Unit Dual Quaternion Directed Graphs, Formation Control and General Weighted Directed Graphs
Rings and Algebras
2024-11-07 v6
Abstract
We 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 directed graph (UDQDG). We show that a desired relative configuration scheme is reasonable or balanced in a UDQDG if and only if the dual quaternion Laplacian is similar to the unweighted Laplacian of the underlying directed graph. A direct method and a unit gain graph method are proposed to solve the balance problem of general unit weighted directed graphs. We then study the balance problem of general non-unit weighted directed graphs. Numerical experiments for UDQDG are reported.
Cite
@article{arxiv.2401.05132,
title = {Unit Dual Quaternion Directed Graphs, Formation Control and General Weighted Directed Graphs},
author = {Liqun Qi and Chunfeng Cui and Chen Ouyang},
journal= {arXiv preprint arXiv:2401.05132},
year = {2024}
}