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Time-Independent Planning for Multiple Moving Agents

Time-Independent Planning for Multiple Moving Agents

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  1. Time-Independent Planning for Multiple Moving Agents Keisuke Okumura, Yasumasa Tamura

    & Xavier Defago Feb. 2–9, 2021 Tokyo Institute of Technology, Japan ౦ژ޻ۀେֶ 5PLZP*OTUJUVUFPG5FDIOPMPHZ virtual conference AAAI-21
  2. /44 2 MAPF: Multi-Agent Path Finding given agents (starts) graph

    goals solution paths without collisions
  3. /44 3 Applications YouTube/Mind Blowing Videos Twitter/@PDChina Twitter/@knaohiro1

  4. /44 4 Planning 1 2 1 2 3 4 Execution

    assume that agents move synchronously
  5. /44 5 Imperfect Execution 1 2 1 2 3 4

    delay reality gap reality is asynchronous
  6. /44 6 Execution Policies [Ma+ AAAI-17] Fully Synchronized Policies Minimum

    Communication Policies wait check temporal dependencies 1 2 1 2 3 4 => preserved, go arrival time: 3 arrival time: 2
  7. /44 7 move very slowly / crash Minimum Communication Policies

    check temporal dependencies 1 2 1 2 3 4 => violate, wait Still Vulnerable to Delays
  8. /44 8 1 2 1 2 3 4 1 2

    3 4 5 6 delay negative effect typical MAPF instance (without delays) 60 agents, solved by PIBT huge potential for unexpected interference
  9. /44 9 We propose an alternative approach: Time-Independent Planning define

    time-independent model: represent reality as a transition system Causal-PIBT, based on an MAPF solver PIBT [Okumura+ IJCAI-19] offline MAPF plan + online execution by Causal-PIBT validated in MAPF with Delay Probabilities [Ma+ AAAI-17] online & distributed without any timing-assumptions
  10. /44 10 given agents (starts) graph goals termination execution model?

  11. /44 11 Time-Independent Model inspired by models on theoretical distributed

    algorithms c.f., [Tel, 2000]
  12. /44 12 agent transition system reality transition system consisting of

    transition systems spontaneously change its state, e.g., location, destination, mode, internal variables change its configuration according to atomic actions of agents i.e., agents
  13. /44 13 Mode & Transition contracted requesting extended if unoccupied

    contracted
  14. /44 14 configuration 𝛾 configuration 𝛾′ agents execute atomic actions

    spontaneously without synchronization Activation contracted requesting extended if unoccupied state 𝜎 state 𝜎′
  15. /44 15 interaction transit atomically … … contracted requesting extended

    if unoccupied *address communication as a blackbox at most one agent is activated
  16. /44 16 strong termination all agents are on their goals

    weak termination all agents have been on their goals at least once weak termination strong termination
  17. /44 17 given agents (starts) graph goals termination execution challenge:

    design agents tolerant of all possible sequences of actions
  18. /44 18 Algorithms, Agents

  19. /44 19 Toy Example – GREEDY contracted requesting extended if

    unoccupied the nearest adjacent location to the goal deadlock We need a sophisticated one… never back
  20. /44 20 Causal-PIBT perform GREEDY enhanced by PIBT ensure weak

    termination
  21. /44 21 PIBT Priority Inheritance with Backtracking [Okumura+ IJCAI-19] solving

    MAPF iteratively quick & scalable adaptivity for decentralization 500 agents within 0.05 sec Applicable to Multi-agent Pickup & Delivery [Ma+ AAMAS-17] sub-optimal
  22. /44 22 How PIBT works – 1/5 repeat one-timestep prioritized

    planning high low mid stuck
  23. /44 23 How PIBT works – 2/5 high low mid

    as high priority inheritance [Sha+ 1990]
  24. /44 24 How PIBT works – 3/5 high as high

    as high as high as high stuck
  25. /44 25 How PIBT works – 4/5 invalid valid re-plan

    re-plan valid You can move invalid You must re-plan, I will stay introduce backtracking
  26. /44 26 In biconnected graphs the agent with highest priority

    can move to any adjacent locations all agents reach their goals within finite timesteps +dynamic priorities c.f. , weak termination How PIBT works – 5/5
  27. /44 27 Make PIBT Time-Independent child parent seen as DFST:

    depth first search tree root move
  28. /44 28 Concept of Causal-PIBT Find an empty location by

    the construction of DFST between agents, rooted at the agent with locally highest priority, by priority inheritance 1. Move all agents on the path from the root to the empty location 2. repeat until terminate + dynamic priorities In biconnected graphs with |A| < |V|, Causal-PIBT ensures weak termination
  29. /44 29 + reset params is activated – 1/5 Details:

    when +cut off parent & child contracted requesting extended if unoccupied
  30. /44 30 priority inheritance high low high low as high

    parent child high low high low as high parent child is activated – 2/5 Details: when contracted requesting extended if unoccupied
  31. /44 31 +cut off parent & child lower priority higher

    priority is activated – 3/5 Details: when contracted requesting extended if unoccupied
  32. /44 32 deadlock resolution ancestor stuck parent child backtracking invalid

    case +prohibit to back to is activated – 4/5 Details: when +prohibit to back to contracted requesting extended if unoccupied
  33. /44 33 stuck child parent &root cut off child +reset

    params is activated – 5/5 Details: when stuck activated cut off parent & child
  34. /44 34 Planning 1 2 1 2 3 4 Execution

    Time-Independent Model Causal-PIBT enhance offline online
  35. /44 35 In Causal-PIBT, agents act short-sighted high low result

    ideal
  36. /44 36 given agents (starts) graph termination execution goals +

    offline MAPF plan contracted requesting extended if unoccupied make agents follow the MAPF plan as much as possible MAPF Plans as Hints the nearest adjacent location to the goal
  37. /44 37 Evaluation in a simulated environment with stochastic delays

  38. /44 38 MAPF-DP (with Delay Probabilities) [Ma+ AAAI-17] 1 −

    𝑝! 𝑝 ! success fail emulate imperfect execution of MAPF plans by introducing the possibility of unsuccessful moves
  39. /44 39 Time-Independent Model => MAPF-DP 1. activate all agents

    in extended with probability 1 − 𝑝! success fail 1 − 𝑝! 𝑝 ! 2. repeat until stable: randomly activate one agent in contracted or requesting regard as one-timestep
  40. /44 40 upper bound of delay probabilities 𝑝! sum of

    costs x10^3 Fully Synchronous Policies Minimum Communication Policies Causal-PIBT Causal-PIBT +MAPF plan 32x32,20% obstacles 30 agents 100 repetitions MAPF plan by ECBS [Barer+ SoCS-14] Fix Agents
  41. /44 42 agents sum of costs x10^3 Fully Synchronous Policies

    Minimum Communication Policies Causal-PIBT Causal-PIBT +MAPF plan 32x32,20% obstacles upper bound of delay prob. : 0.5 100 repetitions MAPF plan by ECBS [Barer+ SoCS-14] Fix Delay Prob.
  42. /44 44 Concluding Remarks time-independent planning, Causal-PIBT to overcome asynchrony

    in reality motivation our approach target multiple moving agents algorithms ensuring strong termination future directions address communication explicitly apply to real robots