Overview: Generalizations of Multi-Agent Path Finding to Real-World Scenarios
Hang Ma, Sven Koenig, Nora Ayanian, Liron Cohen
Wolfgang Hönig, T. K. Satish Kumar, Tansel Uras, Hong Xu
Department of Computer Science
University of Southern California
{hangma,skoenig,ayanian,lironcoh,whoenig,turas,hongx}@usc.edu, tkskwork@gmail.com
Craig Tovey
School of ISyE
Georgia Institute of Technology
ctovey@isye.gatech.edu
Abstract
Multi-agent path finding (MAPF) is well-studied
in artificial intelligence, robotics, theoretical
computer science and operations research. We
discuss issues that arise when generalizing MAPF
methods to real-world scenarios and four research
directions that address them. We emphasize the
importance of addressing these issues as opposed
to developing faster methods for the standard
formulation of the MAPF problem.
1
Introduction
Multi-agent path finding (MAPF) has been well-studied by
researchers from artificial intelligence, robotics, theoretical
computer science and operations research. The task of
(standard) MAPF is to find the paths for multiple agents in a
given graph from their current vertices to their targets without
colliding with other agents, while at the same time optimizing
a cost function. Existing MAPF methods use, for example,
reductions to problems from satisfiability, integer linear
programming or answer set programming [Yu and LaValle,
2013b; Erdem et al., 2013; Surynek, 2015] or optimal,
bounded-suboptimal or suboptimal search methods [Silver,
2005; Sturtevant and Buro, 2006; Ryan, 2008; Wang and
Botea, 2008; Standley, 2010; Standley and Korf, 2011; Wang
and Botea, 2011; Luna and Bekris, 2011; Sharon et al., 2013;
de Wilde et al., 2013; Barer et al., 2014; Goldenberg et
al., 2014; Wagner and Choset, 2015; Boyarski et al., 2015;
Sharon et al., 2015].
We have recently studied various issues that arise
when generalizing MAPF to real-world scenarios, including
Kiva (Amazon Robotics) warehouse systems [Wurman et
al., 2008] (Figure 1) and autonomous aircraft towing
vehicles [Morris et al., 2016].
These issues can be
categorized into two general concerns: 1. Developing faster
methods for the standard formulation of the MAPF problem
is insufficient because, in many real-world scenarios, new
structure can be exploited or new problem formulations are
required. 2. Studying MAPF or its new formulations only as
Guni Sharon
Department of Computer Science
The University of Texas at Austin
gunisharon@gmail.com
combinatorial optimization problems is insufficient because
the resulting MAPF solutions also need to be executed. We
discuss four research directions that address both concerns
from different perspectives:
1. In many real-world multi-agent systems, agents are
partitioned into teams, targets are given to teams, and
each agent in a team needs to get assigned a target from
the team, before one finds paths for all agents. We have
formulated the combined target assignment and path
finding (TAPF) problem for teams of agents to address
this issue. We have also developed an optimal TAPF
method that scales to dozens of teams and hundreds of
agents [Ma and Koenig, 2016].
2. In many real-world multi-agent systems, agents are
anonymous (exchangeable), but their payloads are
non-anonymous (non-exchangeable) and need to be
delivered to given targets. The agents can often
exchange their payloads in such systems. We have
formulated the package-exchange robot routing (PERR)
problem as a first attempt to tackle more general
transportation problems where payload transfers are
allowed [Ma et al., 2016]. In this context, we have also
proved the hardness of approximating optimal MAPF
solutions.
3. In many real-world multi-agent systems, the consistency
of agent motions and the resulting predictability of
agent motions is important (especially in work spaces
shared by humans and agents), which is not taken into
account by existing MAPF methods. We have exploited
the problem structure of given MAPF instances in two
stages: In the first stage, we have developed a scheme
for finding paths for the agents that include many
edges from user-provided highways, which achieves
consistency and predictability of agent motions [Cohen
et al., 2015]. In the second stage, we have developed
methods that automatically generate highways [Cohen
et al., 2016].
4. MAPF is mostly motivated by navigation or motion
planning for multi-robot systems.
However, the
• The anonymous variant of MAPF (also called goalinvariant MAPF) results from TAPF if only one team
exists (that consists of all agents). The agents can get
assigned any target and are thus exchangeable. It can
be solved optimally in polynomial time with flow-based
MAPF methods [Yu and LaValle, 2013a; Turpin et al.,
Figure 3: A small region of a Kiva layout. The green cells represent pod storage locations, the orange ovals the robots (with
2014].
pods not pictured), and the purple and pink regions the queues around the inventory stations.
Figure 1: Autonomous drive units and storage pods that
to move the inventory pods with the correct bins from
The state-of-the-art optimal TAPF method, called the
contain products and can be moved byused
drive
units
theirthe
storage locations
to the inventory
stations where a pick
worker removes the desired products from the desired bin.
Min-Cost Flow [Ma and Koenig, 2016],
Note that the pod has four system
faces, and the drive unit mayConflict-Based
need
(left) and the layout of a typical Kiva warehouse
to rotate the pod in order to present the correct face. When a
picker is done with a pod, the drive unit stores it in an empty
combines search and flow-based MAPF methods.
It
(right) [Wurman et al., 2008].
storage location.
Each station is equipped with a desktop computer that
generalizes
to dozens of teams and hundreds of agents.
controls pick lights, barcode scanners, and laser pointers
that
Figure 5: The Kiva demonstration facility.
Acknowledgments
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Building a working MVS requires a core set of great mechanical, electrical, and software engineers. It is yet another thing to turn it into a commercial product and manage
the manufacture, assembly, and deployment of these systems. We thank the world-class Kiva employees who have
breathed life into this vision.
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are used to identify the pick and put locations. Because every product is scanned in and out of the system, overall pick-
errors go down, which potentially eliminates the need
optimality or bounded-suboptimality ofing
solutions
forMAPF
post-picking quality
control. In general, every station is
capable of being either a picking station or a replenishment
3 Package-Exchange Robot Routing (PERR)
station.
In practice,
pick stations will be located near outdoes not necessarily entail their robustness,
especially
bound conveyors, and replenishment stations will be located
near pallet drop off points.
and New Complexity Results for MAPF
given the imperfect plan-execution capabilities
realThe power of the Kivaof
solution
comes from the fact that
it allows every worker to have random access to any invenin the warehouse. Moreover, that
inventory can be retrieved
world robots. We have developed atory
framework
in parallel. When the picker is filling several boxes Agents
at the
are often anonymous but carry payloads (packages)
time, the parallel, random access ensures that she is
efficiently postprocesses the output of same
awaiting
MAPF
method
not
on pods to arrive.
In fact, by keeping a small
that
are
assigned targets and are thus non-anonymous. For
of work at the station, the Kiva system delivers a new
pod can
face everybe
six seconds,
which sets a baseline picking
to create a plan-execution schedule thatqueue
executed
lines
rate of 600 lines per hour. Peak rates can exceed 600example,
in a Kiva warehouse system, the drive units are
per hour when the operator can pick more
off
by real-world multi-robot systems [Hönig
et al., 2016]. than one itemanonymous
a pod.
but the storage pods they carry are assigned
1759
2
3
For a large warehouse, the savings in personnel can be
Consider, for example, what a Kiva implemenlocations and are thus non-anonymous. If each
tation these
of the book warehouse
would involve. A busy storage
bookWe now showcase the practicality ofsignificant.
research
seller may ship 100,000 boxes a day. With existing automation, this level of output would employ perhaps 75 workers
agent carries one package, the problem is equivalent to
directions to demonstrate that, in order to generalize
MAPF
(standard) MAPF. In reality, the packages can often be
methods to real-world
addressing
both concerns is
Figure 2:scenarios,
A Kiva drive unit and storage
pod.
transferred among agents, which results in more general
as important, if not more, than developing faster methods for
transportation problems, for example, ride-sharing with
the standard formulation of the MAPF problem.
passenger transfers [Coltin and Veloso, 2014] and package
1755
delivery with robots in offices [Veloso et al., 2015]. We have
2 Combined Target Assignment and Path
formulated PERR as a first step toward understanding these
Finding (TAPF) for Teams of Agents
problems [Ma et al., 2016]. In PERR, each agent carries one
package, any two agents in adjacent vertices can exchange
Targets are often given to teams of agents. Each agent in
their packages, and each package needs to be delivered to a
a team needs to get assigned a target given to its team so
given target. PERR can thus be viewed as a modification of
that the paths of the agents from their current vertices to
(standard) MAPF:
their target optimize a cost function. For example, in a
Kiva warehouse system, the drive units that relocate storage
• Packages in PERR can be viewed as agents in (standard)
pods from the inventory stations to the storage locations
MAPF which move by themselves.
form a team because each of them needs to get assigned an
• Two packages in adjacent vertices are allowed to
available storage location. Previous MAPF methods assume
exchange their vertices in PERR but two agents in
that each agent is assigned a target in advance by some targetadjacent vertices are not allowed to exchange their
assignment procedure but, to achieve optimality, we have
vertices in (standard) MAPF.
formulated TAPF, which couples the target-assignment and
the path-finding problems and defines one common objective
K-PERR is a generalization of PERR where packages
for both of them. In TAPF, the agents are partitioned into
are partitioned into K types and packages of the same type
teams. Each team is given the same number of unique targets
are exchangeable. Since, in TAPF, agents are partitioned
as there are agents in the team. The task of TAPF is to assign
into teams and agents in the same team are exchangeable,
the targets to the agents and plan collision-free paths for the
K-PERR can be viewed as a modification of TAPF with
agents from their current vertices to their targets in a way
K teams in the same sense that PERR can be viewed as
such that each agent moves to exactly one target given to its
a modification of (standard) MAPF. We have proved the
team, all targets are visited and the makespan (the earliest
hardness of approximating optimal PERR and K-PERR
time step when all agents have reached their targets and stop
solutions (for K ≥ 2). One corollary of our study is that
moving) is minimized. Any agent in a team can get assigned
both MAPF and TAPF are NP-hard to approximate within
a target of the team, and the agents in the same team are
any factor less than 4/3 for makespan minimization, even
thus exchangeable. However, agents in different teams are
when there are only two teams for TAPF. We have also
not exchangeable. TAPF can be viewed as a generalization of
demonstrated that the addition of exchange operations to
(standard) MAPF and an anonymous variant of MAPF:
MAPF does not reduce its complexity theoretically but makes
PERR easier to solve than MAPF experimentally. There is
• (Standard) MAPF results from TAPF if every team
a continuum of problems that arise in different real-world
consists of exactly one agent and the number of teams
scenarios: “One agent with many packages” yields the classic
thus equals the number of agents. The assignments of
rural postman problem; “as many agents as packages” yields
targets to agents are pre-determined and the agents are
MAPF, TAPF or PERR. Understanding both extremes helps
thus non-anonymous (non-exchangeable).
2
This statistic is based on single unit picks and has been reproduced for extended periods in the Kiva test facility.
3
This statistic was verified when a small Kiva demonstration
system was brought to a drugstore distribution center where operators picked at nearly 700 lines per hour.
Area1
10,577
10,396
10,272
Area2
= 1.5
SolCost
10,588
10,603
10,313
10,639
(1.5) and
algorithm
5, 2.0},
es. The
shows
WY(2.0)
untime
g again
neficial.
olution
hich is
uts and
but no
paramrmance
w2 ∈
of the
ing the
t-most,
ouragee edges
se with
to cirSecond,
es well
e paths,
ve over
costs or
=3
SolCost
11,354
11,707
11,414
11,319
11,363
11,245
Y(w2 ) for
. Cells are
minate
ike ine highe corriaths for
Figure 4: Kiva-like domain on which we compare ECBS(w) and
Figure
2: User-provided highways in a simulated Kiva
ECBS(w1 )+HWY(2.0).
warehouse
system.
one
attackinside
the middle,
required
150 to
agents
Area1as
and
Area2.by
Inmany
thoseother
areas,real-world
CBS has
scenarios.
less flexibility than ECBS(w) to avoid collisions by moving
agents around other agents, which could explain why it fails
solutions within
runtime Structure
limit.
4to find
Exploitation
of the
Problem
and
Predictability of Motions
Conclusions
Agents share their work spaces with humans, and the
We presented
newmotions
bounded-suboptimal
MAPF
approach
consistency
of atheir
and the resulting
predictability
that
takes
advantage
of
additional
inputs
that
represent
a
of their motions are important for the safety of the humans,
highway
and
a
parameter
w.
It
uses
the
highway
to
dewhich existing MAPF methods do not take into account.
rive new
w-admissible
heuristic
that
encourage
path
This
motivates
us to exploit
the values
problem
structure
of given
finding to
return paths
that include
the edges
the highMAPF
instances
and design
a scheme
that ofencourages
way. The
level of
encouragement
with w.
Our
agents
to move
along
user-providedincreases
sets of edges
(called
new
bounded-suboptimal
variants
of
CBS
and
ECBS(w),
[
]
highways) Cohen et al., 2015 . We use highways in the
called CBS+HWY(w)
and ECBS(w
encour1 )+HWY(w
context
of a simple inflation
scheme
based on2 ),the
ideas
age a global
behavior
of the
agentsetthat
[Phillips
behind
experience
graphs
al.,avoids
2012]collisions.
to derive
On the
theoretical
side,
weencourage
developed MAPF
a simple
approach
new
heuristic
values
that
methods
to
that
uses
highways
for
MAPF
and
provides
suboptimality
return paths that include the edges of the highways, which
guarantees.
On the experimental
side, we
demonstrated
that
avoids
head-to-head
collisions among
agents
and achieves
ECBS(w1 )+HWY(w
the runtimes
and so2 ) can decrease
consistency
and predictability
of their motions.
For example,
lution
costs
of ECBS(w)
in Kiva-like
domains
with many
in
a Kiva
warehouse
system,
we can design
highways
along
agents
if
the
highway
captures
the
problem
structure
well.as
the narrow passageways between the storage locations
In future
work,
we in
plan
to develop
that deshown
by the
arrows
Figure
2. Weapproaches
have demonstrated
termine
good highways
automatically,
whether
in
a simulated
Kiva warehouse
system investigate
that such highways
inflating the
edge methods
costs of the
given graph
(bymaintaining
increasing
accelerate
MAPF
significantly
while
costs of bounded-suboptimality
highway edges to w) in
to inflating
the desired
of addition
the MAPF
solution
the heuristic
values provides
benefits,
out
costs.
The problem
structure additional
of TAPF and
PERRfigure
instances
can
also be
exploitedmovement
with the same
We haveedges
also
whether
penalizing
costs methods.
against highway
developed
thatmaps
automatically
generate
highways
that
(similar tomethods
direction
(Jansen and
Sturtevant
2008))
are
competitive
user-provided
in ourapproaches
feasibility
helps
to improvewith
the performance
of ones
our MAPF
]. suboptimality guarantees, exstudy
Cohen et al.,to2016
while [continuing
provide
tend ECBS(w1 )+HWY(w2 ) to split the user-provided subbound
w dynamically
w1 and w2 (sim5optimality
Dealing
with
Imperfect between
Plan-Execution
ilar to how ECBS(w) splits the suboptimality bound w dyCapabilities
namically between the high-level and low-level searches),
and explore highways
context
of other
MAPF
algoState-of-the-art
MAPF in
or the
TAPF
methods
can find
collisionrithms,
such for
as M*
and inflated
free
paths
hundreds
of M*.
agents optimally or with
user-provided sub-optimality guarantees in a reasonable
amount of computation
time. They perform well even in
Acknowledgments
cluttered and tight environments, such as Kiva warehouse
We thank Maxim
Likhachev
Michael
for helpsystems.
However,
agentsand
often
have Phillips
imperfect
planful
discussions.
We
also
thank
Ariel
Felner,
Guni
Sharon,
execution capabilities and are not able to synchronize
their
and Maxim
Barer for
theircan
CBSresult
and ECBS(w)
source
motions
perfectly,
which
in frequent
and code,
timewhich we used
in our experiments.
was sup-a
expensive
replanning.
Therefore, Our
we research
have proposed
ported by NSF
numbers
1409987
andnetwork
1319966.
framework
that under
makesgrant
use of
a simple
temporal
to
The views and conclusions contained in this document are
postprocess a MAPF solution efficiently to create a planexecution schedule that works for non-holonomic robots,
takes their maximum translational and rotational velocities
into account, provides a guaranteed safety distance between
them and exploits slack (defined as the difference of the latest
and earliest entry times of locations) to absorb imperfect
plan executions and avoid time-intensive replanning in many
cases [Hönig et al., 2016]. This framework has been
evaluated in simulation and on real robots. TAPF and PERR
methods can also be applied in the same framework. Issues
to be addressed in future work include adding user-provided
safety distances, additional kinematic constraints, planning
with uncertainty and replanning.
6
Conclusions
We discussed four research directions that address issues
that arise when generalizing MAPF methods to real-world
scenarios and exploit either the problem structure or existing
MAPF methods. Our goal was to point out interesting
research directions for researchers working in the field of
MAPF.
7
Acknowledgments
The research at USC was supported by ARL under grant
number W911NF-14-D-0005, ONR under grant numbers
N00014-14-1-0734 and N00014-09-1-1031, NASA via
Stinger Ghaffarian Technologies and NSF under grant
numbers 1409987 and 1319966. The views and conclusions
contained in this document are those of the authors and
should not be interpreted as representing the official policies,
either expressed or implied, of the sponsoring organizations,
agencies or the U.S. government.
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