2020/10/01 by Leonardo Colombo, Héctor García de Marina, Colombo, Leonardo +1
Economics, Econometrics and Finance · Mathematics · #FOS: Electrical engineering #Mathematical Biology Tumor Growth #Numerical methods for differential equations #Stochastic processes and financial applications #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2010.00425
openalex publication_date 2020/10/01 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Formation control of autonomous agents can be seen as a physical system of\nindividuals interacting with local potentials, and whose evolution can be\ndescribed by a Lagrangian function. In this paper, we construct and implement\nforced variational integrators for the formation control of autonomous agents\nmodeled by double integrators. In particular, we provide an accurate numerical\nintegrator with a lower computational cost than traditional solutions. We find\nerror estimations for the rate of the energy dissipated along with the agents'\nmotion to achieve desired formations. Consequently, this permits to provide\nsufficient conditions on the simulation's time step for the convergence of\ndiscrete formation control systems such as the consensus problem in discrete\nsystems. We present practical applications such as the rapid estimation of\nregions of attraction to desired shapes in distance-based formation control.\n