A Variational Integrator for the distance-based formation control of multi-agent systems

Leonardo J. Colombo, Hector Garcia de Marina

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Distance-based formation control of second order agents can be seen as a physical system of particles linked by springs, whose evolution can be described by a Lagrangian function. An interesting family of geometric integrators, called variational integrators, is defined by using discretizations of the Hamilton's principle of critical action. The variational integrators preserve some geometric features such as the symplectic structure, they preserve the momentum map, and the evolution of the system's energy presents a good (bounded) behavior. We derive variational integrators that can be employed in the context of distance-based formation control algorithms. In particular, we provide an accurate numerical integrator with a lower computational cost than traditional solutions. Consequently, we can provide a faster identification of regions of attraction for desired distance-based shapes, and more computationally efficient estimation algorithms like Kalman filters that employ distance-based controllers as prediction models. We use a formation consisting of four autonomous planar agents as an example and benchmark to test and compare the performances of the proposed variational integrator.

Original languageEnglish
Book seriesIFAC-PapersOnLine
Issue number23
Pages (from-to)76-81
Publication statusPublished - 2018
Event7th IFAC Workshop on Distributed Estimation and Control in Networked Systems - Groningen, Netherlands
Duration: 27. Aug 201828. Aug 2018


Conference7th IFAC Workshop on Distributed Estimation and Control in Networked Systems



  • Distribute control
  • Formation control
  • Geometric integration
  • Multi-agent systems
  • Variational integrators
  • Variational principles

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