부산대학교 도서관

We first study the multi-agent formation control problem in a directed graph. The relative configurations are expressed by unit dual quaternions (UDQs). We call such a weighted directed graph a unit dual quaternion weighted directed graph (UDQWDG). We show that a desired relative configuration scheme is reasonable in a {UDQWDG} if and only if for any cycle in this directed graph, the product of relative configurations of the forward arcs, and inverses of relative configurations of the backward arcs, is equal to $1$. We then show that a desired relative configuration scheme in a {directed connected} graph {is reasonable if and only if} the dual quaternion Laplacian is similar to the unweighted Laplacian of the directed graph. Then for a reasonable desired relative configuration scheme, we build the relationship between the desired formation and the eigenvector corresponding to the zero eigenvalue. A numerical method and a control law {are} presented. We then study dual quaternion weighted directed graphs (DQWDG). Ordinary graphs, gain graphs, signed directed graphs, complex weighted directed graphs and UDQWDGs are special cases of DQWDGs. A general theory of DQWDG is presented.