宁夏大学学报（自然科学版中英文）2026，Vol.47Issue(3)：193-202,10.DOI:10.20176/j.cnki.nxdz.20260502
网络化系统中的图形状唯一性与角度刚性理论
Shape Uniqueness and Angle Rigidity Theory of Graphs in Networked Systems
摘要
Abstract
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.关键词
图刚性理论/角度刚性理论/网络化系统/刚性编队控制/传感器网络定位Key words
graph rigidity theory/angle rigidity theory/networked systems/rigid formation control/sensor network localization分类
信息技术与安全科学引用本文复制引用
黄锦鹏,井冈山,赵凯,宋永端..网络化系统中的图形状唯一性与角度刚性理论[J].宁夏大学学报（自然科学版中英文）,2026,47(3):193-202,10.基金项目
国家重点研发计划青年科学家项目(2025YFA1018800) （2025YFA1018800）
国家自然科学基金面上项目(62573068) （62573068）
国家自然科学基金重点项目(62533002) （62533002）
