García De Marina Peinado, Héctor JesúsJiménez Castellanos, Juan FranciscoYao, Weijia2026-01-092026-01-092021H. G. de Marina, J. Jimenez Castellanos and W. Yao, "Leaderless collective motions in affine formation control," 2021 60th IEEE Conference on Decision and Control (CDC), Austin, TX, USA, 2021, pp. 6433-6438, doi: 10.1109/CDC45484.2021.9682800.978-1-6654-3658-80743-154610.1109/CDC45484.2021.9682800https://hdl.handle.net/20.500.14352/129810This paper proposes a novel distributed technique to induce collective motions in affine formation control. Instead of the traditional leader-follower strategy, we propose modifying the original weights that build the Laplacian matrix so that a designed steady-state motion of the desired shape emerges from the agents' local interactions. The proposed technique allows a rich collection of collective motions such as rotations around the centroid, translations, scalings, and shearings of a reference shape. These motions can be applied in useful collective behaviors such as shaped consensus (the rendezvous with a particular shape), escorting one of the team agents, or area coverage. We prove the global stability and effectiveness of our proposed technique rigorously, and we provide some illustrative numerical simulations.engconference paper2576-2370https://doi.org/10.1109/CDC45484.2021.9682800https://ieeexplore.ieee.org/document/9682800https://dx.doi.org/10.48550/arXiv.2104.03412open access004Laplace equationsShapeConferencesNumerical simulationStability analysisSteady-stateShearingInformática (Informática)33 Ciencias Tecnológicas