A Distributed Projection-Based Algorithm with Local Estimators for Optimal Formation of Multi-robot System

In general, the optimal formation problem can be modeled as a standard constrained optimization problem according to the shape theory. By adding local supplementary estimators, it can be further modeled as a distributed constrained optimization problem. Then a distributed projection-based algorithm is designed for solving this problem. The aim of the algorithm is to drive a group of robots to move to the desired geometric pattern by minimizing the total travel distance of robots from the initial positions. It is worth noticing that, as long as the graph of the communication network among the robots is undirected and connected, the global convergence of the algorithm can be guaranteed. Moreover, all of the robots finally form an ideal formation in the limited space. Finally, simulation results are provided to verify the effectiveness of the proposed distributed algorithm.