A Review of Swarm Robotics in a NutShell

Abstract

A swarm of robots is the coordination of multiple robots that can perform a collective task and solve a problem more efficiently than a single robot. Over the last decade, this area of research has received significant interest from scientists due to its large field of applications in military or civil, including area exploration, target search and rescue, security and surveillance, agriculture, air defense, area coverage and real-time monitoring, providing wireless services, and delivery of goods. This research domain of collective behaviour draws inspiration from self-organizing systems in nature, such as honey bees, fish schools, social insects, bird flocks, and other social animals. By replicating the same set of interaction rules observed in these natural swarm systems, robot swarms can be created. The deployment of robot swarm or group of intelligent robots in a real-world scenario that can collectively perform a task or solve a problem is still a substantial research challenge. Swarm robots are differentiated from multi-agent robots by specific qualifying criteria, including the presence of at least three agents and the sharing of relative information such as altitude, position, and velocity among all agents. Each agent should be intelligent and follow the same set of interaction rules over the whole network. Also, the system’s stability should not be affected by leaving or disconnecting an agent from a swarm. This survey illustrates swarm systems’ basics and draws some projections from its history to its future. It discusses the important features of swarm robots, simulators, real-world applications, and future ideas.

1. Introduction

A swarm of robots refers to the coordination of multiple individual entities, which traditionally operate without centralized control and instead rely on simple local behaviors to cooperate. Robot technology, particularly Unmanned Aerial Systems (UAS), is becoming more affordable, efficient, and is boosting the transmission capacity of robots as solutions to problems ranging from disaster relief to research mapping. Independent robots can perform tasks that need simple, ready to go solutions and a consistent real time approach. The autonomous robot can be a part of a robot swarm, if it fulfills at least three significant characteristics. These characteristics include the following: the minimum number of individual entities must be three or more, minimal or no human control, and cooperation between these robots based on a simple set of rules as depicted in Figure 1. Swarm robotics include a group of independent robots working collaboratively to complete a shared task without relying on any external infrastructure or a centralized control system/robot. Figure 2 illustrates how the fundamental concept of the swarm may be comprehended. In Figure 2a, the system is a robot swarm which consists of three autonomous agents that cooperate in response to the orders received from a single ground control station. Figure 2b indicates that the system is a sensor network rather than a swarm of robots. Each sensor is neither a robot nor an intelligent agent, and is solely responsible for providing data through readings without the capability of taking any actions. Figure 2c does not depict a robot swarm since a swarm necessitates more than two agents. Despite the robots working together towards a shared objective, each one has its own designated tasks to accomplish, which are directed by a separate operator. Figure 2d depicts a software system comprising multiple agents, which cannot be classified as a robot swarm as the agents are not autonomous robots, despite their collaboration on a shared hardware platform.

Swarm robotics involves a group of robots that collaborate to address problems through the development of advantageous structures and behaviours that resemble those observed in nature, such as birds, fish, and bees. These robots, which can be either homogeneous or heterogeneous, form an intelligent network of a swarm, enabling individual robots to interact autonomously with each other and their environment by leveraging onboard communication, processing, and sensing capabilities. Such behaviours can be classified into four categories, namely navigation, spatial organization, intelligent and precise decision-making, and miscellaneous [1]. This study offers an in-depth analysis and mathematical comprehension of swarm intelligence algorithms. It also provides a comprehensive review of the evolution of swarm robotics from its inception to the present day and highlights the future ambitions of this field. Our aim is to present a broad overview of swarm robotics by exploring its history, current research, and future directions. The main contributions are as follows:

• To understand the fundamental difference between multi-agent and swarm of robots, along with the natural behaviours of a swarm.
• Multiple swarm intelligence algorithms derived from the natural set of rules and constraints for their transformation on multi-agent robots.
• Industrial and academic utilization of swarm robotics keeping in view the history and future perspectives.
• The objective is to address the research gap that exists between theoretical and industrial research in the field of swarm robotics. Theoretical research mainly involves simulating swarm behaviours using algorithms, while research in industrial settings are primarily focused on designing and developing hardware capable of executing swarm behaviour. Therefore, it is imperative to deploy swarm algorithms using specific hardware that can accommodate swarm behaviour functionality.

Figure 2. Comparison of Multi-agent Systems and Robot Swarm [2]. (a) depicts swarm robotics system, while (b–d) show non-swarm systems.

Figure 2. Comparison of Multi-agent Systems and Robot Swarm [2]. (a) depicts swarm robotics system, while (b–d) show non-swarm systems.

Figure 3 depicts the deployment of swarm behaviours in simulation and hardware, which is thoroughly explored in Section 2 of this article. The behaviours are simulated using existing and state-of-the-art swarm intelligence algorithms, as explained in Section 3 with mathematical reasoning. The simulation results demonstrate high accuracy in replicating natural animal behaviours. For the past two decades, the main research challenge in swarm robotics has been to develop multi-robot systems that are robust, flexible, fault-tolerant, and capable of incorporating self-organizing behaviours dynamically and by design. The swarm robotics field has evolved from algorithmic studies to mature academic, laboratory, and industrial-based solutions since the early 2000s. A comprehensive review of swarm robotics and its applications is presented in

Table 1. Era of Swarm Robotics: Past, Present, and Future Perspectives.

1990–2000	The first robot tests show self-organization through indirect and local interactions, clearly inspired by swarm intelligence.	SW
2000–2005	The ability to generate swarms of robots that work together has now been expanded to a variety of additional tasks, including object handling, task allocation, and occupations that require significant teamwork to achieve.	SW
2002–2006	Swarm-bots is a project that shows how robot swarms self-assemble. Robots can construct pulling chains and massive constructions capable of transporting large loads and dealing with tough terrain.	HW and SW
2004–2008	The evolving swarm robotics technique was devised after the first demonstrations of autonomous assembly of robot swarms using evolutionary algorithms.	SW
2005–2009	For swarm robotics research, the first attempts at building standard swarm robotics platforms and small robots.	HW
2006–2010	Swarmanoid showed heterogeneous robot swarms made up of three different types of robots: flying, climbing, and ground-based robots for the first time.	HW and SW
2010–2015	Advanced autonomous design methods such as AutoMoDe, novelty search, design patterns, mean-field models, and optimal stochastic approaches are all employed in the creation of robot swarms.	SW
2016–2020	Decentralized solutions have been investigated and deployed as swarms of flying drones become available for investigation.	HW and SW
2020–2025	The first example of robot swarms that may self-learn suitable swarm behaviour in response to a specific set of challenges.	SW
2025–2030	Marine and deep-sea robotic swarms will be utilized for ecological monitoring, surveillance, and fishing, among other things.	HW
2030–2040	Small rover swarms will be utilized for the first mission to the Moon and Mars to expand the exploration area and showcase on-site construction capabilities.	HW
2040–2045	Soft-bodied robot swarms measuring in millimeters will be deployed to explore agricultural fields and aquatic areas to identify plastic usage and assist with pest control.	HW and SW
2035–2050	Clinical research with human volunteers will begin after nanoscale robot swarms have been shown for therapeutic objectives such as customized medication delivery.	HW and SW

and Section 4, respectively. Despite significant progress, cooperation and coordination in deploying the developed swarming algorithms among swarm robots remain limited [3]. Section 5 provides a brief overview of the era of swarm robotics, and the article concludes in the final section.

2. Swarm Robotics Fundamental Behaviours

Swarm algorithms are characterized by individual entities following local rules, resulting in the emergence of overall behaviour through swarm interactions. In swarm robotics, robots exhibit local behaviours based on a set of rules ranging from basic reactive mapping to complex local algorithms. These behaviours often involve interactions with the physical environment, such as other robots and surroundings [4]. The interaction process involves retrieving environmental values and subsequently processing them to drive the actuators in accordance with a set of instructions. This recurring process is referred to as the fundamental activity and persists until the desired state is attained. Figure 4 illustrates a summary of several naturally occurring behaviours that are further elaborated in the subsequent subsection.

2.1. Spatial Organization

These behaviours allow robots in a swarm to move around the environment and spatially arrange themselves around things.

Object Clustering and Assembly allow a swarm of robots to control geographically dispersed things. These are critical for construction processes. Pattern Formation organizes the robot swarm into a precise form. Chain Formation is a specific instance where robots construct a line to establish multi-hop communication between two places [1,5]. Self-assembly links robots to form structures. They can be connected physically or remotely via communication lines [1,6]. Morphogenesis is a specific instance in which the swarm grows into a predetermined form [1,7,8]. Aggregation pushes the individual robots to gather spatially in a certain location of the environment. This permits swarm members to get geographically near to one another for further interaction [1,9,10].

2.2. Navigation

These characteristics enable a swarm of numerous robots in the environment to move in unison. Thus, a group of robots move in harmony from one location to another or from a source to a final destination [1,11].

Collective Localization allows the swarm’s robots to determine their location and orientation relative to one another by establishing a local coordinate system across the swarm [1]. In Collective Transport, a swarm of robots may collectively move things that are too heavy or massive for individual robots [1]. Coordinated Motion moves the swarm in a configuration that must have a well-defined shape or structure, such as a line, triangle, or arbitrary formation of robots, as in flocking [1]. Collective Exploration navigates the environment to examine things, monitor the environment, or create a robot-to-robot communication network [1,12].

2.3. Decision Making

This characteristic of swarm robotics facilitates collective decision-making for accomplishing specific tasks collaboratively. The Group Size Regulation feature empowers the swarm’s robots to create groups of the required size, and if the swarm’s size exceeds the required group size, it automatically divides into multiple groups or sub-swarms [1,13]. Additionally, the Collective Fault Detection feature detects individual robot shortcomings inside the swarm, enabling the identification of robots that deviate from the expected behaviour due to hardware or some algorithmic issues [1,14]. Furthermore, Synchronization aligns the frequency and phase of the swarm’s oscillators, enabling the robots to share a common perception of time and execute tasks in synchrony. The Collective Perception feature aggregates the locally collected data from the swarm’s robots into a comprehensive image. It allows the swarm to make collective decisions, such as accurately classifying objects, allocating a suitable percentage of robots to a given task, or determining the best solution to a global problem [1]. Moreover, the Task Allocation feature dynamically assigns emergent tasks to individual robots, aiming to maximize the overall performance of the swarm system. In cases where the robots possess diverse skill sets, the work can be assigned differently to further enhance the system’s performance [1,15]. Finally, the Consensus feature allows the swarm of robots to converge on a single common point from multiple available options [1,16].

2.4. Miscellaneous

The swarm robots exhibit additional behaviours beyond the previously discussed categories. Self-healing behaviour allows the swarm to recover from individual robot failures, improving the swarm’s reliability, resilience, and overall performance [1,17]. Self-reproduction enables a swarm of robots to add new robots/agents or replicate the patterns created by several individuals, thereby increasing the swarm’s autonomy by eliminating the need for human intervention in the construction of additional robots. Human-swarm Interaction facilitates communication between humans and the swarm of robots, either remotely via a computer terminal or in a shared area using visual or auditory cues [1].

3. Swarm Intelligence Algorithms

Swarm Intelligence (SI) is a collective intelligence employed in various applications, including self-organized and decentralized systems [18]. Some examples are collective sorting, cooperative transportation, group foraging, and clustering. Self-organization and division of work are two essential notions in SI. The ability of robots to evolve into a proper pattern without external assistance is referred as self-organization. In contrast, division of labor refers to the simultaneous execution of multiple tasks by individual robots. It enables the swarm to execute a challenging task that requires individuals to collaborate. Genetic Algorithm (GA), Ant Colony Optimization (ACO), Particles Swarm Optimization (PSO), Differential Evolution (DE), Artificial Bee Colony (ABC), Glowworm Swarm Optimization (GSO), and Cuckoo Search Algorithm (CSA), are all examples of famous and currently used swarm intelligence algorithms.

3.1. Genetic Algorithm

Genetic Algorithms (GA) were introduced in 1975 by John Holland [19,20]. This type of algorithm mimics natural existing biological behaviours in order to evaluate the survival of the fittest. In a genetic algorithm (GA), a specified number of individuals, also known as members, comprise the population. Mathematical operators such as crossover, reproduction, and mutation are used to manipulate the genetic makeup of individuals. Based on these operators, the fitness value of each member is calculated and ranked accordingly. The previous population’s traits, represented by chromosomes (or strings), are combined with new traits to generate a new population [21,22,23,24]. A GA algorithm with five basic steps is shown in Figure 5. The fitness function evaluates population members, which begins with an initial population that can be generated randomly or through a heuristic search. After the population members are assessed, the lowest-ranked chromosome is eliminated, and the remaining members are used for reproduction. The final step is mutation, in which the mutation operator modifies genes on a chromosome to ensure that every part of the problem space is explored. This process of evaluating and generating new populations continues until the best solution is found.

It has a vast area as an application, which includes, navigation and formation control [25], path planning [26], scheduling [27,28], machine learning [29], robotics [30,31], signal processing [32], business [33], mathematics [34], manufacturing [35] and routing [36].

Figure 5. Flow Chart of Genetic Algorithm [37].

Figure 5. Flow Chart of Genetic Algorithm [37].

3.2. Ant Colony Optimization

Ant Colony Optimization (ACO) is a heuristic search-based algorithm that uses the ant colony system to solve problems. It was proposed by Marco Dorigo as part of his Ph.D. study in 1992 [38]. The four fundamental components of the ant-inspired foraging algorithm are the ant, pheromone, daemon action, and decentralized control. The ant acts as an imaginary agent which mimics the behaviour of exploitation and exploration processes in a search space and produces a chemical substance called pheromones. Its intensity varies with the passage of time due to the evaporation process and serves as a global memory for the ant’s path of travel. Daemon activity is used to gather global data whereas, the decentralized control is used for the robustness of the ACO algorithm and to maintain flexibility within a dynamic environment. The Figure 6a–c show the initial, mid-range, and final outcomes of the ACO algorithm, respectively [38,39]. Figure 6a shows the initial random environment in which the agent (or ant) from the nest begins the process. When ants discover numerous viable paths from the nest to the source, they go through many iterations of execution, as shown in Figure 6b. The ant has chosen the shortest possible path, which contributes to the pheromone trail’s high intensity. Equation (1) below is used as an initial step in determining the optimal solution to select the best node from the current search space.

$$p_{(n,m)}^u\left(t_o\right)=\frac{\left({\left[{\tau }_{nm}\left(t_o\right)\right]}^{\alpha }·{\left[{\eta }_{nm}\right]}^{\beta }\right)}{\left({\sum }_{u\in I_u}{\left[{\tau }_{nm}\left(t_o\right)\right]}^{\alpha }·{\left[{\eta }_{nm}\right]}^{\beta }\right)}$$

(1)

The probability of travelling from node n to node m is $p_{(n,m)}$, $I_u$ are the nodes to which the ant is permitted to go from node n, whereas ${\eta }_{(}nm)$ adds to visibility between nodes n and m and it indicates the quantity of un-evaporated pheromone between nodes at a time $t_o$. $\alpha$ and $\beta$ in Equation (1) regulate the impact of ${\tau }_{nm}\left(t_o\right)$ and ${\eta }_{nm}$, where, if $\alpha$ is larger, the ant’s searching behaviour is more pheromone-dependent, and if $\beta$ is higher, then the ant’s searching depends on its visibility or knowledge.

In order to deposit a pheromone, the following equation is used:

$$\Delta {\tau }_{nm}^u\left(t\right)=\left\{\begin{array}{c}\frac{Q}{L_u}\left(t\right)\hfill \\ 0\hfill \end{array}\right.$$

(2)

Q is a constant, L is the cost of the ant’s tour that represents the length of the created path, t is the iteration number and u shows a specific ant. Another key factor is pheromone evaporation rate, which shows exploration and exploitation behaviour of the ant. In Equation (3), s is the number of ants in the system and p is the pheromone evaporation rate or decay factor.

$${\tau }_{nm}(t+1)=(1-p).{\tau }_{(n,m)\left(t\right)}+\sum _{k=1}^s[\Delta {\tau }_{n,m}^u\left(t\right)]$$

(3)

Compared to other heuristic-based approaches, ACO guarantees to converge, but the time required for it is uncertain and for better performance, the search space should be small [40,41]. Its applications include vehicle routing [42,43], network modelling problem [44,45], machine learning [46], path planning robots [47], path planning for Unmanned Aerial Vehicles (UAVs) [48], project management [49] and so on.

3.3. Particle Swarm Optimization

Kennedy and Eberhart invented Particle Swarm Optimization (PSO) in 1995, and it uses a simple method to encourage particles to explore optimal solutions [50]. It is based on flocking bird and schooling fish behaviours [51], by exhibiting three simple behaviours: separation, alignment, and cohesiveness. Separation is used to avoid congested local flock-mates, alignment is the travelling of one flock-mate in the same average direction of the other flock-mates, and cohesiveness is the movement of flock-mates toward the average position. The PSO algorithm is as follows [50,52,53]:

$$\begin{array}{c}{v}_{id}^{t+1}=v_{id}^t+c_1·rand(0,1)·\left(p_{id}^t-x_{id}^t\right)+c_2·rand(0,1)·\left(p_{gd}^t-x_{id}^t\right)\\ x_{id}^{t+1}=x_{id}^t+v_{id}^{t+1}\end{array}$$

(4)

where $v_{id}^t$ and $x_{id}^t$ are particle velocity and position, whereas d is search space dimension, i represents particle index and t shows the iteration number. $c_1$ and $c_2$ depict the speed and regulating length of the swarm when it travels towards the optimal particle position. The optimal position attained by particle i is $p_i$ and the best position found by neighbouring particles of i is $p_g$. The process of exploration ensues if either or both of the differences between the best of particle $p_{id}^t$ and the previous position of particle $x_{id}^t$ and between the population all-time best $p_{gd}^t$ and the previous particle’s position $x_{id}^t$ are large. Similarly, the process of exploitation happens when both of these values are small. PSO has been demonstrated as an effective, robust, and stochastic optimization algorithm for high-dimensional spaces. The key parameters of PSO include the position of the agent in space, the number of particles, velocity, and the agent’s neighbourhood [54,55,56].

The PSO algorithm begins by initializing the population, and the second step is to calculate the fitness of each particle. Whereas, the third step is followed by updating the individual and global best. In the fourth step velocity and neighbourhood of the particles are updated. Steps two to four keep repeating until the terminating condition is satisfied [51,54,57,58].

Figure 7 shows the working of the PSO method, where the particles are spread out in the first iteration to discover the best exploration. The best solution is identified in terms of neighbourhood topology, and each member’s personal and global best particles are updated. As indicated in the figure, the convergence would be determined by attracting all particles towards the particle with the best solution.

PSO is simple to configure for efficient global search, has few parameters to set, is scale-insensitive, and parallelism for concurrent processing is also easy. Population size is one of the key factors that ensures precise and fast convergence for large population sizes [51,59]. Networking [60], power systems [61], signal processing [62], control systems [63], machine learning [64], and image processing [65,66,67] are some of the applications.

3.4. Differential Evolution

Differential Evolution (DE) is similar to GA, using the same crossover, mutation, and selection operators. The fundamental difference between the two algorithms is that the DE utilizes the mutation operator while GA uses the crossover operator to produce a superior solution. Price and Storn first introduced it in 1997 [68]. DE repeatedly generated new populations using three properties: mutant vector, target vector, and trail vector explained in Figure 8. A crossover process between the target and mutant vectors produces the trailing vector. The mutant vector represents the mutation of the target vector, whereas the target vector represents the vector holding the search space solution [69,70]. The DE algorithm starts with population initialization and then evaluates the population to find the fittest members. The weighted difference between the two population vectors is added to the third vector to create new parameter vectors and this process is known as mutation. The vector is blended within the crossover to perform a final selection.

N parameter vector mutation is generated by using the following equation:

$$v_{j,N+1}=x_{l1,N}+F\left(x_{l2,N}-x_{l3,N}\right).$$

(5)

i shows the index of the 2D vector. $x_{l1}$, $x_{l2}$, and $x_{l3}$, are solution vectors selected randomly and the values of l1, l2l3 and i should not be equal to each other. F is the scaling factor ∈ [0,1], while, a crossover procedure is employed to improve the variety of the disconcerted parameter vectors. The parent and mutant vectors are combined in the following method to create a trial vector:

$$u_{i,G+1}=\left\{\begin{array}{c}{v}_{i,G+1}\mathrm{if}{R}_j\le CR\hfill \\ x_{i,G}\mathrm{if}{R}_j>CR\hfill \end{array}\right.$$

(6)

where $CR$ denotes the crossover constant. $R_j$ denotes a random real number $ϵ$ [0,1] while j depicts the resultant array’s $j^{th}$ component.

The primary distinction between DE and GA operations is that in DE, the probability of being selected as a parent is not based on fitness value. Increasing the population size can significantly improve DE performance.

DE can be found in a variety of fields, including, robot path planning [71,72] engineering [73], image processing domain [74], machine learning [75], and economics [76].

3.5. Artificial Bee Colony

Dervis Karaboga presented Artificial Bee Colony (ABC) as an important SI algorithm in 2005 [77]. Its performance is thoroughly examined in [78], which concluded that ABC outperforms other techniques. It is based on honey bees’ intelligent behaviour in locating food and communicating information about that food with other bees. ABC is as straightforward as PSO, and DE [78], which divides artificial agents into three types: employed, observer, and scout bees. Each agent bee is given a particular task to finish the algorithm process. The employed bee concentrates and memorizes the food supply. The employed bee provides the observer bee with the information about the hive’s food supply. The scout bee is on the lookout for new nectar and its sources. Figure 9 presents the algorithmic flow of the ABC. The ABC method’s overall procedure and specifications of each step are explained below [77,78,79]:

Step 1. Initialization: Food sources, $x_i$, are initialized with $i=1...N$, where N is the number of scout bees in the population. $l_i$ and $u_i$ are the control parameters represent lower and upper limits, respectively. The following Equation (7) represents the initialization phase:

$$x_i=l_i+rand(0,1)\ast \left(u_i-l_i\right)$$

(7)

Step 2. Employed Bees: The search capacity for finding new neighbour food source $v_i$ increases to accumulate more nectar around the neighbour food source $x_i$. Once they identify a nearby new food source supply, its profitability and fitness value are assessed. The following formula is used to define the new nearby food source:

$$v_i=x_i+{\varphi }_i\left(x_i-x_j\right)$$

(8)

where $x_j$ is a randomly selected food source. ${\varphi }_i$ has random numbers of range between [−a, a]. After the profitability of the new source $v_i$ is determined, a greedy selection is used between $\overrightarrow{x_i}$ and $\overrightarrow{v_i}$. The process of exploration occurs if $x_i$−$x_j$ is greater, otherwise exploitation happens. The fitness value $fi{t}_i\left(\overrightarrow{x_i}\right)$ is computed by the following Equation (9) and objective function with solution value $x_i$ is $f_i\left(\overrightarrow{x_i}\right)$.

$$fi{t}_i\left(\overrightarrow{x_i}\right)=\left\{\begin{array}{c}\frac{1}{1+f_i\left(\overrightarrow{x_i}\right)}\mathrm{if}{f}_i\left(\overrightarrow{x_i}\right)\ge 0\hfill \\ 1+abs\left(f_i\left(\overrightarrow{x_i}\right)\right)\mathrm{if}{f}_i\left(\overrightarrow{x_i}\right)<0\hfill \end{array}\right.$$

(9)

Step 3. Onlooker Bees: After calculating the fitness value and by obtaining information from employed bees, a probability value $p_i$ is computed by using Equation (10), and this value is then shared with the waiting bees in the hives for selecting food sources. These bees are known as onlooker bees.

$$p_i=\frac{fi{t}_i\left(\overrightarrow{x_i}\right)}{{\sum }_{i=1}^{SN}fi{t}_i\left(\overrightarrow{x_i}\right)}$$

(10)

Step 4. Scout Bees: Employed bees that cannot raise their fitness values after multiple repetitions become scout bees. These unemployed bees choose sources at random.

Step 5. Best Fitness: The best fitness value and the exact position with an associated value are memorized.

Step 6. Termination Checking Phase: The program terminates upon meeting the termination condition. If the termination condition may not be reached, the program goes back to step 2 and repeats the process until it is.

Since ABC has only two control factors, colony size and maximum cycle number, it is straightforward to set up, robust and customize-able. It is also possible to add and remove bees without re-initializing the algorithm [80,81]. The disadvantage of ABC is that additional fitness tests for new parameters are required to increase the algorithm’s overall performance. It is also slow when a large number of objective function evaluations are required [82]. Path planning for multi-UAVs [83], engineering design difficulties [84,85], networking [86], electronics [87], scheduling [87], and image processing [87] are some of the disciplines where it is used.

3.6. Glowworm Swarm Optimization

Glowworm Swarm Optimization (GSO) is a new SI based approach presented by Krishnanad and Ghose in 2005 [88,89] to optimize multimodal functions. In GSO, glowworms are real-life tangible creatures. There are three key parameters in a glowworm m condition at time t: a search space position $x_m\left(t\right)$, a luciferin level $l_m\left(t\right)$, and a neighbourhood range $r_m\left(t\right)$ [88,89,90]. These variables change over time, whereas the glowworms are distributed throughout the work area at random initially, and then the other settings are set using pre-determined constants. It is similar to earlier algorithms, where three phases are continued until the termination condition is reached. The three steps of [88] are luciferin level update, glowworm migration, and neighbourhood range update. The fitness value of glowworm m’s current position of luciferin level is updated by using the following equation:

$$l_m\left(t\right)=(1-p)·l_m(t-1)+\gamma J(x_m\left(t\right)$$

(11)

where p is the luciferin evaporation factor and J represents the objective function. For position update in the search space, the following equation is used:

$$x_m\left(t\right)=x_m(t-1)+s\frac{(x_n(t-1)-x_m(t-1)}{\left|\right|(x_n(t-1)-x_m(t-1)||}$$

(12)

where s is the step size, and ||.|| is euclidean norm operator. Exploration and exploitation behaviours occur on the basis of $x_n$ and $x_m$ difference. Greater difference leads to exploration and smaller to exploitation behaviour.

If a glowworm has several neighbours to choose from, one is selected using the following probability equation and the glowworm m is the neighbour of glowworm n only if the distance between them is shorter than the neighbourhood range $r_m\left(t\right)$:

$$p_{\mathrm{m}}\left(\mathrm{t}\right)=\frac{l_{\mathrm{m}}\left(\mathrm{t}\right)-l_{\mathrm{n}}\left(\mathrm{t}\right)}{{\sum }_{\mathrm{k}\in \mathrm{Ni}\left(\mathrm{t}\right)}{l}_{\mathrm{k}}\left(\mathrm{t}\right)-l_{\mathrm{n}}\left(\mathrm{t}\right)}$$

(13)

The following equation is used to compute the neighbourhood range:

$$r_m(t+1)=min\left\{r_s,max\left[0,r_m\left(t\right)+\beta \left(n_d-\left|n_m\left(t\right)\right|\right)\right]\right\}$$

(14)

$r_s$ represents sensor range, $n_d$ is the desired number of neighbours, $|n_m\left(t\right)|$ is several neighbours of the glowworm m at time t, and $\beta$ is a model constant. The diagram below demonstrates two hypothetical scenarios in which agents developing methods result in distinct behaviours depending on the agents’ placement in the search space and the accessible nearby agents. The glowworm’s agents are represented by i, j, and k. Figure 10a signifies agent j’s sensor range, whereas $r_d^j$ denotes agent j’s local-decision range. The same is true for i and k, where $r_s^i$ and $r_d^i$, $r_s^k$ and $r_d^k$ respectively denote sensor range and local-decision range. It is applied in the circumstances where agent i is in the sensor range of agent j and k. Only agent j uses the input from agent i because the agents have different local decision domains. Glowworm agents are a, b, c, d, and e in Figure 10b. The glowworm agents are ranked 1, 2, 3, 4, and 5, depending on their luciferin values.

The following modifications can be considered to improve the performance of GSO. (i) To include all agents in the solution, consider increasing the number of neighbourhoods. When the best solution has been identified, all the agents can travel in the direction of the agent which has the best solution, because more agents will be within the optimal solution range and it will also increase the efficiency of exploitation; (ii)In the neighbourhood range, smallest possible number should be selected to increase the convergence rate of GSO. Since there are fewer calculations needed to estimate the probability and direction of the GSO’s movement, this action may decrease the GSO’s processing time.

GSO is useful in situations when only a small sensor range is required. It can detect many sources and can be used to resolve problems of numerical optimization [88,89,90]. It is also inaccurate and has a slow convergence rate [91,92]. 3-Dimensional path planning [93], self-organization based clustering scheme for UAVs [94], routing [95], swarm robotics [96], image processing [97], and localization [98,99] difficulties have all been solved using GSO.

3.7. Cuckoo Search Algorithm

Yang and Deb in 2009 proposed Cuckoo Search Algorithm (CSA) as one of the most current meta-heuristic techniques. The behavior of cuckoos, i.e., brood parasites, and the properties of Levy flights [100] inspired this algorithm. Three steps are followed throughout the implementation of this approach. First, in each repetition, each cuckoo lays one egg, and the nest in which the cuckoo lays its egg is chosen at random by the cuckoo. Quality eggs and nests are passed down from generation to generation in the second step. In the third step, the number of possible host nests are fixed, and a host bird uses probability $p_a$$ϵ$ [0,1] to find a cuckoo egg. In other words, the host can either reject the egg or depart the nest and start over. These three major criteria are used to present the specifications of the acts taken in CSA. The following Levy flight equation is used to construct a new solution, $u(i+1)$ [100,101]:

$$u_m(i+1)=u_m\left(i\right)+\partial \oplus Levy\left(\beta \right)$$

(15)

$$Levy\sim s=t^{-1-\beta }(0<\beta <2)$$

(16)

The product ⊕ is an indication of multiplication, follows the same rules as entry-wise matrix multiplication, and ∂ is the step size and, in most circumstances, $\partial =1$. The step size begins with a large value and gradually decreases until the last generation, allowing the population to converge on a solution, similar to the processes involved in reducing PSO linearly. Yang [102] introduces the additional component as follows:

$$u_m(i+1)=u_m\left(i\right)+\partial \oplus Levy\left(\beta \right)\sim 0.01\frac{s}{{\left|v\right|}^{1/\beta }}\left(u_n\left(i\right)-u_m\left(i\right)\right)$$

(17)

where s and v are selected using the normal distribution, which is defined as follows:

$$s\sim N\left(0,{\sigma }_s^2\right),v\sim N\left(0,{\sigma }_s^2\right)$$

(18)

where;

$${\sigma }_u={\left\{\frac{\left(\gamma (1+\beta )sin\left(\frac{\pi \beta }{2}\right)\right)}{(\gamma [1+\beta )/2]\beta 2^{\frac{\beta -1}{2}}}\right\}}^{1/\beta },{\sigma }_v=1$$

(19)

$\gamma$ is the standard gamma function [102]. Exploration happens when the difference between $u_n$ and $u_m$ is high, while exploitation occurs when the difference is minor.

Compared to other approaches, CSA offers the advantage of multi-model objectives and requires fewer parameters to fine-tune them. It is used in a variety of settings, including path planning for UAVs [103], neural networks [104], embedded systems [105], electromagnetics [106], economics [107], business [108], and the Traveling Salesman Problem (TSP) issue [109].

4. Applications of Swarm Robotics

Swarm robotics is an emerging area of research and development that has yet to gain significant industrial adoption. Still, academics have created a variety of platforms to test and analyze the algorithm. In [110], the authors mentioned that they are researching for future industrial platforms. Swarm robotics research (see Figure 11), and industrial efforts & products (see Figure 12), are the two areas of the survey which will be discussed later. Industrial projects and products are examples of deployment in a real-time scenario. The swarm robotics research platform assists researchers in demonstrating, verifying, and experimenting with swarming algorithms in a laboratory setting. The four categories for both platforms are terrestrial, aerial, aquatic, and extraterrestrial. Robotic vehicles include Unmanned Submarine Vehicles (UUV), Unmanned Aerial Vehicles (UAVs), Unmanned Surface Vehicles (USVs), and Unmanned Ground Vehicles (UGVs).

4.1. Research Platforms

This section includes the application from swarm algorithms to swarm robots. Advanced robotics research platforms, such as the balboa robot and others, exist but are not included in Figure 11 because, they are not designed to use in swarm applications.

4.1.1. Terrestrial

The kilobot swarm is widely considered the best swarm of robots ever produced for educational and research purposes. They are little, measuring 33 mm in diameter. For propulsion, vibration motors are employed, and for communication, infrared light reflected from the ground is used. For swarming, 1024 robots are used and they are well-known for their capacity to self-assemble into various forms [111]. It is open-source and commercially accessible through K-Teams. Jasmin, an open-source platform, was created with a large-scale swarm investigation that required touch, proximity, distance, and color sensors. Alice [112] is another platform, with additional sensors, including a linear camera, increases the functionalities of swarming. Similarly, AMiR [113] and Colias [114] are open-source and commercially available swarm robots that provide a foundation for a number of research platforms. Mona is a commercial product as well as an open-source initiative. However, R-One may be used as a swarm robotics platform since it comes with a camera for ground-truth localization and software to connect all devices. The swarming platform Elisa-3 incorporates an Arduino with eight infrared sensors, three accelerometers, and four ground sensors, all of which can be charged by a charging station and communicate through infrared or radio waves. The Khepera IV [115] was created for indoor use. K-Team is a tiny and unique swarming research platform with a linux core, color camera, WLAN, bluetooth, USB, accelerometer, loudspeakers, gyroscope, three RGB LEDs, and it is also commercially available. The GRITSbot [116] is an open-source robot found at Georgia Tech’s Robotarium in Atlanta. Researchers can utilize the resources by uploading code, performing experiments, and gathering data using Robotarium’s remote access. As the size and quantity of these robots increase, more maintenance and usability aspects become crucial.

The e-puck and its successor, the e-puck2, are designed to make programming and controlling robot behavior simple for research and education. It includes an infrared proximity sensor, a CMOS camera, and a microphone. Both commercial and open-source versions are available. Its new edition, Xpuck, introduces new features, including aggregation of raw processing power, which is used in current mobile system-on-chip (SoC) devices with roughly two teraflops of processing power.

ArUco marker tracking in image processing computations is another example [117]. Similarly, Thymio II [118] swarm robots offer a range of sensors, including temperature, infrared distance, microphone, and accelerometer. Visual and text-based programming are also available. Thymio II is open-source and commercially available at Thymio, whereas Pheeno [119] is also a free and open-source swarm robotics platform for teaching and research. Custom modules with three degrees of freedom may be employed, and an IR sensor is used to communicate with the outside world. The open-source and locomotion-capable Spiderino [120] has six legs and has a hexapod toy-like design with an Arduino CPU, WLAN, and some reflected infrared sensors on a PCB.

I-Swarm (Intelligent Small-World Autonomous Robots for Tiny-Manipulation) is a swarming microrobot. Its sizes are 3 × 3 × 3 mm, and it is solar-powered without a source. It travels by vibrating and communicates using infrared transceivers to establish a swarm of 1000 robots [121]. The prototype is on exhibit at the technology museum in Munich. The Zooids [122] human-computer interface is a novel type of HCI that handles interaction and presentation. It was built as a unique open-source robotics platform. Light patterns projected from an overhead projector regulate the swarming of Zooids. The APIS, or adaptable platform for an interactive swarm, comprises several components, i.e., the swarm’s infrastructure and testing environment, software infrastructure, and simulation [123]. The focus is to experiment with human-swarm interaction. The platform uses an OLED display and a buzzer. With the help of the swarm, clean up the environment Wanda [124] is a robotics platform that might be useful. The authors have built the entire tool-chain from robot design and simulation to deployment. Droplet [125], a spherical robot that can organize itself into complex shapes with the help of vibration locomotion, is another ideal platform for education and study. The powered floor, which features alternating positive charge and ground stripes, has been used for both charging and communication between swarm robots. Swarm-bots [126,127] may automatically align themselves to various 3D shapes. Its design is open-source, and robots are made up of various insect-like shapes. They are built with low-cost, readily available components. They can adapt to any environment due to their self-assembling and self-organizing capabilities. The swarm can move heavy goods that would be too heavy for individual robots. Swarmanoid and its successor, are the first study of integrated design, development, and control of heterogeneous swarm robotics systems. It is open-source, and includes three types of autonomous robots. Eye-bots (UAVs that can stick to an interior ceiling), Hand-bots (UGVs that can climb), and Footbots (UGVs that can self-assemble) are among the varieties of UAVs that are developed [128]. Surprisingly, the termes robots [129] interact without the need for communication or GPS to build huge constructions using modular components. It is based on how termites construct their nests in nature, and they are block-carrying climbing robots that can also construct similar structures in unstructured situations. Other swarming platforms for research are symbrion and replicator [130]. They are two projects that are pretty much identical in terms of developing autonomous platforms for swarms. By physically connecting to each robot in the swarm, they may function individually or in a certain form and the goal was to devise a strategy for achieving robot organism evolvability. PolyBots [131] are self-configurable robots that can move in many ways. They have interchangeable object manipulation modules that may take on a variety of shapes depending on the situation, such as an earthworm for slithering over barriers or a spider for marching through hilly terrain. These robots are ideal for multitasking and usage in new areas. M-TRAN I [132], M-TRAN II [133], and M-TRAN III [134] are self-configurable robotics technologies. ATRON [135], CONRO [136], sambot [137], and molecube [138] are all open-source robotic systems and robots.

4.1.2. Aerial

Miniature and micro unmanned aerial vehicles ($\mu$UAVs) for swarming are affordable robots available for research and education [139] and Swetha et al. [140] both look into small-scale UAVs. Several off-the-shelf Micro Air Vehicles ($\mu$AVs) are available and famous in the gaming and commercial industries. Three rate gyroscopes and three accelerometers are used in UAVs developed for swarming robots in $\mu$AVs in [141], together with one ultrasonic sensor and four IR sensors. The Distributed Flight Array [142] is a popular platform used to construct swarmanoid [128] on it. Each UAV adds a single rotor to a big array. The module self-assembles into a multi-rotor system, in which all robots must exchange coordinates and local parameters for coordinated flying. Crazyflies [143], which are available commercially and open-source at Bitcraze, make use of a variety of sensors, including a high-precision pressure sensor, an accelerometer, a magnetometer, and a gyroscope. It can conduct experiments while minimizing the risk to humans because of its light weight of about 27 g. In FINken-III [144], is a powerful copter equipped with a better communication module (802.15.4) to communicate between ground station and other copters, and sensors like optical flow, infrared distance, and four sonar sensors.

4.1.3. Aquatic

The Collective Cognitive Robotics (CoCoRo) project has been developed with 41 heterogeneous Unmanned Underwater Vehicles (UUVs). Electric fields and sonar sensors are used to communicate, and the system applies to environmental monitoring, water pollution assessment in rivers and oceans, and global warming consequences. The Monsun [145] has two communication modes: a camera for identifying other swarm members and an underwater acoustic modem for transmitting data. CORATAM (Control of Aquatic Drones for Maritime Tasks) [146] has also been developed for swarms of USVs, with uses such as sea border patrols, marine life localization, and environmental monitoring. This open-source platform uses evolutionary computing to evaluate swarm methods [147].

4.1.4. Outer Space

NASA has developed swarmies to gather water, ice, and minerals on Mars. They have also established a swarmathon to aid academics in developing an ant-based swarm algorithm. In-situ Resource Utilization (ISRU) is the name given to this application. Twenty swarmies cover a distance of 42 km in around 8 h. Another NASA Innovation Advanced Concept (NIAC) program project aims to enrich knowledge on the Mars exploration swarm of Marsbees [148]. These have the size of the bumblebee for robotics flapping wing flyers. They can explore and discover themselves in an unfamiliar place. With NIAC financing, a flapping flyer with insect-like wings will be offered as a technical implementation.

4.2. Industrial Projects and Products

These include UAV, UGV, UUV, and USV swarm robots developed for industrial projects and products. The available robot with respective type has been shown in Figure 12.

4.2.1. Terrestrial

Agriculture is essential to a country’s growth. Food demand is growing, but the output is still insufficient [149]. SwarmBot 3.0 is being used to monitor fields autonomously using Unmanned Ground Vehicles (UGVs). Before beginning the specified task, this swarm collaborates via a centrally controlled timetable. The large area is automatically subdivided into smaller fields and then allocated to an individual robot in the swarm [150]. Their tasks include sowing, applying fertilizers to the assigned areas, harvesting, and irrigation which is the requirement of the agriculture sector. Another fascinating innovation from the Fendt firm is the UGV Xaver, which is used for seeding and is powered by a battery [151].

The GUARDIANS (Group of Unmanned Assistant Robots Deployed in Aggregative Navigation by Scent) [152] has been used for emergency and rescue missions. They are used in places where human presence is prohibited or where the environment severely impairs human senses. This project assists in searching and warns against toxic chemicals using mobile communication links. They can form and navigate using potential fields and achieve the assigned task without explicit communication between the robots.

Another autonomous Ocado [153] warehouse has been developed that has a swarm of homogeneous cuboids and is being utilized for grocery orders and dispatching. A total of 1100 collaborative swarms of robots are used for the order and dispatch, where the workers put the customer order together. Robots are controlled from a central location by a cloud server, and data are exchanged via cellular technology between the robot and the cloud. Amazon [154], which employs Kiva, is the most prominent player in the swarming of robots in warehouses. An A* algorithm (with visual tags on the ground) searches for humans who assemble the customer’s order. WLAN is used for the communication of robots, and dispatching is organized centrally. A low battery of robots is handled by the charging stations automatically. Alibaba [155] retailers are using a similar system for the autonomous order of goods and dispatching.

4.2.2. Aerial

The OFFSET (OFFensive Swarm Enabled Tactics) [156] projects are mostly deployed in military applications, although they can also be applied in other situations. This project aims to improve intra-city observations using UAVs and UGVs. These swarms of robots are capable of detecting hazards from the surroundings. Perdix [157], a military application swarm supported by the business. It is capable of performing its tasks without human piloting and has the ability to communicate with other drones to work collaboratively and achieve a common goal. These drones operate in a swarm of 20 or more and coordinate their actions to accomplish the desired outcome. Pentagon consisting of 103 drones, is another military application swarm. This swarm is not controlled by a single leader and can adapt to UAVs. They can fly in formation and make decisions as a group, making them useful for covert operations and targeted assassinations. The autonomous swarm is developed to install and manage WLAN network [158] as part of the Swarming Micro Air Vehicle Network (SMAVNET) project [159] in the emergency and rescue application sector. The project aims to gather rescue teams when disaster places have been explored and located. SWARMIX [160] is a similar search and rescue initiative in which a swarm of heterogeneous agents, such as humans, dogs, and Unmanned Aerial Vehicles (UAVs), create a swarm and engage in a search and eventually rescue operation.

Using a swarm of autonomous aerial vehicles, the Swarm robotics for Agricultural Applications (SAGA) project [161] seeks to do weed-spread monitoring and mapping. A swarm’s fitness is decided by trade-off exploration and weed detection time in smart farming. Weeds and plants are detected and identified using a visual approach.

Nowadays, swarms are also providing entertainment in terms of light shows. The UAVs are equipped with colorful LEDs and perform the formation of different patterns accomplished by music to create a beautiful scene. In Spaxels, Flyfire, Ehang, Intel [162], and Lucie micro, 1000 Unmanned Aerial Vehicles (UAVs) are controlled from a central location and follow pre-programmed patterns.

4.2.3. Aquatic

Swarms are commonly used in aquatic environments to monitor the environment. Platypus [163] offers autonomous swarm robotics boats as USVs. They are utilized to keep track of water quality, produce a dense map of defined bodies beneath the surface, and stratify salinity and oxygen levels. Apium Data Diver is a prototype vehicle with a maximum depth of 100 m. It is meant for swarm operations on the surface and underwater, with temperature, pressure, and GPS among the sensors on board. It finds its application areas in defense, oceanography, hydrographic survey, and aquaculture. This type of swarm can be found in UUVs and USVs. It can accept high-level commands from a human operator and build a wide range of patterns [164]. Hydromea’s Vertex Swarm is available in UUVs and can assess water quality in various places up to 300 m deep. It generates 3D data with great spatial and temporal resolution that is faster and more precise than manual approaches. The major purpose of the SWARMs (Smart Networking Underwater Robots in Cooperation Meshes) project [165] is to develop surface and underwater vehicles that can operate in maritime and offshore operations. It is responsible for designing and developing software and hardware components for the next generation of maritime vehicles, as well as assisting in the improvement of autonomy, robustness, cooperation, dependability, and cost-effectiveness. It uses offshore installations, chemical pollution monitoring, and plume tracking. Research focus lies on reliable underwater communication [166] and leveraging topology control [167].

The military has employed the CARACaS software kit, which is used in aquatic environment. NASA developed CARACaS (Control Architecture for Robotic Agent Command and Sensing), which has now been upgraded by ONR (Office of Naval Research) for autonomous Navy operations in the United States where USVs communicate with one another [168]. It enables USVs to choose their courses, protect assets in the navel, and intercept enemy boats as a group. In a demonstration at the James River in Virginia in 2014, CARACaS was installed on rigid-hulled boats and proved to be magnificent and successful [169]. Based on the discoveries of the CoCoRo, Submarine Cultures (SubCULTron) conduct long-term robotic exploration of unusual environmental niches. It is used on UUV robots to assess factors such as learning and self-sustainability.

4.2.4. Outer Space

Swarm was launched in 2013 and is made up of three identical spacecraft, two of which are side-by-side at 450 km and the third at 530 km above the ground. The mission of each satellite was to research the earth’s magnetic field, and each was nine meters long [169]. Cluster II is a tetrahedral arrangement of four identical cylindrical spacecraft that was launched in 2000. It was initially capable of sending three-dimensional solar wind data on the earth’s magnetosphere to investigate the sun’s influence on the environment [170].

5. Swarm Robotics: Past, Present and Future Perspective

Social insects, fish schools, and bird flocks are examples of naturally self-organizing systems that display emergent collective behavior based on simple local knowledge [171,172]. Swarm robotics emerged as a branch of swarm intelligence, or the computational modeling of collective, self-organizing activity, which has yielded many successful optimization methods [173,174] that are now used in fields ranging from telecommunications [175] to crowd simulation, and prediction [176]. In contrast, swarm behavior in robots necessitate the installation of swarm intelligence algorithms on current robotic systems. Because of the expected ubiquity of autonomous robots in real-world applications and the challenge of allowing them to interact with one another and with their human users while avoiding the drawbacks of centralized control, swarm robotics research is gaining traction. Swarm robotics research will be crucial in addressing complex coordination problems in future robotics applications. It includes cooperative (i.e., robots working together to complete a common task) and semi-cooperative (i.e., self-interested robots benefiting from a globally efficient organization of activities, such as autonomous vehicles) scenarios. In the future, it will become a new and powerful tool in precision medicine, allowing for personalized therapies such as minimally invasive surgery or direct polytherapy delivery to malignant cells inside the human body [177,178]. Large numbers of robots with limited computation and communication capabilities, on the other hand, will push swarm robotics to its limits, necessitating the development of new conceptual tools in addition to tiny hardware or robotics devices [179].

In lab settings, robot swarms are shown using a small number of tiny robots [128,180]. Although technology advancements are pushing the bounds to ever-smaller sizes [177,181] and greater numbers [6,7], but the road to real-world applications remains lengthy and arduous. For example, group scale, from a few dozen to millions of people constituting the swarm and physical scale, from micro/nanorobots to massive terrestrial, aerial, and aquatic robots. Swarms that display prompt intervention and adaptability in a quickly changing environment to robots that work on months-long missions are examples of temporal scale (e.g., on a distant planet) from small-scale deployments to large-scale deployments and geographical scale. Previous, current, and future robotics achievements in terms of software, hardware, or a combination of the two are explained in the Table 1. Figure 13 shows the evolution of swarm robotics, to the best of our knowledge, from algorithmic research to the real-time best-performing swarm of robots.

6. Conclusions

Swarm robotics aims to develop simple, autonomous or self-governing robots that can cooperate to solve real-world problems collectively. Intelligent swarm algorithms are needed to enable the robots to interact autonomously and coordinate together without centralized control. The research on the swarm robotics domain started in the late 1900s, and the development work started in the early 2000s, gradually evolving the previous research and simulation work towards the actual real-world projection of swarm robotics. But there is a gap between theoretical and industrial research in swarm robotics. Theoretical research mainly focused on simulating swarm behaviours, while industrial research focuses on designing hardware that can execute swarm behaviour. Therefore, it is crucial to deploy swarm algorithms on hardware that can accommodate swarm behaviour functionality.

This article provides a comprehensive overview to new researchers of the swarm robotics field. It classifies the definition of swarm robots and identifies the difference between a multi-agent system and an actual swarm of agents. A detailed review of the swarm’s most emerging swarm behaviors, and swarm intelligence algorithms is captured, keeping in view the limitation and the transformation towards the industrial application and development of the swarm robotic platform. In addition to the industrial application, this paper reviewed several research hardware platforms specifically designed to demonstrate or replicate any swarm behaviour. Finally, this paper concludes by reviving the era of swarm robotics from the past, present, and future projections with expected timelines of evolving the system and having real-world application, agnostic of swarm robotics platforms.

This article provides valuable insights for researchers in swarm robotics by highlighting various areas of research gaps, including algorithmic and hardware implementation. It emphasizes the importance of addressing these gaps to enable effective collaboration among robots. Researchers can bridge the gap between theoretical and industrial research in swarm robotics, leading to advancements in the field.