Optimizing formation rigidity under connectivity constraints

This paper studies the problem of finding the most rigid formation for a multi-agent system. The worst-case rigidity index (WRI) and the mean rigidity index (MRI) are proposed as the quantitative measures of formation rigidity. From a practical point of view, the values of these indices characterize the stability and robustness of the multi-agent system in maintaining a given formation. An iterative algorithm is presented for finding the most rigid formation through the joint optimization of both the positions of agents and their connection topology. The effectiveness of the algorithm is illustrated through numerical examples.