Adapted Conﬂict Detection for Conﬂict Based Search

Avgi Kollakidou

and Leon Bodenhagen

Mærsk Mc-Kinney Møller Institute, University of Southern, Denmark

Keywords:

Conﬂict Based Search, Multi-Agent Path Finding, Navigation.

Abstract:

Mobile robots are increasingly deployed in various applications, including autonomous vehicles and logistics.

Conﬂict-Based Search (CBS) is a promising approach for Multi-Agent Path Finding (MAPF), but has limita-

tions when applied to real-world scenarios. This paper explores the challenges of adapting CBS to real-world

mobile robotics, focusing on additional conﬂicts caused by imperfect navigation. We propose an Adaptive

Conﬂict Detection (ACD) approach that proactively identiﬁes conﬂicts within a rolling time window, making

CBS more suitable for real-world applications. Both virtual and real robots are used to evaluate the impor-

tance of an adaptation to CBS if adapted to real scenarios. Experimental results show that ACD outperforms

traditional CBS when penalties for conﬂict resolution are applied, demonstrating its potential for improved

performance and reliability in practical multi-agent path planning applications.

1 INTRODUCTION

Mobile robots have found their way into an ever-

expanding array of applications, from autonomous

vehicles and trafﬁc management to automated ware-

house logistics and robotics. With their increasing

deployment in real-world scenarios in particular un-

structured environments, we encounter a host of com-

plex challenges that push the boundaries of conven-

tional navigation algorithms.

One of the fundamental problems in multi-robot

systems is Multi-Agent Path Finding (MAPF), which

involves ﬁnding collision-free paths for a group of

agents operating simultaneously within a shared en-

vironment. The input to the MAPF problem is an

undirected, unweighted graph G = (V, E), and a set

of k agents with a starting vertex s

and target vertex

each. The MAPF solution S = {π

, ..., π

} is a set

of action sequences for each agent π

= (α

, ..., α

) ,

with all sets able to be carried out concurrently with-

out conﬂicts. The complexity of MAPF increases

with the number of agents and the intricacy of the

environment they must navigate. The search for op-

timal solutions in such scenarios is notoriously time-

consuming and computationally demanding.

Conﬂict Based Search (CBS) (Sharon et al., 2015)

has emerged as a promising two-stage strategy for

tackling the MAPF problem. CBS revolves around

https://orcid.org/0000-0002-0648-4478

https://orcid.org/0000-0002-8083-0770

the identiﬁcation and resolution of conﬂicts that arise

during the path planning process. While CBS pro-

vides an effective framework for MAPF, it is not with-

out its shortcomings, especially when confronted with

the realities of the real world.

One signiﬁcant limitation of CBS becomes appar-

ent when we attempt to adapt it to the complexities

of real-world mobile robotics. In the virtual world of

CBS, units of time and velocity are abstract concepts

that often do not seamlessly translate into the physical

reality of real robots. In the real world, factors such

as acceleration, deceleration, dynamic obstacles, and

varying terrains introduce complexities that challenge

the assumptions made by traditional CBS algorithms,

as can also be seen in ﬁg. 1.

These disparities indicate the necessity of reeval-

uating and enhancing CBS for real-world mobile

robotics applications. We must address the limita-

tions stemming from the mismatch between the per-

fect model and the physical world. Our goal is to de-

velop solutions that account for the nuances of real

robots and unpredictable real-world scenarios.

In this work, we delve into the inherent limitations

of CBS when applied to real-world scenarios, particu-

larly focusing on the challenge of additional conﬂicts

occurring due to imperfect navigation.

Kollakidou, A. and Bodenhagen, L.

Adapted Conﬂict Detection for Conﬂict Based Search.

DOI: 10.5220/0012438000003636

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 16th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2024) - Volume 1, pages 367-373

ISBN: 978-989-758-680-4; ISSN: 2184-433X

367

(a) Mission 3. (b) Mission 5.

Figure 1: Robot trajectories in lab experiments (2 out of 6

missions). Blue: single robot runs; Red: multi-robot runs.

2 RELATED WORK

The ﬁeld of Multi-Agent Path Finding (MAPF) has

evolved considerably in recent years, driven largely

by the expanding role of mobile robotics across var-

ious domains, such as warehouse logistics (Wurman

et al., 2008) or video games (Ma et al., 2017). In

this context, Conﬂict-Based Search (CBS) has been

a method for addressing the MAPF problem. This

section examines the current scope of CBS, its limi-

tations, and the emerging research trends that empha-

sise the necessity to tailor CBS for the intricate de-

mands of real-world mobile robotics as well as strate-

gies for real time conﬂict avoidance.

CBS (Sharon et al., 2015) is an optimal solution

to the MAPF problem and is divided into two levels

each having a distinct task: individual path planning,

and constraint deﬁnition from detected conﬂicts. On

the low level, each agent searches for a path individu-

ally and independently, ignoring all other agents’ po-

sitions or plans, using the A* algorithm. A list of con-

straints, derived from previously existing conﬂicts, is

provided by the upper-level. For the ﬁrst low level

search, an empty list of constraints exists. If a node

is generated where agent α

needs to occupy vertex

v at time t and a constraint exists that involves the

same conﬁguration, that node is discarded. Likewise,

if agent α

is to traverse edge e at time t and a con-

straint exists involving that edge, the node is also dis-

carded. However, the method encounters substantial

challenges when transposed into real-world scenarios.

Primary among these challenges is the abstraction

of unit time and velocity in CBS. In theoretical mod-

els, actions are assumed to occur in ﬁxed, discrete

time steps, a simpliﬁcation that does not translate well

to the real world, where mobile robots exhibit var-

ied velocities and motions are continuous. This dis-

crepancy limits CBS’s direct applicability in practical

settings, where factors like acceleration, deceleration,

and dynamic obstacles play a signiﬁcant role. Several

works have attempted to bridge this gap by expand-

ing CBS into continuous-time frameworks e.g. with

Increasing Cost Tree Search (Walker et al., 2021) or

by calculating safe intervals representing time peri-

ods when an agent can occupy a vertex without collid-

ing with moving obstacles (Andreychuk et al., 2021).

These, however, have not been adequately tested in

the real world.

Planning for multiple robots while considering

synergies and their temporal dependencies was also

considered with promising results (Jiang et al., 2019).

The paper assumes that robots can communicate con-

tinuously and cost-free, which presents challenges for

practical implementation in the real world.

Traditional navigation techniques, delegate the

tackling of any agents that might be encountered

when navigation to their local planners. Local plan-

ning is of course a large research ﬁeld with many ap-

proaches. For example, the Dynamic Window Ap-

proach (DWA) is known for its ﬂuid movement in

trajectory planning, though it faces challenges in ef-

ﬁciency due to limited perception of obstacle den-

sity (Fox et al., 1997). The Enhanced Vector Field

Histogram, a reﬁned version of the Vector Field His-

togram (VFH), demonstrates notable effectiveness in

obstacle avoidance, with enhancements like VFH+

ensuring smoother trajectories and greater reliabil-

ity (Borenstein et al., 1991; Ulrich and Borenstein,

1998).

Furthermore recent works use learning-based

strategies in multi-robot navigation. Integration of

deep learning with traditional robotic control strate-

gies to enhance efﬁciency and adaptability in dy-

namic environments is proposed in (Han et al., 2022).

This is a distributed approach combining the recip-

rocal velocity obstacle (RVO) concept with deep re-

inforcement learning, offering a solution for recipro-

cal collision avoidance in complex scenarios was in-

troduce. A combined model utilising convolutional

neural networks and graph neural networks, enabling

effective communication and decision-making among

robots was suggested for decentralised path planning

(Li et al., 2020). (Bae et al., 2019) proposes a rein-

forcement learning-based path planning method using

Deep Q-learning combined with CNNs.

CBS provides a solid theoretical foundation for

MAPF, but its idealised assumptions necessitate

signiﬁcant modiﬁcations to effectively address the

challenges posed by real-world conditions such as

continuous-time motion, dynamic environments, and

complex terrains. The ongoing research in this ﬁeld

suggests that bridging the theoretical-practical di-

vide in CBS is an area ripe for exploration, offering

ICAART 2024 - 16th International Conference on Agents and Artiﬁcial Intelligence

368

substantial opportunities for advancements in mobile

robotics deployed in real-world settings.

In the following sections, we delve deeper into

the inherent limitations of CBS in practical scenar-

ios, particularly emphasising the additional conﬂicts

arising due to imperfect navigation. Our methodol-

ogy aims to address these limitations, and our exper-

imental ﬁndings offer insights into developing more

robust and adaptable solutions for real-world mobile

robotics.

3 METHODOLOGY

In this section, we delve into the real-world limita-

tions of Conﬂict-Based Search (CBS) as applied to

Multi-Agent Path Finding (MAPF). CBS relies on

certain assumptions which often diverge signiﬁcantly

from the complexities of the real world. To assess the

impact of these deviations, we conducted experiments

with MiR200 robots, exploring how multiple robots

assigned different assembly missions affect task com-

pletion times. We also introduced noise elements

to replicate real-world irregularities and propose an

adaptive conﬂict resolution method. This approach

considers a time window to proactively detect and ad-

dress conﬂicts, making CBS more suitable for real-

world scenarios. Furthermore, we discuss the possi-

bility of dynamically determining the rolling window

size based on map topology, path cost, and the number

of robots, to optimise coordination in various settings.

3.1 CBS Limitations in the Real World

MAPF depends on several assumptions: Time is dis-

cretised in unit time steps during which, an agent can

occupy one vertex and each vertex can accommodate

only a single agent. Two types of actions can be per-

formed with unit cost: move to an adjacent vertex,

or wait in the current vertex. Reality, however, dif-

fers substantially. Robots do not move with constant

velocity or at unit time. Additionally, the grid oc-

cupancy of an agent is usually larger than a single

grid cell, as not only is its footprint larger, but also

a buffer area around the robot is considered for safety.

If another robot or an obstacle is within this area, the

robots in the real world will engage the emergency

break and stop moving.

To assess how much robots deviate from their

planned trajectories in the real world, we conducted

a series of experiments to investigate the navigational

performance of agents in controlled lab conditions.

The experimental environment was designed to repli-

cate a ﬂexible assembly setting featuring multiple

Figure 2: Mean of mission completion times for single and

multi-robot runs with their respective standard deviations.

workstations. We used MiR200 robots equipped with

the 3.12 software version. The primary objective was

to investigate how the introduction of multiple robots,

each assigned different assembly missions, inﬂuenced

the overall running time of the tasks. Our experimen-

tal setup involved two key scenarios: one with a single

robot executing all missions sequentially, and another

with three robots, each independently assigned mis-

sions. Both scenarios were repeated 10 times to allow

for deviations, and the average time was calculated.

The aim was to assess the impact of multiple robots

working simultaneously within the same space.

For the second scenario, we introduced three

robots, with each robot assigned random assembly

missions. These missions were randomly assigned,

and the planning of the path to accomplish each mis-

sion remained consistent with the single robot sce-

nario. We monitored and documented the time taken

by each robot to complete their respective missions.

The trajectories of an agent during single-robot

(SR) and multi-robot (MR) runs can be seen in ﬁg. 1

for two different missions. Trajectories for SR runs

are very similar but not identical which can then lead

to conﬂicts as timings vary. Trajectories of MR runs

include larger deviations as well as detours. The ef-

fect of such deviations can be seen on the mission

completion times ﬁg. 2.

3.2 Noise Introduction

In order to replicate real-world irregularities in sim-

ulation, noise was introduced in the agents’ paths.

This noise was incorporated by introducing waiting

actions. At each step along the path a vertex had the

possibility of being repeated with a speciﬁed proba-

bility. For the purposes of our experiments, we set

this probability at 10%. As the identical goal ver-

tex is inserted in the plan, the robot waits for one

time-step at said vertex. This intentional inclusion of

noise allowed us to more accurately replicate the un-

predictable nature of real-world scenarios and assess

Adapted Conﬂict Detection for Conﬂict Based Search

369

Figure 3: Conﬂicts deﬁnitions: Vertex conﬂict (left), Edge

conﬂict (right).

the robots’ planning in challenging, dynamic environ-

ments.

3.3 Adaptive Conﬂict Resolution

Considering the previous experiments, where robots

encountered conﬂicts despite optimal path planning,

we recognise the need to adapt existing coordination

and conﬂict resolution methods to better address real-

world scenarios. In particular, we propose an adap-

tive approach based on Conﬂict-Based Search (CBS),

which considers the inherent uncertainties and dy-

namic nature of robot coordination in practical set-

tings.

In traditional CBS, conﬂict detection typically oc-

curs for a single time instance, and assumes perfect

execution of robot plans. There are several types

of MAPF conﬂicts discussed in the literature (Stern

et al., 2019b). In this work, we consider two types:

vertex and edge conﬂicts (ﬁg. 3). A vertex conﬂict

arises when two agents, a

and a

, are planned to oc-

cupy the same vertex, v, during the same time step

and is deﬁned as C

= ⟨a

, a

, v, t⟩. An edge conﬂict

occurs when two agents are planned to traverse the

same edge, connecting vertex v

and v

, during the

same time step and is deﬁned as C

= ⟨a

, a

, v

, t⟩.

While this approach is well-suited for perfect sce-

narios, it often falls short in addressing real-world

complications, such as minor deviations from planned

paths, variations in robot speed, or dynamic environ-

mental factors.

3.3.1 Rolling Window Conﬂict Detection

To enhance the CBS framework’s adaptability to real-

world conditions, we introduce the concept of Rolling

Window Conﬂict Detection. This method involves

observing the robots’ plan within a time window,

rather than at a single instance. The rolling window

allows us to monitor the robots’ movements and iden-

tify potential conﬂicts that might arise due to imper-

fect plan execution.

By increasing the time period where conﬂicts are

considered, we can proactively detect conﬂicts and

initiate conﬂict resolution strategies in advance. This

adaptability to real-time conditions mitigates the im-

pact of conﬂicts and should minimise delays upon ex-

ecution. Additionally, reducing the conﬂicts that the

robots will encounter upon execution, will increase

reliability and consistency. Execution consistency is

a well sought after attribute for mobile robots that

should be deployed along humans, as they increase

the trust in the agent by the user as well as bystanders.

Assuming:

s – is the window size.

– is the agent of interest.

v – is the vertex where agent α

is positioned.

t – is the current time.

We expand the search for vertex conﬂicts as fol-

lows:

C⟨α

, v, t, s⟩ =

s−1

[

τ=t−

s−1

= ⟨a

, a

, v, t⟩ (1)

Where:

τ – is a time variable that iterates through the time

interval from t −

s−1

to t +

s−1

Conﬂicts(α

, v, τ) – represents the set of conﬂicts

that may arise at time τ between agent.

3.3.2 Dynamic Rolling Window Size

We propose a dynamic determination of the rolling

window size to the speciﬁc characteristics of the robot

coordination scenario. This adaptability is achieved

by considering a combination of map topology, path

cost, and conﬂicts arising from the inclusion of noise

in the robot’s plan.

• Map Topology: The rolling window size is re-

lated to the map’s size. In scenarios with larger

and sparser workspaces, a smaller rolling win-

dow may be preferable, as robots should come

into fewer conﬂicts. Conversely, in more intricate

or congested workspaces, a larger rolling window

might be suitable, as robots encounter a higher

density of potential collision points. By aligning

the rolling window size with the map’s complex-

ity, we can optimise robot coordination in differ-

ent environments.

• Path Cost: The cost of the planned paths also

plays a crucial role in determining the rolling win-

dow size. Higher-cost paths may necessitate a

larger rolling window, as they can pose a greater

risk of conﬂict due to longer traversal times. Con-

versely, lower-cost paths may allow for smaller

rolling windows, as the paths are inherently less

likely to result in conﬂicts. By adapting the rolling

ICAART 2024 - 16th International Conference on Agents and Artiﬁcial Intelligence

370

Figure 4: Effects of noise addition and conﬂict penalties

after post-noise conﬂict detection in multi-robot runs (mean

values).

window size to the path cost, we strike a balance

between efﬁciency and conﬂict prevention.

• Number of Robots: in the environment is a cru-

cial factor inﬂuencing the rolling window size.

In cases with a larger number of robots, a larger

rolling window may be beneﬁcial, as it enhances

conﬂict detection in crowded settings. Con-

versely, with fewer robots, a smaller rolling win-

dow can be employed, allowing for less lengthy

conﬂict checks and facilitating smoother coordi-

nation among a smaller group.

4 RESULTS

4.1 Noise and Penalties

Following the introduction of noise, the revised paths

underwent a comparison to identify any emergent

conﬂicts. This enabled us to replicate real-world sce-

narios where conﬂicts may arise as a result of im-

perfect velocities or time delays. In the event a con-

ﬂict was detected, a conﬂict penalty was assigned to

the overall cost, to emulate the evading manoeuvre

or waiting actions the agent would have to employ to

overcome the detected conﬂict. For the purpose of

this evaluation, the conﬂict penalty value was set to 3.

Figure 4 shows the effect the inclusion of noise

has on the path costs of agents. Six simulated mis-

sions were used, with varying lengths and complexi-

ties as seen in ﬁg. 5. The missions were executed 10

times and the reported numbers represent their mean.

The optimal path cost for each mission is presented,

along with the cost for the same agent when navi-

gating in the environment along other agents. The

included noise for both sessions as well as the de-

duced conﬂict penalty is shown to demonstrate the

importance of a more robust CBS solution when in-

tended for the real world. The mean penalties as-

Figure 5: Missions used for evaluation and optimal paths

derived with A*.

signed amount to up to 21.6% of the ﬁnal path cost

(minimum: 3.5%).

4.2 Adaptive Conﬂict Detection

In order to evaluate the impact of the Adaptive Con-

ﬂict Detection approach on multi-agent path planning,

a series of experiments were conducted on a dataset

of simulated missions. The experiments were con-

ducted on a simpliﬁed map scenario produced by us

as well as the MAPF dataset (Stern et al., 2019a),

which provides a diverse set of benchmark scenarios

for MAPF. These scenarios encompass a wide range

of complexities, map topologies, and mission char-

acteristics, making them a valuable resource for as-

sessing the performance of path planning algorithms

in diverse and challenging real-world-inspired envi-

ronments. In this section, we present and discuss the

results of these experiments, and potential beneﬁts of

the Adaptive Conﬂict Detection (ACD) approach in

real-world MAPF applications.

Initially, the ACD approach showed, as expected,

a higher path cost compared to traditional CBS, pri-

marily due to the increased number of detected con-

ﬂicts. The rolling window approach yielded higher

path costs at a maximum of 18% increase. How-

ever, with the introduction of noise, and the penal-

ties resulting from the subsequent search for arising

conﬂicts, the ACD approach demonstrated superior

performance. Conﬂict penalties applied on the multi-

robot path costs resulting from simple CBS were up

to a mean of 27.9% of the initial path cost for mis-

sion 1 and a minimum mean of 18.6% for mission

2, whereas the maximum penalty applied on a path

Adapted Conﬂict Detection for Conﬂict Based Search

371

Figure 6: Comparison of CBS with rolling window conﬂict

detection against basic CBS when noise is included.

resulting from the ACD approach was 5.1% for mis-

sion 3 (minimum 0%) (ﬁg. 6). This outcome suggests

that the ACD approach, with its adaptability and early

conﬂict detection capabilities, is well-suited for real-

world scenarios where deviations from planned paths

and unexpected factors can impact multi-agent coor-

dination.

4.3 Conﬂict Penalty Size

In the evaluation of the Adaptive Conﬂict Detection

approach, an essential aspect was the determination

of an appropriate conﬂict penalty size. Three distinct

considerations were taken into account to make an in-

formed decision regarding penalty values.

Firstly, a conservative conﬂict penalty of 3 was

considered in simulation to avoid collisions during a

conﬂict as the agent would need to a) detect the con-

ﬂict, b) move to avoid it and c) return to its original

path.

Secondly, the effect a conﬂict has on mission com-

pletion times in simulation was considered. This was

calculated by comparing the increased mission com-

pletion time of agents when considering the multi-

robot scenarios against the optimal solution of single-

agent runs, divided by the amount of conﬂicts that oc-

curred.

Finally, the time taken in real-world experiments

to overcome conﬂicts were calculated. The variance

of the additional actions required to complete a mis-

sion in case of a conﬂict was very large, spanning

from 15% increase of the path length to 100% dou-

bling the distance travelled by the agent.

With all three considerations taken, the conserva-

tive conﬂict penalty was used to avoid inﬂating the ad-

vantages of ACD, but it is evident that such a penalty

in the real world would be larger.

5 DISCUSSION

The effectiveness of our Adapted CBS in real-world

scenarios is depended on map topology. The com-

plexity and layout of the environment, such as nar-

row passageways, play an important role in both the

performance and applicability of the algorithm. In

densely populated or cluttered spaces the frequency

and complexity of conﬂicts increase, thereby increas-

ing the need for conﬂict resolution and requires larger

window sizes. On the other hand, simpler maps with

large open spaces, would, in theory, feature fewer

conﬂicts and therefore the need of adaptation might

be smaller. A consideration for applying the method

locally in critical areas might be worthwhile.

The mission selection is another critical factor that

could potentially inﬂuence our results. The inher-

ent complexity of the chosen missions - whether they

are relatively straightforward or particularly challeng-

ing, clustered together in certain areas, or spread out

through the map - directly affects the performance

of the adapted CBS methodology. Simple missions,

with direct paths and minimal obstacles, may not ad-

equately test the robustness and adaptability of the

algorithm, potentially leading to an overestimation

of its effectiveness in more complex scenarios. On

the other hand, excessively difﬁcult missions could

push the system to its limits, potentially highlighting

weaknesses that are less pronounced in standard op-

erational conditions. In our study, we attempted to

choose missions that were neither too easy nor too

hard. This way, we could properly test our system

without pushing it too far. Our goal was to see how

well the algorithm works under realistic conditions,

but without making the tasks overly complicated.

6 CONCLUSIONS

In this study, we conducted an evaluation of an Adap-

tive Conﬂict Detection (ACD) approach for multi-

agent path planning, aimed at addressing the com-

plexities and uncertainties of real-world scenarios.

Our experiments revealed insights into the adaptabil-

ity and effectiveness of the ACD approach.

The introduction of noise in our simulations, mim-

icking real-world irregularities, initially led to an in-

creased path cost as conﬂicts were detected more

frequently. However, our approach, with its abil-

ity to adapt and proactively identify conﬂicts within

a rolling time window, demonstrated its true poten-

tial when penalties for conﬂict resolution were ap-

plied. These penalties, chosen through a combi-

nation of practical considerations, showed that the

ICAART 2024 - 16th International Conference on Agents and Artiﬁcial Intelligence

372

ACD approach outperformed traditional Conﬂict-

Based Search (CBS) in real-world-inspired scenarios,

where deviations from planned paths and unexpected

factors could inﬂuence multi-agent coordination.

In our exploration of penalty size, we considered

multiple factors, including conservative values, simu-

lated mission impact, and insights from real-world ex-

periments. This comprehensive approach to penalty

selection ensures that the penalties are not exagger-

ated purposefully to magnify the approach’s advan-

tages but show a fair if not understated estimate of the

method’s effect.

In summary, the results of our experiments sug-

gest that the Adaptive Conﬂict Detection approach is

a promising candidate for addressing the challenges

of real-world multi-agent path planning. By proac-

tively detecting and resolving conﬂicts, this approach

showcases its potential for improved performance and

reliability in practical applications.

ACKNOWLEDGEMENTS

This work is supported by the Innovation Fund Den-

mark for the project DIREC (9142-00001B) and the

SDU Industry 4.0Lab.

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