Distributed Optimization Algorithm for Multi-Robot Formation with Virtual Reference Center

In this letter, we use a distributed optimization approach to solve a class of multi-robot formation problem with virtual reference center. We investigate the design and analysis of the constrained consensus algorithm to solve the optimization problem with a sum of objective functions with some local constraints. In the multi-robot system with virtual reference center, each robot has messages on its own constraints and objective function, as well as the message about the formation that interacts with the virtual reference center. At the same time, all the robots collaborate to find the minimum value of the function defined by the formation. To find the optimal formation, we propose an algorithm with fixed step size with better performance. In addition, we use a combination of the Hungarian assignment algorithm and the proposed formation algorithm to get the optimal matching formation of the multi-robot system.