Mathematical modeling of fuzzy communication in multi-robot systems based on pseudoanalog signals

Abstract

The article presents the results of a study devoted to modeling communication in multi-robot systems using fuzzy (pseudoanalog) signals. In modern conditions, when groups of autonomous robots operate in complex and dynamically changing environments, the tasks of ensuring effective, stable and energy-saving information exchange between agents are extremely relevant. Traditional approaches to inter-robot communication – mostly discrete and based on rigid binary protocols – often do not allow achieving sufficient adaptability in noisy, unstructured or resource-limited environments. They tend to rely on constant signal retransmission and error-correction procedures, which increases energy costs and reduces real-time responsiveness. In response to these challenges, the author proposed a hybrid model that imitates the principles of communication inherent in biological systems, in particular the variability and context dependence of analog signals used in flocks of birds, schools of fish or insect colonies. Such natural communication is not strictly digital: it combines amplitude, frequency and temporal modulation, enabling organisms to convey uncertainty, urgency or intent even under external disturbances. The developed mathematical model applies the concept of fuzzy logic, in which each transmitted signal is represented by three parameters – amplitude, frequency and duration – interpreted in linguistic categories such as high, medium, low, alert or coordination. Membership functions determine the degree to which a received signal corresponds to a specific linguistic value, enabling each agent to form a flexible response depending not only on the signal itself but also on the situational context. This reduces the need for exact matching of discrete messages and allows communication to remain functional even when signals are partially lost or distorted. A series of experiments was conducted in a simulation environment representing predator–prey interactions, in which “Lions” acted as pursuing agents while “Antelope” could exchange messages about detected danger or decreasing energy reserves. Three categories of environments were modeled: a basic scenario with ideal discrete communication, a scenario with partial signal loss, and one with distortion introduced during pseudoanalog transmission. The results demonstrated that the fuzzy model enables maintaining the same level of agent survival and task completion efficiency as in ideal discrete communication, while reducing overall energy consumption by approximately 18 %. Furthermore, the swarm demonstrated significantly higher robustness under conditions of interference or incomplete data, as fuzzy interpretation prevented critical communication breakdowns. The use of analog-like communication with linguistic interpretation decreases unnecessary agent activation, smooths collective decision-making and increases the overall efficiency of group behavior. The proposed model can be applied to the development of distributed technical systems for search-and-rescue missions, reconnaissance, environmental monitoring, agricultural robotics and low-cost swarm systems, where adaptability and resilience are more critical than precision. The article contributes to the advancement of flexible decentralized communication protocols capable of maintaining functionality under uncertainty and without centralized control.