Robustness and Scalability of Incomplete Virtual Pheromone Maps for Stigmergic Collective Exploration

Abstract

The Swarm Guiding and Communication System (SGCS) is a decision-making and information-sharing framework for robot swarms that only needs close-range peer-to-peer communication and no centralized control. Each robot makes decisions based on an incomplete virtual pheromone map that is updated on each interaction with another robot, imitating ant colonial behavior. Similar systems rely on continuous communication with no range limitations, environment modification, or centralized control. A computer simulation is developed to assess the effectiveness and robustness of the framework in covering an area. Consistency and the time needed for 99% coverage are compared with an unbiased random walk. The pheromone approach is shown to outperfom the unbiased one regardless of number of agents. Innate resilience to individual failures is also demonstrated.

1. Introduction

Complex systems, most often biological ones, often exhibit what is known as emergent behavior. Emergent behavior refers to an observable behavior of a system constrained only by the rules of the environment (environmental conditions) and, more importantly, the rules that each participant follows independently. Such systems are capable of collectively accomplishing tasks that no individual would be able to do alone. Moreover, some of these can function without expensive communication to a central command center. As in [1], expensive could refer to time or another resource like energy.

The concept of emergent behavior is already finding uses in technology. As per [2], swarm robotics is a subfield of robotics that explores methods for the coordination of groups of robots towards achieving a common goal or task. Inspiration is often drawn from seemingly simplistic non-intelligent creatures in nature that can achieve wonders through collaboration.

Ant colonies are one of the most well-known examples of a system that exhibits emergent behavior, where individuals can exchange information outside of the central hub(nest). They are capable of task allocation, deciding between nest maintenance, foraging, and patrolling, using only environmental and social cues with no central authority, as shown in [3]. Furthermore, according to [4], the way an ant colony performs such tasks is also demonstrative of emergent behavior. Once again, they are collaboratively able to achieve their goal.

Stigmergy is a form of indirect communication through the modification of the environment. In essence, modifications of the environment made by an individual can be detected by other participants to obtain information. As per [5], French zoologist Pierre-Paul Grassé introduces the concept in 1959 to explain how the observed coordination of insects’ activities emerges from independent actions of the individual.

In [5], two main types of stigmergy are identified. Quantitative stigmergy refers to the use of a single type of stimuli and its quantity affects the response probability of the individual. Qualitative stigmergy, on the other hand, refers to the use of multiple kinds of stimuli that vary in type and can thus provoke a set of distinct actions by the individual, depending on both the type and quantity of sensed stimuli.

As stated in [6], trail pheromones, a form of stigmergy, are used by a variety of ant species in nature. Pheromones in nature are chemical substances produced and released into the environment by an animal with the purpose of indirect communication. Furthermore, information can be encoded in the pheromone trail. Resource quantity or proximity can be indicated by an intensification of the trail or already visited areas can be marked with repellent pheromones [6]. Hence, a pheromone map is created around the colony’s nest, which is used by patrollers and foragers for navigation.

Here, we show our ant-inspired Swarm Guidance and Communication System which uses quantitative stigmergy for the task of area exploration by swarms of resource constrained, as in limited communication capabilities and computing power, agents. We focus on robustness, or how well the system responds to failures of agents, and scalability, i.e., how does an increase in the number of agents affect performance.

2. Background

Swarm organization systems that do not rely on emergent behavior do exist. For instance, Karma, presented in [7], utilizes a beehive model, where participants with very simple software and hardware are governed by a central computer. Only when an individual is attached to the central hub does communication occur between the two. Hence, expensive and energy-demanding communication hardware is avoided. Although [7] demonstrates some adaptability, the lack of in-field communication is a limiting factor. Furthermore, a centralized hub is a single point of failure, reducing robustness even if the system is tolerant to individual failures.

In [8], a heterogenous swarm of mother and daughter ships performs search and tracking. The motherships perform task allocation among each other through negotiation, and then each one coordinates its subswarm of daughter ships. In [9], Marino et al. present a patrolling system and showcases how it adapts to individual failures. A dynamic programming solution algorithm for swarm coordination is used in [10].

As per [2], true emergent behavior remains rare in practice. Industrial applications still by and large rely on centralized control even if basic swarm behaviors are integrated, and thus the system is referred to as a “swarm”. According to [11], non-bioinspired coordination of swarms robust to individual failures do exist but do not cover the environment completely, whereas purely mathematical strategies are unable to cope with agent failure. Random walk methods are evaluated and improved upon in [12]. Stigmergic emergent behavior can be used in robotics for building structures like in [13]. The individuals use the current state of the structure they are building to guide their behavior. However, this concept is obviously inapplicable to area surveillance.

Instead, variations of the concept of pheromones are most common in this domain. Refs. [14,15] present similar approaches to trail pheromones in nature. Each robot can project UV light on photochromic material, and thus leave artificial pheromones, which can then be detected by other individuals of the swarm. In [16], Fujisawa et al. use ethanol instead. However, these environmental modifications rely on a controlled environment, limiting their practical applications. Similarly, in [17,18], cameras and LCD screens are used. In [19], a novel neural network model for foraging is proposed but, along with [11], it assumes indirect environmental communication, which requires specialized hardware and/or a controlled environment.

According to [20], a more versatile approach is the use of digital or virtual pheromones, shared globally throughout the swarm. In essence, swarm agents remember where pheromones are and repeatedly update that map to simulate phenomena such as decay, a gradual decrease in strength, or diffusion. For example, in [21,22], such systems that use a centralized synchronization node, which maintains a global pheromone map, are demonstrated. Nevertheless, this approach makes impractical assumptions such as infinite communication range or relies on some sort of centralization, negating many of the benefits of a truly distributed swarm system. Various works such as [23,24] rely on either of the former two approaches. Ref. [23], however, uses relatively similar conditions for its simulation and is thus included in our discussion. In [25,26,27], the generation of a map is avoided; instead, they rely only on peer-to-peer communication. In the former two, the swarm agents themselves act as pheromones of sorts. In [28], pre-set communication nodes are used to establish communication within the swarm.

In [29], Van Dyke Parunak et al. consider military applications and propose the concept of place agents, representing parts of the physical space and the strength of each flavor of pheromone in it, and thus the graph of these place agents is a virtual map. Walker agents represent the physical individuals of the swarm and can move from one place agent to another, guided by gradients. Notably, the concept of ghost agents is also introduced. They do not represent a physical entity but behave as one. A walker agent repeatedly simulates ghost agents navigating the field, and these simulations help the physical (walker) agent decide on a direction or even plan a path to its target. The computational power needed for such simulations on the fly, however, falls outside of the capabilities of systems that SGCS targets. Furthermore, the map is also assumed to be globally synchronized between walker agents. In [30], Sauter et al. also note that a fixed pattern search covers an area faster than its pheromone-guided counterpart. However, their fixed pattern search has no mechanism to deal with individual failures. In [31], a method for the deployment of an ad hoc wireless communication network of UAVs between two ground users is presented. Pheromones are deposited on swarm agents themselves due to the lack of positioning information needed for a virtual map.

In [32], Kuiper and Nadjm-Tehrani utilize the concept of local virtual repellent pheromone maps that are shared when agents are within communication range of one another. Likewise, in [33], Parunak et al. make use of this concept in combination with task allocation for target search and imaging. In [34], Pack and York utilize a similar approach even if pheromones are not explicitly mentioned. All of the above, however, are concerned with relatively small swarm sizes with 0% individual failure chance. Hunt et al. even suggest that repellent pheromone robotic swarm systems are not scalable, i.e., the efficiency decreases with a higher number of participants due to pheromone saturation and is even comparable to random walk algorithms in [20].

In [35], local virtual pheromone maps are also used for surveillance of an indoor area. The effect of the communication range is explored but for a maximum of 36 agents. Furthermore, a 0% individual failure chance is assumed. Similarly, in [36], Stolfi et al. use a genetic algorithm to optimize swarm parameters for the communication of incomplete virtual pheromone maps. Hecker and Moses in [37] also utilize a genetic algorithm for foraging and, additionally, to account for sensor errors.

Adaptive fault recovery strategies for swarms are discussed in [38]. Collective fault detection is demonstrated in [39], but how these failures affect the performance is not considered. Byzantine fault tolerance is implemented by Liao et al. in [40]. In [41], the reliability of a swarm performing flocking and beacon-taxis is examined, whereas in [42], Winfield and Nembrini employ Failure Mode and Effect Analysis.

Overall, little research has been conducted on large swarms (>50 agents) and how well they handle individual failures without an additional fault tolerance mechanism. In this work, we demonstrate the superiority of our pheromone approach over a random walk algorithm for a swarm size of up to 1000 agents and assess its inherent fault tolerance to random individual failures.

3. Approach and Algorithm

SGCS uses partial virtual pheromone maps that are only updated when two participants come within communication range of each other. No direct environment modification or central control is used. This approach has the following advantages:

• No preparation of the site of operation is needed prior to deploying the system.
• Environmental modification is not used; consequently, no hardware to perform or sense such modifications is needed
• Energy consumption for communication is reduced due to the low range requirements.
• The system is agnostic to the communication hardware, allowing adaptability to the environment where the system is deployed. For example, RF communication could be used for aerial swarms and sonar for underwater operations.
• Failure of any individual participant does not cause failure of the entire swarm.

Some of the disadvantages are the hardware requirements listed in Section 7.3.

The algorithm executed by each agent independently consists of repeatedly performing the following steps:

• For each pheromone on the agent’s virtual pheromone map, decrease its strength $S$ as such:

  $$S=0.98S_{initial}{e}^{-\lambda t}$$

This model is proposed in [6] for ant foraging pheromone trails in nature; hence, it is used in this paper to emulate that same behavior found in nature. t is the time since deposition.

The virtual pheromone is destroyed when $S\le 0.1$ to conserve computational resources for the simulation. In line with [6], $\lambda =0.02$ is used for this paper.

2.

Every $N_p$-th time step drop a new pheromone with strength $S=S_{initial}$ at the agent’s current position, denoted by $\overrightarrow{r}$.

3.

Every $N$-th time step, pick $n$ random directions and for the $k$-th ($0\le k<n$) direction calculate a desirability rating $d_k$ as such:

3.1.

Randomly generate $\overrightarrow{e_k}$ as a possible future direction with $\theta <{90}^{\circ }$, where $\theta$ is the angular distance between $\overrightarrow{e_k}$ and the current direction $\overrightarrow{e_c}$.

3.2.

With a virtual pheromone map of $m$ pheromones:

$$d_k=1+\sum _{i=1}^m{\displaystyle \frac{S_i{\theta }_k}{{|\overrightarrow{r}-\overrightarrow{r_i}|}^2}}$$

$S_i$ is the strength of the $i$-th pheromone, $\overrightarrow{r_i}$ is its position, and ${\theta }_k$ is the angular distance between the pheromone’s position relative to the agent as expressed by a radius vector with an origin in the current agent position $\overrightarrow{p_i}=\overrightarrow{r_i}–\overrightarrow{r}$ and the considered future direction of the agent $\overrightarrow{e_k}$. In case the agent is directly on top of a pheromone ($\left|\overrightarrow{p_i}\right|=0$), this pheromone is not factored in the calculation of $d_k$.

4.

Pick the direction $\overrightarrow{e_k}$ with the highest $d_k$ as the new $\overrightarrow{e_c}$

5.

Move along the direction of $\overrightarrow{e_c}$: $\overrightarrow{r_{new}}=\overrightarrow{r}+v\overrightarrow{e_c}$

6.

Communication is facilitated by the simulation

Figure 1 depicts the algorithm that governs the behavior of each agent graphically. The outer loop is executed once every simulation time step, while the inner loop represents the choice of future direction (Step 3).

The algorithm has a complexity of $O\left(n^2\right)$ with respect to the number of considered future directions and the number of pheromones on the virtual map of the agent. The number of pheromones, in turn, depends on other factors such as the pheromone drop rate (dropping pheromones more frequently results in an overall increase in the number of pheromones), the pheromone decay model used (faster decay leads to a decrease in the total pheromone count), or the number of agents and their communication range (an increase in either would also lead to a higher number of pheromones).

No separate fault tolerance mechanisms are implemented.

4 “fence” repellent pheromones with strength α, situated on the 4 borders of the working field, are added to each agent’s virtual map as shown in Figure 2. These pheromones prevent agents from getting stuck on the perimeter.

4. Simulation Environment

A 2D simulation is developed to assess the performance of SGCS and specifically its robustness.

The following parameters can be set at the start: simulation steps ($T$), area width ($W$) and height ($H$), number of agents ($n_r$), decison steps ($N$), considered directions ($n$), communication range ($R_{comm}$), sensor range ($R_{sens}$), speed ($v$), pheromone drop steps ($N_p$), initial pheromone strength ($S_{initial}$), fence strength coefficient ($\alpha$), and pheromone decay rate ($\lambda$). Additionally, a failure chance, i.e., the probability that an agent might fail on each simulation time step, is specified for each trial.

The simulation parameters and their values are summarized in

Table 1. Simulation Parameters.

Agent Count	$\mathit{\alpha }$	Trials	Common Parameters
10	0.1	5	$\mathrm{W}$	801 m
20	0.075		$\mathrm{H}$	801 m
50	0.01		$\mathrm{v}$	2 m/s
100	1		${\mathrm{R}}_{\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{s}}$	2 cells
250	1		${\mathrm{R}}_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{m}}$	50 m
500	1		${\mathrm{N}}_{\mathrm{p}}$	20 s
750	1		n	5
1000	1		N	10 s
			$\lambda$	0.02
			${\mathrm{S}}_{\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}}$	200

.

In all trials, the agents start from the center of the field. Speed per simulation time step is constant and communication is assumed to be lossless. A 3D simulation is not used as the added complexity is unlikely to greatly influence the results because area coverage underwater or in the air is often performed at a single depth or altitude; hence, after takeoff or diving, the working area can be assumed to be planar. It is reasonable to expect that the results presented here would not differ greatly from a 3D simulation of such scenarios. Similar assumptions are made in [32], for instance. There, it is also noted that including the possibility of collisions in such a simulation would not add significant benefit as in applications that also support vertical movement, small altitude, or depth adjustments can be made for two agents to avoid each other.

The communication and sensing range depend on the real hardware used and can greatly vary between different systems. In [31], a 100 m communication range is assumed but also a realistic communication model is implemented. Since we are using an ideal communication model, we decided to assume a communication range of half that value. SGCS is also targeted towards lower powered vehicles such as [43], where the communication hardware would be significantly less capable.

A grid of $W\times H$ cells is used to keep track of the area covered. Each cell keeps track of how many times it has been visited. The sensing range was initially 1 cell, so an agent had to be within the bounds of a cell to register a visitation, but due to the hardware available to us for simulations, trials were taking a full day to reach only a small percentage of the area covered, so we increased it to two cells. In this case, when an agent is within the bounds of a cell, the visitation counter of that cell is incremented along with those of all neighboring cells.

${\mathrm{S}}_{\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}}$ and $\lambda$ are unitless as they represent relative pheromone strength. Initially, a fence strength coefficient of 1 was used for all trials. However, for smaller agent counts, this resulted in a situation like the one in Figure 3.

A fence strength coefficient that is too strong prevents agents from visiting the areas closer to the borders of the working field. $\alpha$ was consequently reduced for lower swarm sizes, while avoiding the opposite extremity, which can be seen in Figure 4. The values in Table 1 were found to achieve satisfactory performance. Different fence strength coefficients evidently greatly influence the swarm efficiency. However, this investigation is concerned with the relation between agent count with efficiency and robustness. Exploring the effects of other parameters is beyond its scope and remains the subject of future work (See Section 7).

The simulation performs the following steps:

• Execute the main algorithm for each agent as described in Section 3
• Calculate the distance between each pair of individuals $d_{ij}$ and compare it with the communication range $R_{comm}$. If $d_{ij}<R_{comm}$, the pair synchronizes their virtual pheromone maps to simulate communication with limited range.
• Randomly destroy agents, according to the failure chance provided.

The same simulations were also performed for an unbiased random walk that simply picks a random future direction $\overrightarrow{e_f}$ with $\theta <{90}^{\circ }$ (the angular distance between $\overrightarrow{e_f}$ and the current direction $\overrightarrow{e_c}$) every $N$ steps.

Two metrics were used to assess the algorithm in comparison with the unbiased random walk:

• Area covered is the ratio ($\mu$) between cells that have been scanned at least once and those that are yet to be. The time to reach $\mu =99\%$ is compared. Lower time is better.
• Consistency is how close the results of the different trials with the same simulation parameters are:

  $${\displaystyle \frac{{\sum }_{\mathrm{i}=1}^{\mathrm{T}}\sqrt{{\sum }_{\mathrm{j}=1}^{\mathrm{M}}\frac{{({\mu }_{\mathrm{i}\mathrm{j}}-\overline{{\mu }_{\mathrm{i}}})}^2}{\mathrm{M}}}}{\mathrm{T}}}$$

$M$ is the number of trials, ${\mu }_{ij}$ is the area covered on the $i$-th simulation step of trial $j$, and $\overline{{\mu }_i}$ is the mean area coverage on this timestep. A lower consistency score implies higher consistency and is thus better.

5. Results and Analysis

The pheromone approach outperformed the unbiased random walk in every trial according to both metrics. In some of the earliest trials, the unbiased approach yielded better results, but this was determined to be the result of a bad fence strength coefficient ($\alpha$), which was subsequently adjusted. All results presented here use the parameters from Table 1.

Although with a different decision-making strategy, similar results were achieved in [32] even if only for a swarm of 10 agents. Here we show the superiority of the stigmergic approach for larger swarm sizes as well.

Figure 5 shows the % of area coverage over time of the two approaches for 750 agents. The graphs for all swarm sizes follow the same trend, as evident in Figure 6, and only differ significantly by the time step range, as can be seen in Figure 7 and

Table 2. Mean timestep of 99% area coverage.

Agent Count	Biased [s]	Random [s]	Diff. [s]	Ratio
10	27,268.0	32,749.4	5481.4	1.20
20	13,374.4	16,297.6	2923.2	1.22
50	5565.0	6917.2	1352.2	1.24
100	2768.2	3586.8	818.6	1.30
250	1028.0	1707.0	679.0	1.66
500	566.4	1141.0	574.6	2.01
750	387.0	925.0	538.0	2.39
1000	344.4	834.4	490.0	2.42

.

Ref. [20] states that the stigmergic swarm coordination loses its advantages with the increase in the swarm’s size and is eventually outperformed by a random walk approach. The results shown in Figure 7 and in Table 2, however, suggest the opposite.

This is most likely due to the different implementation of the swarm approach, particularly our use of a virtual pheromone map. In [20], each agent makes its decision only based on the presence of a single pheromone in its immediate vicinity. This approach has the inherent disadvantage that agents are unable to sense the density of pheromone. As the authors of [20] point out, swarm agents get stuck in large “patches” of pheromone, resulting in an uneven agent distribution throughout the field, leaving certain areas unexplored. Our approach instead allows the swarm’s efficiency to grow with the swarm’s size because the desirability rating “senses” pheromone density and guides the swarm participants away from high density areas.

Although the difference between the mean timestep of 99% area coverage decreases with the number of agents in the swarm, the ratio grows. Hence, the benefit of the pheromone approach over the random one scales with swarm size. However, the area is covered in much fewer timesteps with both approaches, and thus improvements are, in fact, smaller for large swarms.

Our findings are in line with the results in [23]. As mentioned in Section 2, the simulation conditions in [23] resemble the ones used for our investigation with some notable exceptions. Firstly, the decision-making process is vastly different and relies only on pheromones in the vicinity of the robot, whereas our agents take into consideration all pheromones on their virtual maps. Secondly, the environment includes obstacles, whereas our simulation does not. Thirdly, the pheromone map is represented as a grid, within which pheromones can also diffuse away from their initial deposition site, while in SGCS, pheromones are represented by their spatial position and cannot diffuse. Regardless of these important differences, for both swarm sizes and both field sizes that are simulated in [23], the pheromone approach outperforms the random one just like what our results show.

Table 2 includes another result similar to the results in [23]. For an area of 1600 units, a 24-agent swarm in [23] is able to achieve, on average, 96% coverage in 10,000 time steps, whereas 13,374.4 time steps are needed by a 20-agent SGCS swarm to cover 99% of the same area. This similarity is observed despite the following additional major differences between the simulation setups. In the current paper, our agents are assumed to all start from a single “command center” and disperse from there. Regardless of swarm size, a small region around the starting position of the swarm is repeatedly visited, which unavoidably reduces efficiency. In [23], the agents start from a random position on the field, but this advantage is balanced out by the fact that we use double the speed and double the sensing range, compared with that study.

Consistency is also better with the biased approach regardless of swarm size (see

Table 3. Consistency score comparison.

Agent Count	Biased	Random	Diff.	Ratio
10	0.1107	0.1999	0.0892	1.81
20	0.0245	0.1034	0.0789	4.22
50	0.1048	0.5234	0.4186	4.99
100	0.1161	0.6995	0.5834	6.03
250	0.1407	0.7363	0.5956	5.23
500	0.0747	0.3111	0.2363	4.16
750	0.0805	0.5287	0.4482	6.57
1000	0.0347	0.6903	0.6556	19.89

); no trend is observed, however. A heat map comparison of the two approaches (Figure 8) shows that agents disperse faster away from the starting position due to the high concentration of pheromones there. This reduces the repeated coverage of the area close to the initial position and thus improves efficiency, albeit regions around the starting position of the swarm do remain the brightest, i.e., most visited, as shown in Figure 4.

Notably missing from [20,32] is an assessment of robustness or how failure of agents affects performance, while [38,39,40] implement entirely separate mechanisms. Here, we instead focus on the innate resilience of the swarm if no such mechanisms are implemented. Individual failures have a stronger impact on the swarm’s efficiency with the increase in the failure chance, whereas an increase in the swarm size negates it. Figure 9 shows the effect of failure chance on a swarm of 100 and 500 agents, respectively. The flat lines are periods after all agents have failed. Little difference is observed in the performance of the 500 agents swarm even with a 10% failure chance, whereas even a 2% failure chance can prevent reaching 99% coverage by the 100-agent swarm.

As expected, the biased method remains more consistent when failures are introduced (see

Table 4. Consistency score comparison with respect to swarm size and failure chance.

Agents		0%	1%	2%	5%	10%	50%
100	Biased	0.1161	0.3641	0.3299	0.4888	0.2526	-
	Random	0.6995	0.5456	0.7156	0.6906	0.1543	-
500	Biased	0.0747	0.0874	0.1259	0.1243	0.1199	0.2079
	Random	0.3111	0.5151	0.4086	0.3266	0.2976	0.4160

). Higher failure chances do tend to introduce randomness and thus reduce consistency even though no exact relation can be determined. For instance, the random walk is more consistent than the pheromone approach with the 100-agent swarm, with a 10% chance of failure, but less area is covered. These trends extend to the other simulated swarm sizes as well.

6. Applications

One of the main intended applications is in agriculture. As the bee population is dwindling, such MAV (micro-aerial vehicle) swarms can prove a suitable replacement and help with sustainability. Moreover, closed-space hydroponics and aeroponics systems currently rely on manual pollination—a task that can be automated with MAV swarms. Some plant species need to be pollinated in bursts due to their short bloom period. Currently, this is achieved by moving bee hives to the desired location, but this could also be achieved with a robotic swarm. All this shows the substantial improvements to agriculture that such a system could bring.

Artificial swarms can also be incredibly useful in search-and-rescue scenarios. Having a fault-tolerant system that quickly covers a wide area, even in difficult conditions, could be the difference between life and death.

A robotic swarm could be used to sweep a battlefield and discover mines and bombs, greatly reducing the risk for teams that dispose of unexploded ordnance.

Identifying radiation, chemical, and biological hazards is another dangerous task that could be effectively performed by artificial swarms. If employed, such a system could protect the health and lives of professionals in the field.

Another possible application is security. A swarm of unpredictably moving tiny robots eliminates blind spots of stationary cameras. This can in turn greatly aid law enforcement and justice.

Exploration of hard-to-reach areas is another task well-suited to artificial swarms, particularly in connection with space exploration and eventual colonization. Yet another possibility is environmental monitoring such as tracking and reducing water pollution. Moreover, it could be used to find and track endangered species, helping with their preservation. Finally, lost farm animals can also be located with such a system.

All these applications involve coverage of an area and can thus benefit from a swarm robotics approach, such as the one presented here. The correct choice of swarm size with respect to the time constraints and the robustness requirements, which is explored in this investigation, is, hence, crucial. However, SGCS is still far from production-ready and does not concern itself with specialized hardware needed to perform specific tasks.

7. Discussion of Future Improvements

7.1. Algorithm

The algorithm currently uses a constant speed. Varying the speed of the agent depending on some factors could lead to an increase in efficiency while reducing power consumption. As can be seen on the heatmaps in Figure 8, the parameter region and the region around the initial agent position are notably more visited than those between the two, reducing the overall efficiency. Further optimizations are required such as tuning the evaporation rate $\lambda$ and the fence strength coefficient $\alpha$ to make the coverage more uniform and increase the efficiency. A method needs to be developed for finding the optimal values for these parameters or an entirely different approach from fence pheromones might be needed.

Little constraints are imposed on the change of direction by the agents, i.e., the algorithm relies on the agents being able to instantaneously change direction up to 90°, which is impossible in practice. The algorithm should factor in the maneuverability of the agents.

Currently, each agent only performs observations and data-collection. Working on a task like pollination (See Section 6) would require a modification of the algorithm that allows the agent to stay in place for some duration to perform the task, for example.

The use of qualitative stigmergy, i.e., different kinds of pheromones, is also not explored. Only repulsive pheromones are used as of now. However, attractive pheromones could be implemented to foster collaboration when performing tasks, like what is observed in nature as noted in [44]. Hence, although currently quantitative stigmergy is implemented, qualitative stigmergy could be as well, potentially unlocking a whole new range of applications.

Data dissemination throughout the network is not considered here. Ant colonial behavior in nature could possibly be used to fulfill this task, like in [4].

The algorithm currently does not avoid collisions between two participants, which is vital for practical applications.

7.2. Simulation

The simulation is currently only 2D; however, as explained in Section 6, SGCS could be particularly useful for aerial or underwater swarms. Hence, a 3D simulation would be a good tool to assess the feasibility of those use cases.

Also, a singular fixed field size is currently used for all simulations. The performance of the system needs to be investigated for other ratios between the field size, agent speed, and sensing and communication range.

No obstacles are currently present in the simulation. The addition of obstacles would provide a more realistic environment for testing the algorithm.

The simulation of communication is also oversimplified. It is instantaneous and fully reliable if the pair of agents are within range of each other or is completely absent otherwise. Using a more unreliable and thus realistic model for communication simulation would allow us to better assess the algorithm’s practical feasibility. Additionally, making obstacles affect communication would be a further improvement.

7.3. Hardware Implementation

The system has not yet been deployed on real hardware. For a swarm of robots to be able to make use of SGCS, each individual must meet the following requirements.

• Processing capabilities are needed for the execution of the above outlined algorithm. Little processing power is needed due to the simplicity of the algorithm.
• Memory capabilities are necessary to record the virtual pheromone map.
• Positioning is needed to place pheromones on the virtual pheromone map as well as to compare the robot’s current position with the recorded pheromones.
• Peer-to-peer communication is required to allow for the synchronization of virtual pheromone maps between participants. The effect of communication range on performance is not explored in this work and needs to be investigated further.

Several research platforms for testing swarm robotics algorithms are reviewed in [2], most of which are suitable for SGCS due to the low requirements outlined above. Testing on a hardware platform would provide a more accurate measure of the algorithm’s efficiency, robustness, and scalability. Moreover, SGCS was initially inspired by the development of the RoboBee, and the need for swarm coordination on a heavily restricted hardware platform like [43]. As such, it is our goal to one day have SGCS perform practical tasks on real hardware.

8. Conclusions

The Swarm Guiding and Communication System (SGCS) framework is demonstrated. Quantitative stigmergy is implemented through a virtual pheromone approach. Each swarm agent periodically records its location as a virtual pheromone on its own virtual pheromone map in memory. When two agents can communicate with each other, they fuse their maps. Agents are repelled by pheromones on their map when deciding on a movement direction. Through a simulation, the speed and consistency of this approach is compared with an unbiased random walk. Resilience to individual failures, i.e., robustness, is also examined. The pheromone approach is shown to be superior to the random walk according to all metrics even for very large swarms. Future improvements with the goal of eventually deploying the framework in practice are discussed.