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Title: Ratio-of-distance rigidity theory with application to similar formation control
Authors: Cao, Kun
Han, Zhimin
Li, Xiuxian
Xie, Lihua
Keywords: Engineering::Electrical and electronic engineering::Control and instrumentation::Control engineering
Engineering::Electrical and electronic engineering::Control and instrumentation::Robotics
Issue Date: 2020
Source: Cao, K., Han, Z., Li, X., & Xie, L. (2020). Ratio-of-distance rigidity theory with application to similar formation control. IEEE Transactions on Automatic Control, 65(6), 2598- 2611. doi:10.1109/TAC.2019.2938318
Journal: IEEE Transactions on Automatic Control
Abstract: This paper develops a ratio-of-distance (RoD) rigidity theory to study when a framework can be uniquely determined by a set of RoD constraints up to similar transformations (translation, rotation, scaling, and reflection). In particular, a framework is specified by a set of RoD constraints (the RoD of a pair of edges joining a common vertex) instead of distance, bearing, and angle constraints assumed in existing literature. Its relations to three existing rigidity theories (distance, bearing, and angle rigidity theories) are established. The proposed RoD rigidity theory is further applied to the RoD-based similar formation stabilization problem, where the desired formation shape is expressed as a set of RoD constraints. Finally, numerical simulations are presented to illustrate the effectiveness of the theoretical results.
ISSN: 0018-9286
DOI: 10.1109/TAC.2019.2938318
Schools: School of Electrical and Electronic Engineering 
Research Centres: ST Engineering-NTU Corporate Lab 
Rights: © 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at:
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:EEE Journal Articles

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