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.
Zhao, S., Sun, Z., Zelazo, D., Trinh, M.H. and Ahn, H.S., 2017, 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, 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.