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Information Sharing for Distributed Planning Prasanna Velagapudi AAMAS 2010 - Doctoral Symposium 1 Large Heterogeneous Teams 100s to 1000s of robots, agents, people Complex, collaborative tasks Dynamic, uncertain environment

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Information Sharing for Distributed Planning

Prasanna Velagapudi

AAMAS 2010 - Doctoral Symposium 1

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Large Heterogeneous Teams

  • 100s to 1000s of

robots, agents, people

  • Complex, collaborative

tasks

  • Dynamic, uncertain

environment

  • Joint planning

intractable

AAMAS 2010 - Doctoral Symposium 2

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SLIDE 3

Scaling Team Planning

  • Independent planners: can’t account for

teammates

  • Existing work: needs specific structure or doesn’t

scale to these sizes

– DPC, Prioritized Planning – JESP, Factored MDP, ND-POMDP

3 AAMAS 2010 - Doctoral Symposium

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Iterated Distributed Planning

  • 1. Factor the problem, enumerate interactions
  • 2. Compute independent plans & potential interactions
  • 3. Exchange messages about interactions
  • 4. Use exchanged information, improve local model

4 AAMAS 2010 - Doctoral Symposium

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Iterated Distributed Planning

  • 1. Factor the problem, enumerate interactions
  • 2. Compute independent plans & potential interactions
  • 3. Exchange messages about interactions
  • 4. Use exchanged information, improve local model

5 AAMAS 2010 - Doctoral Symposium

?

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Iterated Distributed Planning

  • 1. Factor the problem, enumerate interactions
  • 2. Compute independent plans & potential interactions
  • 3. Exchange messages about interactions
  • 4. Use exchanged information, improve local model

6 AAMAS 2010 - Doctoral Symposium

?

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Iterated Distributed Planning

  • 1. Factor the problem, enumerate interactions
  • 2. Compute independent plans & potential interactions
  • 3. Exchange messages about interactions
  • 4. Use exchanged information, improve local model

7 AAMAS 2010 - Doctoral Symposium

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A Tale of Two Distributed Planners

Distributed Prioritized Planning (DPP) L-TREMOR

AAMAS 2010 - Doctoral Symposium 8

5 10 15 2 4 6 8 10 12 14 16 18

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Distributed Prioritized Planning

AAMAS 2010 - Doctoral Symposium 9

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Multiagent Path Planning

5 10 15 2 4 6 8 10 12 14 16 18

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Start Goal

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Multiagent Path Planning

5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40

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Prioritized Planning

  • Assign priorities to agents based on path length

AAMAS 2010 - Doctoral Symposium 12

[van den Berg, et al 2005]

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Prioritized Planning

  • Plan from highest priority to lowest priority
  • Use previous agents as dynamic obstacles

AAMAS 2010 - Doctoral Symposium 13

[van den Berg, et al 2005]

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Distributed Prioritized Planning

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Parallelizable & Equivalent

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Large-Scale Path Solutions

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Large-Scale Path Solutions

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50 100 150 200 5 10 15 Number of robots Number of sequential planning iterations

DPP Results

Fewer Sequential Plans

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50 100 150 200 5 10 15 Number of robots Number of sequential planning iterations 50 100 150 200 1 2 3 4 5 Number of robots Proportion of centralized planning time

DPP Results

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Longer Planning Time Fewer Sequential Plans

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SLIDE 19
  • Prioritized Planning
  • DPP

Why does this happen?

A B C D A B C D Longest planning agents might replan multiple times Individual agent planning times varied by >2 orders of magnitude

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Solution 2: Incremental Planning Solution 1: Prioritize by plan time?

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Summary of DPP

  • Observable, certain world
  • Only one type of interaction: collision
  • Far fewer sequential planning iterations
  • Incremental planning may reduce execution time

AAMAS 2010 - Doctoral Symposium 20

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L-TREMOR

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A Simple Rescue Domain

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Rescue Agent Cleaner Agent Narrow Corridor Victim Unsafe Cell Clearable Debris

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A Simple (Large) Rescue Domain

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Distributed POMDP with Coordination Locales (DPCL)

  • Often, interactions between agents are sparse

AAMAS 2010 - Doctoral Symposium 24

Only fits one agent Passable if cleaned

[Varakantham, et al 2009]

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Distributed POMDP with Coordination Locales (DPCL)

  • Define coordination locales (CLs) where POMDP

model functions are not independent:

AAMAS 2010 - Doctoral Symposium 25

[Varakantham, et al 2009]

<S, A, Ω, P, R, O>

(states) (actions) (obs.) (transition)(reward)(obs. fn)

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Distributed POMDP with Coordination Locales (DPCL)

  • Define coordination locales (CLs) where POMDP

model functions are not independent:

AAMAS 2010 - Doctoral Symposium 26

[Varakantham, et al 2009]

S1, A1 S2, A2 Sglobal R1, P1, O1 R2, P2, O2

Outside CL: (typical)

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Distributed POMDP with Coordination Locales (DPCL)

  • Define coordination locales (CLs) where POMDP

model functions are not independent:

AAMAS 2010 - Doctoral Symposium 27

[Varakantham, et al 2009]

S1, A1 S2, A2 Sglobal R12, P12, O12

Inside CL: (interaction)

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TREMOR

28 AAMAS 2010 - Doctoral Symposium Role Allocation Policy Solution Interaction Detection Coordination

TREMOR

Branch & Bound MDP Independent EVA[3] solvers Joint policy evaluation Reward shaping

  • f independent

models

[Varakantham, et al 2009]

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L-TREMOR

29 AAMAS 2010 - Doctoral Symposium Role Allocation Policy Solution Interaction Detection Coordination

TREMOR

Branch & Bound MDP Independent EVA[3] solvers Joint policy evaluation Reward shaping

  • f independent

models

L-TREMOR

Decentralized Auction Sampling & message passing

Distributed & Parallelizable

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Preliminary Results – Joint Utility

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5 10 15 20 50 40 30 20 10 10 20 30 Iteration Empirical Joint Reward LTREMOR Independent 5 10 15 20 50 100 150 200 250 Iteration Empirical Joint Reward LTREMOR Independent 2 4 6 8 10 12 750 800 850 900 950 1000 1050 Iteration Empirical Joint Reward LTREMOR Independent

N = 6 N = 10 N = 100 (structurally similar to N=10)

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Preliminary Results – Timing

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2 4 6 8 10 12 14 16 18 20 5 10 15 20 25 30 35 40 45 50 Iteration Planning Time per Agent (s) n = 5, complex n = 10, tall n = 100, tall

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Preliminary Results – Model Accuracy

AAMAS 2010 - Doctoral Symposium 32

100 100 200 300 400 150 100 50 50 100 Error between actual and expected value Improvement over independent policy n = 5, complex n = 10, tall n = 100, tall

R = 0.804

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Current Issues

  • Oscillations in solutions
  • Discovery of relevant locales

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?

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Summary of L-TREMOR

  • Partially-observable, uncertain world
  • Multiple types of interactions
  • Role-allocation of tasks
  • Improvement over independent planning
  • Handles large problems
  • Next steps: improving convergence

AAMAS 2010 - Doctoral Symposium 34

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Conclusions

  • Two approaches to distributed planning

– DPP: approaching centralized performance – L-TREMOR: exceeding joint tractability

  • Analogous strategies for distributing planning

– Both iterate independent planners – Both exchange messages about states, actions

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Future Work

  • Generalized framework for distributed planning

through iterative message exchange

  • Reduce necessary communication
  • Better search over task allocations
  • Scaling to larger team sizes

36 AAMAS 2010 - Doctoral Symposium