Using Abstraction to Coordinate Multiple Robotic Spacecraft

1
Using Abstraction to Coordinate Multiple Robotic
Spacecraft

• Brad Clement, Tony Barrett, Gregg
  RabideauArtificial Intelligence GroupJet
  Propulsion Laboratory
• California Institute of Technology
• clement, barrett, rabideau_at_aig.jpl.nasa.gov

Ed DurfeeArtificial Intelligence LabUniversity
of Michigan durfee_at_umich.edu
2
Automated Planning/Scheduling

• Choose and order actions that take robot(s) from
  current state to goal state
• Decompose abstract tasks/goals into detailed
  actions

Current State
Goal State
goal
goal
subgoal
subgoal
3
Planning at Abstract Levels

• Resolve conflicts at high level to minimize
  search time and preserve decomposition choices
• Better solutions may exist at lower levels

crisper solutions
lowerplanningcost
planning levels
flexibility
4
Motivation

• Hierarchical refinement search can reduce the
  search space exponentially when there is no need
  to backtrack up the hierarchy. (Korf 87,
  Knoblock 91)
• Planning problems often have interacting goals
  such that backtracking is necessary.
• By summarizing the state constraints of an
  abstract tasks refinement, an HTN style planner
  can reduce the search space exponentially.
  (Clement Durfee 2000)
• Show that any planner or scheduler can reap the
  benefits of abstraction.
• Apply this work to metric resources in an
  iterative repair planner (ASPEN).

5
Motivation

• Hierarchical plans also exploited by robust
  execution systems (PRS, RAPS, etc.)
• Reasoning about plans at multiple levels of
  abstraction is natural for situated planning
  systems
• human interaction
• continual planning
• coordination across planners

6
Contributions

• Algorithm summarizing metric resource usage for
  abstract activities based on their decompositions
• Complexity analyses showing that scheduling is
  exponentially cheaper at higher levels of
  abstraction using summary information
• Experiments in a multi-rover domain that support
  the analyses
• Search techniques for directing the refinement of
  activities in an iterative repair planner that
  further improve performance

7
Resource Usage
interval of task

• Depletable resource
• usage carries over after end of task
• gas gas - 5
• Non-depletable
• usage is only local
• zero after end of task
• machines machines - 2
• Replenishing a resource
• negative usage
• gas gas 10
• can be depletable or non-depletable

8
Mars Rover
3
D
A
B
C
1
2
F
E
morning activities
sunbathe
move(A, B)
soak raysuse 4W 20 min
soak raysuse 6W 20 min
low path
high path
soak raysuse 5W 20 min
middle path
go(2,B) use 12W 20 min
go(A,1) use 6W 10 min
go(A,B) use 8W 50 min
go(A,3) use 8W 15 min
go(3,B) use 12W 25 min
go(1,2) use 6W 10 min
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Summarizing Resource Usage
soak rays
soak rays
soak rays
soak rays
soak rays
soak rays
soak rays
soak rays
soak rays
-4
-5
-6
-4
-5
-6
-4
-5
-6
low
medium
high
6
6
12
8
8
12
-4
2
7
0
2
1
6
-6
-4
0
4
3
2
-6
-4
3
7
0
4
6
-6
Battery power usage for three possible
decompositions
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Summarizing Resource Usage

• summarized resource usage ?
• lt local_min_range, local_max_range,
  persist_range gt
• Captures uncertainty of decomposition choices and
  temporal uncertainty of partially ordered actions
• Can be used to determine if a resource usage may,
  must, or must not cause a conflict

40
30
20
10
0
-7
-20
lt -20, -7,30, 40,10, 20 gt
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Resource Summarization Algorithm

• Can be run offline for a domain model
• Run separately for each resource
• Recursive from leaves up hierarchy
• Summarizes parent from summarizations of
  immediate children
• Considers all legal orderings of children
• Considers all subintervals where upper and lower
  bounds of childrens resource usage may be
  reached
• Exponential with number of immediate children, so
  summarization is really constant for one resource
  and O(r) for r resources

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Resource Summarization Algorithm
lt0,53,60,6gt
OR
lt2,33,43,4gt
lt0,53,60,6gt
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Resource Summarization Algorithm
Serial AND
lt0,53,60,6gt
lt2,33,43,4gt
lt0,53,103,10gt
14
Resource Summarization Algorithm
Parallel AND
lt0,53,60,6gt
lt2,33,43,4gt
lt2,95,63,10gt
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Resource Summarization Algorithm

• for each consistent ordering of endpoints
• for each subtask/subinterval summary usage
  assignment
• use Parallel-AND to combine subtask/subinterval
  usages by subinterval
• use Serial-AND over the chain of subintervals
• use OR computation to combine profiles

Each iterationgenerates a profile
16
Complexity Analyses

• Iterative repair planners (such as ASPEN)
  heuristically pick conflicts and resolve them by
  moving activities and choosing alternative
  decompositions of abstract activities.
• Moving an activity hierarchy to resolve a
  conflict is O(vnc2) for v state or resource
  variables, n hierarchies in the schedule, and c
  constraints in hierarchy per variable.
• Summarization can collapse the constraints per
  variable making c smaller.
• In the worst case, where no constraints are
  collapsed because they are over different
  variables, the complexity of moving activity
  hierarchies at different levels of expansion is
  the same.

level
branchingfactor b
0
1
. . .
d
1
2
n
c constraintsper hierarchy
vvariables
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Complexity Analyses
level
branchingfactor b
0
1
. . .
d
1
2
n
c constraintsper hierarchy
vvariables

• In the other extreme, where constraints are
  always collapsed when made for the same variable,
  the number of constraints c is the same as the
  number of activities and grows bi for b children
  per activity and depth level i. Thus, the
  complexity of scheduling operations grows
  O(vnb2i).
• Along another dimension, the number of temporal
  constraints that can cause conflicts during
  scheduling grows exponentially (O(bi)) with the
  number of activities as hierarchies are expanded.
• In addition, by using summary information to
  prune decomposition choices with greater numbers
  of conflicts, exponential computation is avoided.
• Thus, reasoning at abstract levels can resolve
  conflicts exponentially faster.

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Decomposition Strategies

• Level expansion
• repair conflicts at current level of abstraction
  until conflicts cannot be further resolved
• then decompose all activities to next level and
  begin repairing again
• Expand most threats first (EMTF)
• instead of moving activity to resolve conflict,
  decompose with some probability (decomposition
  rate)
• expands activities involved in greater numbers of
  conflicts (threats)
• Relative performance of two techniques depends
  decomposition rate selected for EMTF

19
Decomposition Strategies

• FTF (fewest-threats-first) heuristic tests each
  decomposition choice and picks those with fewer
  conflicts with greater probability.

rover_move
path1
path2
path3
10 conflicts
20 conflicts
15 conflicts
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Multi-Rover Domain

• 2 to 5 rovers
• Triangulated field of 9 to 105 waypoints
• 6 to 30 science locations assigned according to a
  multiple travelling salesman algorithm
• Rovers plans contain 3 shortest path choices to
  reach next science location
• Paths between waypoints have capacities for a
  certain number of rovers
• Rovers cannot be at same location at the same
  time
• Rovers cannot cannot cross a path in opposite
  directions at the same time
• Rovers communicate with the lander over a shared
  channel for telemetry--different paths require
  more bandwidth than others

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Experiments using ASPEN for a Multi-Rover Domain

• Performance improves greatly when activities
  share a common resource.

Rarely shared resources (only path variables)
Mix of rarely shared (paths) and often
shared(channel) resources
Often shared (channel) resource only
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Experiments using ASPEN for a Multi-Rover Domain

• CPU time required increases dramatically for
  solutions found at increasing depth levels.

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Experiments in ASPEN for a Multi-Rover Domain

• Picking branches that result in fewer conflicts
  (FTF) greatly improves performance.
• Expanding activities involved in greater numbers
  of conflictsis better than level-by-level
  expansion when choosing a proper rate of
  decomposition

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Summary

• Algorithm summarizing metric resource usage for
  abstract activities based on their decompositions
• Complexity analyses showing that scheduling
  operations are exponentially cheaper at higher
  levels of abstraction when summarizing activities
  collapses state/resource constraints and temporal
  constraints
• Experiments in multi-rover domain support
  analyses
• Reasoning at abstract levels is wasteful when
  hierarchies must be fully expanded and OR branch
  selection is not important
• Search techniques for directing the refinement of
  activities further improve performance

25
Future Work

• How does abstract reasoning affect plan quality
  when using iterative repair?
• How should complex resources be abstracted?
• resource usage functions
• window variables
• geometrical constraints
• volatile objects (file system)
• What is the effect of abstracting over resource
  classes?
• What are efficient protocols for coordinating a
  group of agents plans continually?