网络化系统中的图形状唯一性与角度刚性理论OA

The ability of a graph embedded in Euclidean space to uniquely determine its global geometric shape through local constraints among nodes and edges is critical for the coordination of networked systems,including sensor network localization and multi-agent formation control.Recently,graph rigidity theory has rapidly evolved as a theoretical tool for addressing this issue.In particular,angle-based rigidity theories have emerged as a significant branch of rigidity theory due to their extensive applicability in engineering.This paper systemati-cally reviews recent advancements in angle-based rigidity theories and their implications for shape uniqueness.This study provides a detailed discussion of rigidity theories based on both unsigned and signed angle con-straints.Furthermore,it explores the intrinsic connections between angle-based rigidity theories and matrix completion theory.Finally,it summarizes existing open problems in this field and outlines future research direc-tions,which may inform studies on coordination control and optimization in networked systems based on angle constraints.