A Bi-objective Distributed Optimization Algorithm for Multi-target Encirclement of Multi-robot System with Optimal Formation

This paper focuses on the multi-target encirclement of multi-robot system with different optimal formations. Two objective functions are considered: the distance between robot’s target and initial positions, and the distance between robot’s target position and the containment target’s position. Furthermore, an equality constraint is introduced to achieve a specific formation. Based on the above considerations, the multi-target encirclement problem is transformed into a bi-objective optimization problem, which is further converted into a single-objective optimization problem by employing weighted sum method. Subsequently, a distributed optimization algorithm with a fixed step size is designed based on projection operator. By adjusting the weights of objective functions, the containment effectiveness of multirobot system can be controlled. Additionally, the influence of objective functions’ weights on the containment performance of the multi-robot system and the effectiveness of the proposed algorithm are discussed by two simulation examples.