Triangular angle rigidity for distributed localization in 2D

• Main Author: Chen, Liangming
• Other Authors: School of Mechanical and Aerospace Engineering
• Format: Article
• Language: English
• Published: 2022
• Subjects: Engineering::Mechanical engineering; Triangular Angle Rigidity; Sensor Network Localization
• Online Access: https://hdl.handle.net/10356/163554
• Institution: Nanyang Technological University

Recent advances in sensing technology have enabled sensor nodes to measure interior angles with respect to their neighboring nodes. However, it is unknown which combination of angle measurements is necessary to make a sensor network localizable, and it is also unidentified if there is a distributed localization algorithm whose required communication only consists of the sensor nodes’ measured angles and estimated positions. Motivated by these two challenging problems, this paper develops triangular angle rigidity for those networks consisting of a set of nodes and triangular angle constraints in 2D. First, we transfer the geometric constraint of each triangle into an angle-induced linear constraint. Based on the linear constraint, we show that different from angle rigidity, triangular angle rigidity implies global triangular angle rigidity. More importantly, inspired by Laman's theorem, we propose a topological, necessary and sufficient condition to check generic triangular angle rigidity. Based on the results on triangular angle rigidity, both algebraic and topological localizability conditions are developed, which are necessary and sufficient when the number of anchor nodes in the network is two. Both continuous and discrete localization algorithms are proposed, in which only measured angles and estimated positions are communicated among the sensor nodes. Finally, a simulation example with 32 sensor nodes is used to validate the effectiveness of the proposed approaches.