This paper proposes a fixed-time (FxT) frame (or pose) localization scheme for multi-agent systems based on the inter-agent relative poses specified by SE(3) transformation matrices. Under the localization law, the agents’ local coordinate frames are localized almost globally in fixed-time with regard to a common reference frame. Based on the FxT frame estimation, the SE(3) formation control for multi-agent systems with connected graphs can be simply cast as the stabilization in SE(3) for each individual agent. When the desired formation is specified by the desired inter-agent bearing vectors, FxT bearing-based formation control is presented with no need for the global reference frame common to the agents. Simulation results are provided to support the theoretical development.
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This work is funded by Hanoi University of Science and Technology (HUST) under project number T2022-TT-004. Early version of this work was presented at the 8th IFAC Workshop on Distributed Estimation and Control in Networked Systems .
Quoc Van Tran is a Lecturer with the Department of Mechatronics, the School of Mechanical Engineering, Hanoi University of Science and Technology (HUST), Hanoi, Vietnam. He received his B.E. degree in mechatronics from HUST in 2013, and an M.S. degree in mechatronics and a Ph.D. degree in mechanical engineering both from Gwangju Institute of Science and Technology (GIST), Gwangju, Korea, in 2015 and 2021, respectively. Before joining HUST, he was a Postdoctoral Researcher with the Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea. Dr. Tran serves as an Associate Editor for the International Journal of Control, Automation, and Systems (IJCAS). His research interests include networked system, distributed optimization, and robotics.
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Van Tran, Q. Fixed-time Localization of Local Coordinate Frames: Interpretation and Applications to Formation Control Problems. Int. J. Control Autom. Syst. 21, 4057–4066 (2023). https://doi.org/10.1007/s12555-023-0113-4