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Solving Simultaneous Target Assignment and Path Planning Efficiently with Time-Independent Execution

Solving Simultaneous Target Assignment and Path Planning Efficiently with Time-Independent Execution

More Decks by Keisuke Okumura | 奥村圭祐

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  1. Solving Simultaneous Target Assignment and Path Planning Efficiently with Time-Independent

    Execution Keisuke Okumura & Xavier Defago Tokyo Institute of Technology, Japan ౦ژ޻ۀେֶ 5PLZP*OTUJUVUFPG5FDIOPMPHZ Jun. 21st – 24th, 2022 virtual conf. (Singapore) ICAPS-22
  2. /39 2 https://kei18.github.io/tswap pattern formation async execution complete & sub-optimal

    algorithm (TSWAP) for unlabeled multi-agent pathfinding applicable to both offline & online scenarios ≥1000 agents within 1 sec Summary
  3. /39 3 MAPF: Multi-Agent Path Finding given agents (starts) graph

    goals solution paths without collisions
  4. /39 4 Unlabeled/Anonymous MAPF given agents (starts) graph targets solution

    paths without collisions target assignment
  5. /39 5 Motivation optimal sub-optimal (scalable) MAPF unlabeled-MAPF MAPP [Wang&Botea

    JAIR-11] EECBS [Li+ AAAI-21] PIBT [Okumura+ IJCAI-19] … CBS [Sharon+ AIJ-15] M* [Wagner&Choset AIJ-15] BCP [Lam+ COR-22] … reduction to maximum flow [Yu&LaValle WAFR-13] objective: solve large unlabeled-MAPF with sufficiently good quality in small computation time
  6. /39 6 Existing Optimal Algorithm by reducing to maximum flow

    problem: 𝑂( 𝐴 ⋅ 𝑉 !) * polynomial-time makespan-optimal algorithm exists! [Yu&LaValle WAFR-13] computable but take time (≥1min) fast sub-optimal solver is attractive *assuming |𝐸| = 𝑂(|𝑉|) MAPF benchmarks [Stern+ SOCS-19] 418x530 43,151 257x256 28,178 194x194 14,784 |𝑉|
  7. /39 7 optimal linear assignment collision-free scheduling [Yu&LaValle WAFR-13] Hungarian

    algorithm: 𝑂( 𝐴 ") [Kuhn 1955] lexicographic bottleneck assignment decoupled path planning [Turpin+ AURO-14] [Sokkalingam&Aneja OAL-98] known best algorithm: 𝑂( 𝐴 #) relying on optimal assignments Existing Sub-optimal & Complete Algorithms TSWAP works with arbitrary initial target assignments & applies to online scenarios
  8. /39 8 Proposed Algorithm: TSWAP compute arbitrary initial target assignment

    Step 1. repeat one-timestep path planning with target swapping Step 2. 𝑂( 𝐴 ! ⋅ 𝑑𝑖𝑎𝑚 𝐺 ⋅ (𝛼 + 𝛽)) vertex scoring & deadlock resolution algorithm sketch 2000 agents [Yu&LaValle WAFR-13] optimal algorithm TSWAP 56.3 89.8 230.2 0.4 0.4 1.1 1.36 1.17 1.02 runtime (sec) sub-optimality (makespan) lak303d den520d brc202d evaluation example
  9. /39 9 Algorithm Description

  10. /39 10 Why Not Arbitrary Assignment + MAPF? => incomplete!

    need to swap targets on demand
  11. /39 11 swap targets rotate targets shortest path move shortest

    path TSWAP repeat one-timestep path planning with target swapping Step 2. stay currently assigned target stay (otherwise)
  12. /39 12 Running Example 1 2 3 planning order: timestep:

    t
  13. /39 13 Running Example move shortest path timestep: t

  14. /39 14 Running Example timestep: t

  15. /39 15 Running Example swap targets timestep: t

  16. /39 16 Running Example timestep: t

  17. /39 17 Running Example move shortest path timestep: t

  18. /39 18 Running Example timestep: t

  19. /39 19 Running Example timestep: t+1

  20. /39 20 Running Example timestep: t+1 move shortest path stay

  21. /39 21 Running Example timestep: t+1

  22. /39 22 Running Example timestep: t+2 fin.

  23. /39 23 Completeness the shortest path distance from the current

    location to the target #targets in the shortest path (excluding endpoints) + Σ agent Proof. Using potential function 0 when all agents are on targets
  24. /39 24 the shortest path distance from the current location

    to the target #targets in the shortest path (excluding endpoints) + Σ agent swap targets rotate targets shortest path stay stay move shortest path
  25. /39 25 the shortest path distance from the current location

    to the target #targets in the shortest path (excluding endpoints) + Σ agent swap targets rotate targets shortest path stay stay move shortest path
  26. /39 26 the shortest path distance from the current location

    to the target #targets in the shortest path (excluding endpoints) + Σ agent swap targets rotate targets shortest path stay stay move shortest path
  27. /39 27 the shortest path distance from the current location

    to the target #targets in the shortest path (excluding endpoints) + Σ agent swap targets rotate targets shortest path stay stay move shortest path
  28. /39 28 the shortest path distance from the current location

    to the target #targets in the shortest path (excluding endpoints) + Σ agent swap targets rotate targets shortest path stay stay move shortest path
  29. /39 29 the shortest path distance from the current location

    to the target #targets in the shortest path (excluding endpoints) + Σ agent swap targets rotate targets shortest path stay stay move shortest path for each timestep, at least one agent performs one of the three actions for each timestep, the potential function decreases
  30. /39 30 Initial Target Assignment compute arbitrary initial target assignment

    Step 1. good assignment? => quick & good quality for certain criteria The paper introduces two algorithms using lazy distance (cost) evaluation resulting in good total/maximum traveling time bottleneck assignment 1. quick with acceptable quality: 𝑂( 𝐴 ⋅ ( 𝑉 + |𝐸|)) greedy assignment with refinement 2.
  31. /39 31 Evaluation

  32. /39 32 v.s. Makespan-optimal Alg. 0 200 400 600 0

    10 20 30 random-64-64-20 64x64 (3,270) random-32-32-20 32x32 (819) makespan runtime (ms) 110 agents TSWAP (bottleneck) TSWAP (greedy) optimal alg. [Yu&LaValle WAFR-13] TSWAP is scalable for graph size solution quality is comparable scalability for graph
  33. /39 33 v.s. Makespan-optimal Alg. [Yu&LaValle WAFR-13] TSWAP is scalable

    for #agents (according to assignment algorithms) 0 500 1000 1500 0 5 10 makespan runtime (ms) TSWAP (bottleneck) TSWAP (greedy) optimal alg. 500 agents 2000 agents (extremely dense) random-64-64-20 64x64 (3,270) scalability for #agents
  34. /39 34 Online Planning asynchronous execution

  35. /39 35 How to Model Async Execution? time-independent planning [Okumura+

    AAAI-21] agents sequentially perform atomic actions we cannot control execution schedule given: start target graph or Online Planning / Policy completeness: regardless of execution schedules, all targets are eventually occupied
  36. /39 36 Online TSWAP complete! *this is a centralized algorithm

    algorithm sketch* compute arbitrary initial target assignment 1. offline phase 2. online phase when is activated: same as offline
  37. /39 37 Demo of Time-Independence adaptive to timing uncertainties no

    synchronous procedure
  38. /39 38 8 Robots Demo

  39. /39 39 Concluding Remarks TSWAP algorithm our approach target simultaneous

    target assignment & path planning for indistinguishable agents (unlabeled-MAPF) future directions sub-optimal / complete / quick / scalable applicable to both offline & online decentralization offline planning for async execution c.f., OTIMAPP [Okumura+ IJCAI-22] https://kei18.github.io/tswap