Complex Laplacian approach for formation tracking without velocity measurements

Mojtaba Ranjbar, Mohammad T H Beheshti and Sadegh Bolouki

International Journal of Systems Science, 2025, vol. 56, issue 2, 193-210

Abstract: This paper is focused on formation tracking control of multi-agent systems in a leader–follower setting. The objective is to introduce control algorithms to steer a team of mobile agents into a desired, moving geometrical pattern while the agents are unaware of their own and other agents' velocity information during the entire process. We introduce a formation control law under which the agents asymptotically shape a desired geometrical pattern and track a constant reference velocity. Another control law is then introduced to address the case where the reference velocity is time-varying. Both control laws are based on the complex Laplacian approach and do not require agents' velocity information. The convergence of these algorithms are proved and their performance are examined via numerical examples. Simulation results verify the outperformance of the proposed control laws compared to the rival control schemes in the literature.

Date: 2025
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DOI: 10.1080/00207721.2024.2390170

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