### Resumé

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.

Originalsprog | Engelsk |
---|---|

Bogserie | IFAC-PapersOnLine |

Vol/bind | 51 |

Udgave nummer | 23 |

Sider (fra-til) | 76-81 |

ISSN | 2405-8963 |

DOI | |

Status | Udgivet - 2018 |

Begivenhed | 7th IFAC Workshop on Distributed Estimation and Control in Networked Systems - Groningen, Holland Varighed: 27. aug. 2018 → 28. aug. 2018 |

### Konference

Konference | 7th IFAC Workshop on Distributed Estimation and Control in Networked Systems |
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Land | Holland |

By | Groningen |

Periode | 27/08/2018 → 28/08/2018 |

### Fingeraftryk

### Citer dette

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*IFAC-PapersOnLine*, bind 51, nr. 23, s. 76-81. https://doi.org/10.1016/j.ifacol.2018.12.014

**A Variational Integrator for the distance-based formation control of multi-agent systems.** / Colombo, Leonardo J.; de Marina, Hector Garcia.

Publikation: Bidrag til tidsskrift › Konferenceartikel › Forskning › peer review

TY - GEN

T1 - A Variational Integrator for the distance-based formation control of multi-agent systems

AU - Colombo, Leonardo J.

AU - de Marina, Hector Garcia

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Distribute control

KW - Formation control

KW - Geometric integration

KW - Multi-agent systems

KW - Variational integrators

KW - Variational principles

U2 - 10.1016/j.ifacol.2018.12.014

DO - 10.1016/j.ifacol.2018.12.014

M3 - Conference article

VL - 51

SP - 76

EP - 81

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

SN - 2405-8963

IS - 23

ER -