## 2 Previous Work and Study  
It is very important to create robust control and coordination strategies to avoid and manage failures. Many control algorithms are fault tolerant but often at the cost of high complexity (e.g., complex rules of decision-making and the need for a higher authority). Our goal was to create a robust gracefully degrading multi-agent control system. Pheromone marks are commonly used to handle problems of coordination for a group of individuals (see, e.g., in [28; 29; 35]). However, in our case, we are trying to combine the concept of pheromone marks with population of heterogeneous agents and heterogeneous environment with transportable agents, which can be considered as a novel approach laying framework for future goal-oriented developments.  
Initially, we implemented an algorithm that used artificial pheromone marks for the coordination of a group of robots [36]. We analyzed the properties of the algorithm in a 2D space (a similar work was described in [37]). We investigated the algorithm's properties based on different sizes of swarms and various parameters of the pheromone mark's evaporating times in [35]. We studied the influence of the evaporating time of the artificial pheromone marks on the exploration time. We also experimented with various swarm sizes. Our experiments showed that even in the case that all agents are broken except one, the single individual (agent) can complete the space exploration and monitoring tasks. We have proven the viability of our approach through outdoor tests (Short video from testing is available at [[https://youtu.be/OwG2u9](https://youtu.be/OwG2u9) FNIU]([https://youtu.be/OwG2u9](https://youtu.be/OwG2u9) FNIU)) [36]. We have used UAVs (quadcopters) based on the ardupilot platform, developed in our laboratory ([[http://www.ui.sav.sk/w/en/dep/mcdp/lab/](http://www.ui.sav.sk/w/en/dep/mcdp/lab/)]([http://www.ui.sav.sk/w/en/dep/mcdp/lab/](http://www.ui.sav.sk/w/en/dep/mcdp/lab/))). The algorithm was robust enough to manage the failures of the individual UAVs. Our agent-based solution used broadcast (The design of the real chemical pheromone liquid is challenging, from this reason, we used the broadcast communication in outdoor UAV testing.) communication to share the information of the simulated pheromone marks. Each agent broadcast a message with the information on new pheromone marks. We presented experiments with communication failures in [35]. We proved the fault tolerance and robustness of our method in this regard using outdoor tests [36].  
We described the solution of the same problem in 3D space in [38]. We evaluated the performance improvement of the method in [39] and further elaborated the method in [38], where we reduced the number of conflicts (The conflict represents a situation when two or more agents want to move to the same position or their motion trajectory is being crossed.) by modifying the behavior of the individual agents. The measures taken to reduce the number of conflicts negatively affected the exploration ability of the swarm. However, the conflicts allowed us to focus on the development of the swarm's population size control strategy. In this paper, we propose a decentralized method to control the number of the individuals in the groups operating in heterogeneous space taking into account the reactive nature of the agents. The capabilities of the proposed algorithm for 3D space exploration and the adaptations of the group's population are presented here.