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winPIBT
Extended Prioritized Algorithm for Iterative Multi-Agent Path Finding
Keisuke Okumura, Yasumasa Tamura & Xavier Defago
7th Jan. 2021
IJCAI-20 Workshop on MAPF
Tokyo Institute of Technology, Japan
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5PLZP*OTUJUVUFPG5FDIOPMPHZ
virtual conference
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MAPF: Multi-Agent Path Finding
given agents (starts)
graph
goals
solution paths without collisions
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Motivation
winPIBT: extension of PIBT [okumura+ IJCAI-19]
high
low
result of PIBT ideal
anticipating a single-step ahead
make PIBT anticipating multi-steps ahead
time-window
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PIBT
Priority Inheritance with Backtracking
[Okumura+ IJCAI-19]
solving MAPF iteratively
quick & scalable
adaptivity for decentralization
500 agents within 0.5 sec
Applicable to Multi-agent Pickup & Delivery
[Ma+ AAMAS-17]
sub-optimal
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locations at t=1
t=2
t=3
repeat one-timestep prioritized planning
high low
mid
How PIBT works – 1/6
…
1 2 3
4 5 6
7 8 9
decision order
time-window
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How PIBT works – 2/6
high
low
mid stuck
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How PIBT works – 3/6
high
low
mid as high
priority inheritance
[Sha+ 1990]
+backtracking (skip)
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How PIBT works – 4/6
high as high
as high as high
as high stuck
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How PIBT works – 5/6
invalid
valid
re-plan
re-plan
valid You can move
invalid You must re-plan, I will stay
introduce backtracking
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In biconnected graphs
the agent with highest priority can move to any adjacent locations
reachability: all agents reach their goals within finite timesteps
+dynamic priorities
How PIBT works – 6/6
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one-shot MAPF
reachability ≠ completeness
lifelong scenarios
unsolvable,
but we can ensure reachability
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winPIBT
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A B C D
E F G H
E
C
collision-
free
potentially
collide!
E F G H D
C G
must plan additional paths
Paths with Different Lengths – 1/2
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A B C D
E F G H
E
C
collision-
free
safe
E A B C D
C G G G G
can stay at the last location
two paths are isolated
Paths with Different Lengths – 2/2
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Revisit PIBT
A B
D E
C
F
high
D
C F
F E
D
two paths will not be isolated
=> priority inheritance
as high
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Concept of winPIBT
repeat until terminate
+ dynamic priorities
In biconnected graphs, winPIBT ensures reachability
plan an arbitrary-length path for one agent
reserve nodes in the path sequentially
when violating the isolation with another agent,
make this agent plan a single-step ahead using priority inheritance
so that two paths are isolated
1.
2.
3.
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Example of winPIBT
high
t=0
low
t=0
mid
t=0
time-window:3
locations at t=1
t=2
t=3
high low
mid
1
t=1
goals
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Example
time-window:3
locations at t=1
t=2
t=3
high low
mid
1
2
t=2
goals
low
t=0
mid
t=0
high
t=1
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Example
time-window:3
locations at t=1
t=2
t=3
high low
mid
1
2
t=3
violate, priority inheritance
goals
low
t=0
mid
t=0
high
t=2
3
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Example
time-window:3
locations at t=1
t=2
t=3
high low
mid
1 4
2
3
goals
high
t=2
low
t=0
mid
t=0
t=3
t=1
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Example
time-window:3
locations at t=1
t=2
t=3
high low
mid
1 4
2
3
goals
high
t=3
low
t=1
mid
t=0
5
t=1
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Example
time-window:3
locations at t=1
t=2
t=3
high low
mid
1 4
2
3
goals
high
t=3
low
t=1
mid
t=1
5
t=2
violate, priority inheritance
6
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Example
time-window:3
locations at t=1
t=2
t=3
high low
mid
1 4
2
3
goals
high
t=3
low
t=1
mid
t=1
5
t=2
t=2
6 7
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Example
time-window:3
locations at t=1
t=2
t=3
high low
mid
1 4
2
3
goals
high
t=3
low
t=2
mid
t=2
5
t=3
6 7
8
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Example
time-window:3
locations at t=1
t=2
t=3
high low
mid
1 4
2
3
goals
high
t=3
low
t=2
mid
t=3
5
6 7
8
t=3
9
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Example
time-window:3
locations at t=1
t=2
t=3
high low
mid
1 4
2
3
goals
high
t=3
low
t=3
mid
t=3
5
6 7
8 9
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Evaluation
with fixed time-windows
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agents
cost per agent
2
winPIBT-30
3
10
PIBT
agents
makespan
2
winPIBT-30
3
10
PIBT
empty-32-32
25 instances
One-shot MAPF
the effect is not significant in open space
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agents
runtime (sec)
2
winPIBT-30
3
10
PIBT
agents
success instances
2
winPIBT-30 3 10
PIBT
empty-32-32
25 instances
One-shot MAPF
c.f., reachability ≠ completeness
winPIBT takes time
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Naïve Iterative MAPF kiva-like
2000 targets
10 repetitions
agents
service time
50
30
5 10
PIBT
agents
runtime (sec)
50
30
5
10
PIBT
longer windows need time
winPIBT: good
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Concluding Remarks
develop adaptive windows
future directions
decentralization, c.f., our latest work [Okumura+ AAAI-21]
winPIBT
to overcome short-sighted behavior of PIBT
motivation
proposal
target solving MAPF iteratively, c.f., reachability