Multi-Robot Formation Shape Control Using Convex Optimization and Bottleneck Assignment

This paper considers formation shape control of multiple robots while minimizing the maximum distance of robot covered. Previous studies have shown that the shape of formation is set of similarity transformations of that and solved the problem by using convex optimization. However, not only the similarity transformation but also permutation transformation preserves the shape of formation. Therefore, this work extends the earlier researches by considering the permutation factor. A threshold algorithm is employed to approach the problem finding optimal permutation of final formation, known as bottleneck assignment problem. This paper suggests an algorithm which alternately iterate the convex optimization and the bottleneck assignment algorithm until reaching convergence. The effectiveness of the proposed algorithm is presented by simulation in comparison with the previous work [1]. 