https://doi.org/10.53964/mit.2023001

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MiniReview
A Review of the Consensus Achievement Strategies in the Context of Swarm Robotics
Theviyanthan Krishnamohan1*
1*

University of Westminster, London, UK

Correspondence to: Theviyanthan Krishnamohan, Master, Software Engineer, Computer Science andEngineering, University of Westminster, 309 Regent Street, London W1B 2HW, UK; Email: theviyanthan@outlook.com
Received: January 3, 2023 Accepted: March 09, 2023 Published: March 31, 2023

Abstract
Swarm robotics applies swarm intelligence to robotics to solve real-life problems that cannot be
solved by single, monolithic robots. This review first studies swarm robotics in depth and analyzes thedifferent types of tasks carried out by swarms of robots. Then, the consensus-achievement behavior
is elaborated on and its relation to the collective perception scenario is reviewed. The collective
perception scenario is expounded in detail and the three discreet consensus-achievement strategies,
namely the direct modulation of majority-based decision, direct modulation of voter-based decision,and direct comparison are discussed apropos of the collective perception scenario. This review thencompares these strategies and explores their shortcoming such as the vulnerability to Byzantine robots.
Keywords: swarm robotics, swarm intelligence, collective perception, consensus achievement
Citation: Krishnamohan T. A Review of the Consensus Achievement Strategies in the Context of Swarm Robotics. Mod Intell
Times, 2023; 1: 1. DOI: 10.53964/mit.2023001.

1 INTRODUCTION
Swarm robotics tries to solve problems that cannot be
solved by single, monolithic robots or multi-agent robots
by using the principle of swarm intelligence. Swarm
intelligence is a discipline that takes inspiration from
biological systems found in nature such as bee colonies,
bacterial growth, ant colonies, and bird flocking.
In swarm intelligence, complex problems are solved
through coordination among simple individuals. For
example, simple and almost homogenous individual
insects in insect societies, which are decentralized andnot synchronized, have been shown to be communicatingwith one another using pheromones to find the best path
to a source using a positive feedback mechanism[1].

Robots are devices “capable of both mechanical andinformational behavior”[2]. Swarm robotics makes useof multiple simple robots to imitate simple individuals
found in swarms in nature and can be utilized to solve
real-life problems that cannot be easily solved by othermeans.
Consequently, swarm robotics is formally definedas “the study of how large number of relatively simple
physically embodied agents can be designed such thata desired collective behavior emerges from the local
interactions among agents and between the agents andthe environment”[2].
Even though there does not exist a consensus in

Copyright © 2023 The Author(s). This open-access article is licensed under a Creative Commons Attribution 4.0 International License(https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, sharing, adaptation, distribution, and reproduction in any
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https://doi.org/10.53964/mit.2023001
the literature on the characteristic features of swarm
robotics, the following characteristics are commonly
found in most of the literature[3].
● A large number of members● Simple members● Homogeneity● Decentralization● Distribution● Local sensing and communication
The many advantages of swarm robotics such as being
able to mass-produce robots owing to their simplicity
and the reliability that stems from their redundancy meanthat this technology can be used for tasks such as those“that cover a region”, “that are dangerous”, “that scale
up or down in time”, and “that require redundancy[1,2].
Environmental monitoring for oil leakage or nuclear
radiation is an example of tasks that cover a region.
Tasks that are dangerous are activities like demining
minefields and firefighting. Swarm robotics is suitable
for such tasks because individual robots cost less by
virtue of their simplicity. Besides, the loss of a few
robots will not affect the swarm, thereby ensuring
reliability[2].
Oil leakage from a sunken ship is an excellent
example of tasks that scale up or down in time. Whenswarm robotics is used to contain oil spillage, morerobots can be deployed to the swarm if the oil leakage
increases. An example of tasks that require redundancy
is the use of swarm robotics on battlefields. A swarm ofrobots will continue to function even if a few robots are
hit by bullets and are destroyed[2].
Existing reviews on consensus achievement inswarm robotics have studied the resilience of consensus
protocols such as Linear Consensus Protocol andWeighted Mean Subsequence Reduced to Byzantine
robots and the benefits of using blockchain in swarm
robotics[4,5]. However, there is a dearth of reviews on theconsensus-achievement strategies in the context of thecollective perception scenario and this study attempts tofill this gap.
This paper is divided into 9 sections. The first section
discusses how swarm engineering is classified, while
the second and third sections discuss the consensus
achievement problem and the collective perception
problem respectively. In the fourth section, the different
consensus-achievement strategies are elucidated. The
collective-perception experiments are discussed in thefifth section, whereas the limitations of the consensusachievement strategies are discussed in the sixth section.
The challenges associated with Byzantine robots are
examined in the seventh section, while the last two

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sections discuss what the future holds for consensus
achievement in swarm robotics and the conclusion thatcan be drawn from the study.
2 CLASSIFICATION OF SWARM ENGINEERING
Winfield et al. [6] define swarm engineering as “afusion of dependable systems engineering and swarm
intelligence”. Brambilla et al. [7] classified swarm
engineering based on existing works into two maintaxonomies, namely methods and collective behaviors.
The methods used to design swarm robotics systems
form the basis of the methods taxonomy and, thus, isof little importance to this study. Behaviors of swarms
to solve real-world problems are used to form thecollective-behaviors taxonomy.
Collective behaviors, in turn, are divided into four
major groups, namely spatially organizing behaviors,navigation behaviors, collective decision-making
behaviors, and other collective behaviors.
This study focuses on collective decision-making
behaviors. Brambilla et al.[7] defined collective decisionmaking as “how robots influence each other when
making choices”. Thus, collective decision-making is aprocess by which multiple individuals in a swarm cometo an agreement on a decision[7].
Brambilla et al.[7] argued that the collective decisionmaking behavior can be used to perform two different
functions, namely consensus achievement, and task
allocation. Consensus achievement is the behavior ofreaching an agreement on one decision among manyothers while task allocation is the behavior of robots
delegating different tasks among themselves[7].
Of these two functions, this study concentrates
on the consensus-achievement function. Consensus
achievement is paramount in applications of swarm
robotics such as detecting radiation leakage and oil
spillage and draws inspiration from the behaviors ofbees that collectively decide the best nesting or foraging
location and insect species such as ants that collectively
identify the shortest path with the use of pheromones[8,9].
3 CONSENSUS ACHIEVEMENT
Consensus achievement is having a swarm of robots
come to an agreement on one choice among several
other choices.
Valentini et al.[10] further classified the consensus
achievement behavior into discrete and continuous
consensus achievement. This classification is based upon
the “cardinality of the choices available to the swarm”.
The consensus achievement problem is discrete if the

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choices available to a swarm are finite and countable. On
the other hand, if the choices available are infinite andmeasurable, then the consensus achievement problem issaid to be continuous.
In order to create an abstraction of “the structure andlogic of discrete consensus achievement”, Valentini etal.[10] introduced the best-of-n problem in their paper.
Simply put, the best-of-n problem is choosing an option
i among n number of options so that the quality of i is
maximized and the cost of i is minimized. The quality
and cost associated with an option are both functions of
their environment.
Each robot in the swarm picks an option i, where i Î {1,2, …n}. A collective decision is said to have been madewhen a large majority of the robots, characterized by m,where m ³ (1 - x)n and 0 £ x £ 0.5, agree on an opinion.
Here, x is a threshold value set by the designer of the
problem. If x=0, then it becomes a consensus decision.
The authors further introduced taxonomies predicatedupon the symmetricity of the quality and cost of the bestof-n problem. If all the options available are of equalquality, the quality is symmetric, which also holds true
for cost. If there are options of different quality (or cost),
then the quality (or cost) is said to be asymmetric.
Based on the symmetric and asymmetric nature of
the cost and quality, Valentini et al.[10] (2017) classified
the best-of-n problem into symmetric option qualities
and costs, symmetric option qualities and asymmetric
option costs, asymmetric option qualities and symmetric
option costs, asymmetric option qualities and costs:
synergic case, and asymmetric option qualities and costs:
antagonistic case.
4 COLLECTIVE PERCEPTION
Valentini et al.[11], in a subsequent paper, argued thatthe effectiveness of a collective decision-making strategy
can not only be decided by the accuracy of the decisionand the time taken to make that decision but it can also
be decided by the generality of the strategy. A general
strategy will allow engineers to reuse the high-level
control logic of the strategy to address varying problems.
The authors, in their seminal paper, consequently,
introduced a novel decision-making scenario termed as
the collective perception problem to test the generality ofdifferent decision-making strategies[11].
The collective perception problem is a discrete bestof-n problem where a swarm of robots has to come toan agreement on which of the two colors of black andwhite is most frequently found in the environment.
To draw a real-life parallel, the collective perception

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problem is tantamount to a swarm of robots evaluating“the availability of precious metals”, or “the presence ofpollutants or cancer cells” in an environment.
In the collective perception scenario, there exists asquare area of area 200×200cm2 consisting of a grid that
contains cells each of area 10×10cm2. The square area isbounded by walls and can be detected by the robots toavoid collisions.
Each cell in the square area is either colored black orwhite, with each color being an abstraction of a featurein an environment. Thus, the collective perception
scenario is a best-of-2 problem since the swarm needs tochoose one of the two available options.
The quality of the color is determined by its
frequency. In the collective perception problem, theauthors set black to be the most frequent color. Hence,the swarm is expected to choose black as the best option.
E-puck robots are used as the swarm members in thisproblem. The e-puck robots are equipped with sensors
to both avoid collisions and detect the brightness of thefloor, which they can then use to determine the color[12].
The smaller footprint (a diameter of 7cm) of therobots ensures that the environment is orders ofmagnitude larger than a single robot. Besides, an e-puckcomes equipped with RGB LEDs, an accelerometer, asound sensor, a low-resolution camera, and 8 proximity
sensors. The robot also has three ground sensors that areused to measure the gray-scale values of the surface. Its
battery can last up to 45min and the robot has the ability
to move at 16cms-1.
In the collective perception scenario, the robots startwith an initial opinion. The red LED is lit if their opinionis black, and the blue LED is lit if their opinion is white.
Since its publishing, this collective perception
scenario has been used as a testing ground by subsequent
researchers to test different consensus achievement
strategies.
5 CONSENSUS ACHIEVEMENT STRATEGIES
Valentini et al. [11] used the collective perception
scenario to test three different decision-making strategies
that they had developed. The three strategies employed aset of common routines to find the best color and differed
only in the way they chose the best option. The common
routines are discussed in detail below.
There are two states in these strategies, namely the
exploration state and the dissemination state and these areakin to the waggle dance found in the bee populations[13].

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In the exploration state, as the name implies, the robots
explore their environments by performing random walkand rotations. A robot moves in straight lines for a random
time sampled from an exponential distribution with amean value of 40s. Then, the robot turns for a random
time chosen from a uniform distribution, which is between
0s to 4.5s. The direction of rotations is randomly chosenwith both clockwise and counterclockwise rotations
having an equal probability. Once the rotation is complete,
the robots continue their linear motion.
If a robot stumbles upon an obstacle, either in the wayof another robot or a wall, within approximately 30cm,
the robot pauses its motion, and the obstacle avoidanceroutine is triggered.
During the obstacle avoidance routine, a robot utilizes
its proximity sensors to detect the distance and bearingof each identified obstacle. It, then, makes use of thisinformation to compute a new direction opposite to the
obstacles. Following this, the robot starts its random
walk again.
During this exploration state, the robots use their
ground sensors to measure the quality of their opinion.
To measure the quality of their opinion, the robots sample
the color of the surface as they perform random walk. The
quality pi of an opinion i, where i Î {a, b} (a corresponds
to black and b to white), is defined as the fraction of theamount of time the robot perceived the color of its opinion(ti) over the total amount of time the robot spent in the
exploration state (t). This is given by Equation (1).

For instance, if a robot’s opinion is black (opinion a)and it spends 20s in the exploration state, during which
it perceives the color black on the floor for 10s, then thequality of its opinion pa is given by Equation (2).

This perceived quality is the metric based on which
the swarm decides the best opinion. The exploration
state is followed by the dissemination state. During thedissemination state, a robot engages in random walk,rotation, and obstacle avoidance as it does during the
exploration state.

in the dissemination state for a random amount of timesampled from an exponential distribution with a mean
given by the quality of the robot’s opinion pi times aconstant g. Here, g is a parameter whose value is decided
by the designer. Thus, the higher the quality of opinionpi, the longer the robot remains in the dissemination state.
This ensures that a robot with a higher quality opinion
gets to broadcast its opinion to a lot of neighbors.
In this strategy, pi acts as a modulator, thus, giving
this strategy a part of its name, and g acts as an unbiased
dissemination time.
During the dissemination state, robots broadcast
their opinion pi to their neighbors while receiving theopinions of the neighboring robots. Towards the end of
the dissemination time, a robot changes its opinion to theopinion of the majority, which includes that of its own,
and then switches back to the exploration state[14,15].
5.2 Direct Modulation of Voter-based Decision(DMVD)The DMVD strategy is similar to the DMMD anddiffers only in its decision-making mechanism. Much
like the DMMD strategy, the DMVD strategy also
modulates its dissemination time based on the perceived
quality of its opinion pi.
Nonetheless, when the DMVD strategy is used, robots
adopt the opinion of a random neighbor as their own[11].
5.3 Direct Comparison (DC)The DC strategy does not modulate the dissemination
time like the DMMD and DMVD strategies. Instead, thedissemination time is a random sample drawn from an
exponential distribution with a mean of g.
Moreover, the robots not only broadcast their own
opinion to their neighbors, but they also broadcast thequality of their own opinion. At the same time, robots
compare the quality of their opinion with that of arandom neighbor and adopt the greater of the two as
their own opinion[11].
Consensus is said to have been achieved when all therobots end up having the same opinion (Table 1).

However, in addition to these general routines, therobot also broadcasts its opinion to its neighbors. As towhat else happens during this state is determined by thedecision-making strategy used.

6 COLLECTIVE PERCEPTION EXPERIMENTS
Valentini et al. [11] compared the three strategies
discussed above using the collective perception scenario.
In order to analyze the performance of the decisionmaking strategies, the authors used the exit probability
EN and consensus time TN of the strategies.

5.1 Direct Modulation of Majority-based Decision(DMMD)
When the DMMD strategy is used, a robot remains

The exit probability is the number of times a strategy
resulted in the correct consensus over the total number oftimes the experiment was run. The consensus time is theInnovation Forever Publishing Group

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Table 1. A Summary of the Consensus-achievement Strategies
Strategy

Dissemination Time

What is Broadcast

How Opinions are Updated

DMMD

Randomly drawn from an exponential
distribution with a mean given by the quality
times a constant g

OpinionBased on the opinion of the majority

DMVD

Randomly drawn from an exponential
distribution with a mean given by the quality
times a constant g

OpinionBased on the opinion of a random neighborDC

Randomly drawn from an exponential
distribution with a mean of gOpinion and quality ofopinionThe opinion is compared to the quality ofthe opinion of a random neighbor, and theopinion with the better quality is chosen.

average amount of time taken for a correct consensus.
The authors adjusted the difficulty of the scenario
by adjusting the number of black and white cells. The
difficulty pb* of choosing black as the best opinion is
given by Equation (3).

In Equation (3), pa and pb are given by Equation (4)and Equation (5).

Where na is the number of black cells and nb is thenumber of white cells on the floor. In other words, thedifficulty is the ratio between the percentage of black cells
and white cells on the floor.
Furthermore, the initial number of robots with opiniona (Ea(0)) was also adjusted to study their impact on theperformance, and the size of the swarm was set to 20
robots.
The authors used the ARGoS simulator to carry out theexperiment[16]. Two difficulty values of 0.515 and 0.923
were used. The experiment was repeated 1000 times foreach parameter configuration.
Following the experiment, the authors found that the exit
probability EN increased with the increase in Ea(0) for all
strategies. Besides, the authors also found DMMD to be theleast accurate and DC to be the most accurate. In contrast,
DMMD was the fastest strategy, and DC was the slowest.
In addition, DC was also found to have poor scalability
as its consensus time increased much faster than otherstrategies when the size of the swarm was increased from
20 to 100.
7 LIMITATIONS
Even though Valentini’s decision-making strategies
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performed well in terms of exit probability andconsensus time, they failed to account for Byzantine
robots. Thus, the performance of these strategies in thepresence of Byzantine robots was not studied.
The study conducted by Strobel et al. [19] found
Valentini’s three strategies to fail to converge on the right
opinion in the presence of around 4 or more Byzantine
robots[4].
8 BYZANTINE ROBOTS
Byzantine robots are robots that lead to the Byzantine
generals’ problem. The Byzantine generals’ problem isa situation where consensus needs to be achieved whensome of the actors are unreliable[17]. Thus, Byzantine
robots can be defined as robots that are either malicious
or malfunctioning.
This is a critical issue since, as the study by Higgins
et al.[18] shows, identity and authentication, and intrusion
by foreign robots among others are major security
challenges in a swarm robotic environment.
Subsequent studies have explored the possibility ofusing blockchain to mitigate the threat of Byzantine
robots. Strobel et al.[19] developed a blockchain smart
contract to identify and ignore the opinion of Byzantine
robots. However, this solution suffered from the 51%
attack problem that is endemic to the Proof-of-Workconsensus algorithm used in blockchains. Moreover, thestudy failed to test the feasibility of using blockchain inswarm robots that are simple and powerless by design.
A new blockchain consensus algorithm called Proofof Identity was proposed to address the 51%-attack
threat in Strobel’s solution[20]. Pacheco et al.[21] used theproof of authority algorithm to successfully mitigate the
51%-attack threat while demonstrating the feasibilityof using blockchain in swarm robots by running
experiments using Pi-puck robots.
9 FUTURE WORK
Swarm robotics is still in its infancy and the studies
on consensus achievement augur well for the future
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https://doi.org/10.53964/mit.2023001
of swarm robotics. The use of blockchain to solve
consensus-achievement problems has opened up a
new pathway in swarm robotics even though, this newparadigm is not without its drawbacks. For instance, theuse of blockchain in consensus achievement involves
achieving multiple blockchain consensuses before
a swarm consensus can be reached. This calls into
question the rationale of using blockchain in swarm
robotics. However, since existing studies have alreadydemonstrated the efficacy of blockchain, probably,
future studies can explore the possibility of developing
a blockchain algorithm that can reduce the number ofblockchain consensus needed to reach swarm consensus
while retaining the benefits afforded by blockchain toswarm robotics.
Moreover, the existing consensus-achievement
strategies involve robots broadcasting their opinion only
to their neighboring robots. This can be enhanced byusing mesh-network protocols such as Zigbee that canbe used to broadcast one robot’s opinion to the entire
swarm. Besides, the advent of swarm robots such as
Pi-puck robots that make use of efficient single-board
computers like Raspberry Pi means that even Wi-Fi
can be used to develop new faster, and more efficientconsensus-achievement strategies.
10 CONCLUSION
Swarm robotics uses concepts of swarm intelligenceto solve problems. Consensus achievement is one of the
major behaviors exhibited by swarms of robots, wherea swarm of robots tries to come to a consensus on thebest of many choices available. Consensus achievement
can be categorized into discrete consensus achievement
and continuous consensus achievement based on the
cardinality of the choices available. The collective
perception scenario was introduced to test consensusachievement strategies such as DMMD, DMVD, and
DC. Even though these strategies solve the collective
perception scenario with varying degrees of success,they are all vulnerable to Byzantine robots. Byzantine
robots have been shown to be a security issue of concern.
Thus, it is imperative that a solution to the vulnerability
to Byzantine robots is found in consensus-achievement
strategies.

following: study conception and design, literature
review, analysis and interpretation of results, andmanuscript preparation.
Abbreviation List
DC, Direct comparison
DMMD, Direct modulated majority-based decision
DMVD, Direct modulated voter-based decision
LED, Light emitting diode
RGB, Red green blue
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Acknowledgments
The author would like to acknowledge Mr. Guhanathan
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Conflicts of Interest
There is no conflict of interest.

[12]

Author Contribution
Krishnamohan T confirms sole responsibility for theInnovation Forever Publishing Group

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