Cooperative formation control, as an important field in multi-agent systems, investigates methods and algorithms that allow agents to maintain a specific and desirable arrangement in space. This field specifically focuses on the design and implementation of controllers that can manage the motion and position of agents in a distributed manner without the need for central information. In this framework, agents form and maintain arrangements such as lines, circles, regular networks, or any other arbitrary arrangement using local control rules and interactions with their neighbors. One of the main challenges in formation control is to ensure the stability and convergence of formation under different environmental and dynamic conditions. This issue is particularly important in practical applications such as drones, collaborative robots, and distributed sensor networks, where agents must act in concert while dealing with environmental uncertainties and disturbances. Researches in this field include stability analysis, design of robust control algorithms, and eva‎luation of the efficiency of formation control systems in different conditions. The results of this research can lead to improving the efficiency and reliability of multi-agent systems in performing complex and multi-stage missions. In this research, the modeling of factors has been done using first-order holonomic dynamics. Two different approaches have been used to design the control law. In this way, a biased extremum seeking controller has been used for the initial and final agents so that it can converge to a certain distance from the source, and a different control law has been considered for the rest of the agents. In this way, by using the relationships between three consecutive points on the arc of the circle, a relationship was obtained based on the distance of the points from each other, and that relationship was considered as the second control law for other agents that act cooperatively. Ordinary differential equations have been used to calculate the second control law, and due to the flexibility of complex coordinates, all control laws are expressed in complex coordinates. In order to check the stability of both control laws, the averaging theorem has been used. Finally, using the obtained control rules, the circular, spiral and linear arrangement was simulated.

محسن مجيري فروشاني

مرضيه كمالي , جواد عسگري مارناني