Distributed Formation Control via Distributed Optimization

In this paper, we formulate a class of distributed formation control problems where the correspondence between agent labels and geometric vertices of the formation shape is not specified a prior. The new formation control problem is then decomposed into two steps including finding the correspondence between agent labels and formation’s geometric vertices and the formation stabilization. As a relaxation of an integer programing, a linear program is formulated to seek the correspondence and a distributed optimization algorithm is proposed. The distributed formation stabilization control is then proposed to achieve the formation shape in a distributed way. The freedom of choosing the correspondence between agent labels and formation’s geometric vertices during the group coordination could lead to potential applications where the formation is required to be adjusted in real time as a response to the environmental change.