n } –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) ->  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?

SCOPE – Safe, Conformant, Optimizing Planning Engine Approach: Manipulate the scope of the problem While (Time  0) select constraints from {G  S  Worlds} FragPlan(constraints)

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

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

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