Distributed formation control for a cooperative multi-agent system using potential function and extremum seeking algorithm

The formation control and communication optimization problem of a multi-agent system is considered in this article. A classical approach for the formation control problem is potential function method. With potential function, agents are kept a given separation distance with neighbors. Since communication quality will generally change due to the physical environment during formation, a given separation distance might not always be the desired communication distance. In this paper, a distributed scheme integrating potential function and extremum seeking algorithm is proposed to obtain the desired separation distance between neighboring agents in real-time. A comprehensive performance index related to the environment is presented first, capturing a trade-off between formation tasks and communication quality. Since it is difficult to predict the gradient of the performance in physical environments, an adaptive model-free extremum seeking algorithm is developed, which calls for no knowledge of the gradient of the performance. Then the desired separation distance can be obtained dynamically by maximizing the performance with extremum seeking algorithm. Simulation results demonstrate effectiveness of the proposed scheme.