Link resource allocation for maximizing the rigidity of multi-agent formations

In this paper, the problem of optimizing the rigidity of multi-agent formations is formulated and solved using convex optimization methods. Two rigidity indices, the worst-case rigidity index (WRI) and the mean rigidity index (MRI), are proposed to measure the rigidity of formations of multiple agents connected by links with adjustable strengths. Under the assumption of limited total link resources, we develop efficient algorithms that can find the optimal allocation of link resources for maximizing the rigidity indices. Furthermore, through a sensitivity analysis of the optimization problems, the significance (priorities) of the different links are also characterized. Some simulations results are presented.