Graph rigidity theory
Graph rigidity theory
Graph rigidity is the cornerstone of formation control and network localization. A rigidity problem involves determining how a framework should be constructed such that some geometric variables are preserved with regard to trivial infinitesimal motions.
References
Minh Hoang Trinh, "Reconfiguration of four-degree limited Laman graphs," IFAC Journal of Systems and Control, Vol. 29, Sep. 2024, 100277.
Minh Hoang Trinh, Quoc Van Tran, Hyo-Sung Ahn, "Minimal and redundant bearing rigidity: conditions and applications," IEEE Transactions on Automatic Control, Vol. 65, Iss. 10, Oct. 2020, pp. 4186 - 4200.
Shiyu Zhao, Zhiyong Sun, Daniel Zelazo, Minh Hoang Trinh, Hyo-Sung Ahn, December. Laman graphs are generically bearing rigid in arbitrary dimensions. In Proc. of the IEEE 56th Annual Conference on Decision and Control (CDC), Melbourne, Australia, 2017, pp. 3356-3361.
Minh Hoang Trinh, Shiyu Zhao, Zhiyong Sun, Daniel Zelazo, Brian D. O. Anderson, Hyo-Sung Ahn, “Bearing-based formation control of a group of agents with leader-first follower structure,” IEEE Transactions on Automatic Control, Vol. 64, Iss. 2, Feb. 2019, pp. 598 - 613.