LaCAM: Search-Based Algorithm for Quick Multi-Agent Pathfinding

AAAI-23
https://kei18.github.io/lacam/

Transcript

1. LaCAM: Search-Based Algorithm
   for Quick Multi-Agent Pathfinding
   Keisuke Okumura
   Tokyo Institute of Technology, Japan
   ౦ژ޻ۀେֶ
   5PLZP*OTUJUVUFPG5FDIOPMPHZ
   Feb. 7st – 14th, 2023
   Washington, DC, USA
   AAAI-23
   10k agents, 10sec
   400 agents, 30ms 4 agents, 72ms
   https://kei18.github.io/lacam
   

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   2
   MAPF: Multi-Agent Path Finding
   given agents (starts)
   graph
   goals
   solution paths without collisions
   optimization is intractable in various criteria
   [Yu+ AAAI-13, Ma+ AAAI-16, Banfi+ RA-L-17, Geft+ AAMAS-22]
   

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   3
   quick
   scalable
   complete
   optimal
   Trade-off in MAPF Algorithms
   

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   4
   
   
   
   
   
   solved instances (%; 13,900)
   runtime
   (sec)
   Results on
   MAPF Benchmark [Stern+ SOCS-19]
   13900 instances
   - 33 grid maps
   - random scenario
   - every 50 agents, up to max. (1000)
   tested on desktop PC
   33 grid maps
   0.0%
   A* [Hart+
   68]
   

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   5
   
   
   
   
   
   solved instances (%)
   runtime
   (sec)
   0.0%
   A* [Hart+
   68]
   0.4%
   ODrM* [W
   agner+ AIJ-15]
   complete & optimal
   Results on
   MAPF Benchmark [Stern+ SOCS-19]
   13900 instances
   - 33 grid maps
   - random scenario
   - every 50 agents, up to max. (1000)
   tested on desktop PC
   

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   6
   
   
   
   
   
   solved instances (%)
   runtime
   (sec)
   0.0%
   A* [Hart+
   68]
   0.4%
   ODrM* [W
   agner+ AIJ-15]
   8.3%
   CBS [Sharon+ AIJ-15; Li+ AIJ-21]
   10.7%
   BCP [Lam+
   COR-22]
   Results on
   MAPF Benchmark
   13900 instances
   - 33 grid maps
   - random scenario
   - every 50 agents, up to max. (1000)
   tested on desktop PC
   solution complete* & optimal
   *SC: solution complete: unable to
   distinguish unsolvable instances
   comp & optimal
   

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   7
   
   
   
   
   
   solved instances (%)
   runtime
   (sec)
   0.0%
   A* [Hart+
   68]
   0.4%
   ODrM* [W
   agner+ AIJ-15]
   8.3%
   CBS [Sharon+ AIJ-15; Li+ AIJ-21]
   10.7%
   BCP [Lam+
   COR-22]
   30.9%
   I-ODrM* [W
   agner+ AIJ-15]
   Results on
   MAPF Benchmark [Stern+ SOCS-19]
   13900 instances
   - 33 grid maps
   - random scenario
   - every 50 agents, up to max. (1000)
   tested on desktop PC
   comp & bounded sub-opt
   SC* & optimal
   *SC: solution complete: unable to
   distinguish unsolvable instances
   comp & optimal
   

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   8
   
   
   
   
   
   solved instances (%)
   runtime
   (sec)
   0.0%
   A* [Hart+
   68]
   0.4%
   ODrM* [W
   agner+ AIJ-15]
   8.3%
   CBS [Sharon+ AIJ-15; Li+ AIJ-21]
   10.7%
   BCP [Lam+
   COR-22]
   30.9%
   I-ODrM* [W
   agner+ AIJ-15]
   50.5%
   EECBS [Li+ AAAI-21]
   Results on
   MAPF Benchmark [Stern+ SOCS-19]
   13900 instances
   - 33 grid maps
   - random scenario
   - every 50 agents, up to max. (1000)
   tested on desktop PC
   comp & bounded sub-opt
   SC & bounded sub-opt
   SC* & optimal
   *SC: solution complete: unable to
   distinguish unsolvable instances
   comp & optimal
   

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   9
   
   
   
   
   
   solved instances (%)
   runtime
   (sec)
   0.0%
   A* [Hart+
   68]
   0.4%
   ODrM* [W
   agner+ AIJ-15]
   8.3%
   CBS [Sharon+ AIJ-15; Li+ AIJ-21]
   10.7%
   BCP [Lam+
   COR-22]
   30.9%
   I-ODrM* [W
   agner+ AIJ-15]
   50.5%
   EECBS [Li+ AAAI-21]
   61.4%
   PP [Silver AIIDE-05]
   80.9%
   LNS2 [Li+ AAAI-22]
   comp & bounded sub-opt
   SC & bounded sub-opt
   incomp & sub-opt
   SC* & optimal
   comp & optimal
   Results on
   MAPF Benchmark [Stern+ SOCS-19]
   13900 instances
   - 33 grid maps
   - random scenario
   - every 50 agents, up to max. (1000)
   tested on desktop PC
   [Stern+ SOCS-19]
   *SC: solution complete: unable to
   distinguish unsolvable instances
   67.4%
   PIBT [Okumura+ AIJ-22]
   90.5%
   PIBT+ [Okumura+ AIJ-22]
   

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    10
    
    
    
    
    
    85.6%
    LaCAM
    complete & sub-optimal
    Proposed Algorithm:
    LaCAM (lazy constraints addition search for MAPF)
    start breaking
    the trade-off
    

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    11
    Algorithm Description
    

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    12
    Planning Horizon
    agents
    1
    2
    N
    …
    0 1 T
    …
    timestep
    long planning horizon
    location
    A* [Hart+ 68] CBS [Sharon+ AIJ-15]
    complete, optimal
    agents
    1
    2
    N
    …
    0 1 T
    2 …
    timestep
    short planning horizon
    PIBT [Okumura+ AIJ-22] WHCA* [Silver AIIDE-05]
    quick, scalable
    

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    13
    …
    … …
    … …
    search node
    (configuration)
    Vanilla A* for MAPF
    greedy search: 44 nodes
    in general: (5^N)xT nodes
    N: agents, T: depth
    intractable even with
    perfect heuristics
    goal configuration
    complete but slow
    

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    14
    PIBT for MAPF
    PIBT
    PIBT
    PIBT
    greedy search: 44 nodes
    only 4 configurations
    repeat one-timestep planning until termination
    use PIBT to guide exhaustive search
    initial configuration
    goal configuration
    [Okumura+ AIJ-22]
    quick but incomplete
    

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    15
    …
    … …
    … …
    Concept of LaCAM
    PIBT
    PIBT
    PIBT
    use other MAPF algorihtms
    to generate a promising configuration
    configurations are generated
    in a lazy manner
    by two-level search scheme
    exhaustive search but node
    generation are dramatically reduced
    => quick & complete MAPF
    

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    16
    Lazy Constraints Addition
    constraint tree
    (maintained implicitly)
    invoked multiple times
    during the search
    

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    17
    1st invoke
    configuration generation with
    Lazy Constraints Addition
    no constraint
    

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    18
    Lazy Constraints Addition
    2nd invoke
    configuration generation with
    

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    19
    Lazy Constraints Addition
    e.g., breadth-first search
    24th invoke
    Each configuration eventually generates
    all connected configurations.
    Theorem: LaCAM is complete
    discard node from Open
    configuration generation with
    

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    20
    Evaluation
    

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    21
    prioritized planning
    w/distance-based heuristics [Silver AIIDE-05]
    A* with operator decomposition
    greedy version [Standley AAAI-10]
    EECBS
    CBS-based, bounded sub-optimal [Li+ AAAI-21]
    LNS2
    large neighborhood search for MAPF [Li+ AAAI-22]
    PIBT
    [Okumura+ AIJ-22]
    Performance on
    one-shot MAPF
    25 instances, on desktop PC
    30sec timeout
    194x194 four-connected grid
    LaCAM (w/PIBT)
    sum-of-costs
    (normalized; min:1)
    
    
    
    
    
    
    runtime
    (sec)
    
    
    
    
    
    success rate
    
    
    
    
    
    
    
    agents
    not so bad
    blazing fast!
    worst: 699ms
    perfect!
    (diff from PIBT: tie-breaking)
    

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    22
    agents
    
    
    
    
    
    
    
    room-64-64-8
    64x64, |V|=3,232
    success rate
    in 30sec
    LaCAM
    
    
    
    
    
    
    
    orz900d
    1491x656, |V|=96,603
    agents
    worst: 8sec
    worst: 394ms
    
    
    
    
    
    
    
    random-32-32-20
    32x32, |V|=819
    agents
    worst: 11sec
    100%
    MAPF Benchmark
    LaCAM quickly & sub-optimally solves various problems
    

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    23
    LaCAM (w/PIBT)
    PIBT [Okumura+ AIJ-22]
    PP [Silver AIIDE-05]
    greedy+OD [Standley AAAI-10]
    EECBS [Li+ AAAI-21]
    LNS2 [Li+ AAAI-22]
    6/6
    0/6
    1/6
    6/6
    3/6
    3/6
    solved with 10sec timeout
    tree
    tunnel
    loop-chain
    corners
    string
    connector
    Small Congested
    Instances from [Luna+ IJCAI-11]
    animations display refined solutions
    LaCAM quickly & sub-optimally
    solves various problems
    

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    24
    
    
    
    
    
    
    
    success rate
    in 1,000sec
    
    
    
    
    runtime
    (sec)
    agents (x1000)
    25 instances, timeout of1000 sec, on desctop PC
    warehouse-20-40-10-2-2, 340x164; |V|=38,756
    Performance with
    x1000 agents
    perfect!
    blazing fast!
    worst: 26sec
    for 10,000 agents
    LaCAM
    PIBT
    demo of 10,000 agents
    LaCAM quickly & sub-optimally
    solves various problems
    

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    25
    LaCAM is great but…
    agents
    
    
    
    
    
    
    
    maze-32-32-2
    32x32
    |V|=666
    
    
    
    
    
    
    
    lt_gallowstemplar_n
    251x180
    |V|=10,021
    agents
    
    
    
    
    
    
    
    warehouse-20-40-10-2-1
    321x123
    |V|=22,599
    agents
    0%
    success rate
    in 30sec
    narrow corridors
    can be bottleneck
    LaCAM
    necessity for improvements (e.g. configuration generator)
    

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    Concluding Remarks
    novel MAPF algorithm: LaCAM
    quickly solve
    various MAPF benchmarks
    small congested instances
    instances with 10k agents
    sub-optimal & complete
    theoretical side
    empirical side
    what’s next?
    LaCAM* w/improved configuration generator
    eventually converge to optima
    solve 99% of the MAPF benchmark in 10 sec
    https://kei18.github.io/lacam
    

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