Distributed Aggregative Optimization Algorithm for Solving Multirobot Formation Problem

This article investigates a distributed aggregative optimization problem, focusing on formation control within local constraint sets over a multirobot system. Each robot's local objective function is influenced by its specific decision variables and an aggregation information that incorporates the decision variables of all robots. In the multirobot system, each robot has messages pertaining to its individual constraints and objective function, along with the formation configuration information that interacts with the formation reference center. Drawing on gradient tracking technique and projection method, a fixed-step distributed optimization algorithm is proposed to solve the multirobot formation problem. Utilizing the Lyapunov method, the asymptotic convergence of the algorithm is rigorously analyzed. Furthermore, the proposed algorithm is integrated with the Hungarian algorithm to develop the distributed aggregative task assignment and formation (DA-TAF) algorithm, which addresses formation and task allocation problems in multirobot systems. Finally, the performance of the DA-TAF algorithm is demonstrated through numerical simulations and formation control experiments implemented using automated guided vehicle platforms.