Synchronization on the sphere is important to certain control applications in swarm robotics. Of recent interest is the Lohe model, which generalizes the Kuramoto model from the circle to the sphere. The Lohe model is mainly studied in mathematical physics as a toy model of quantum synchronization. The model makes few assumptions, wherefore it is well-suited to represent a swarm. Previous work on this model has focused on the cases of complete and acyclic networks or the homogeneous case where all oscillator frequencies are equal. This paper concerns the case of heterogeneous oscillators connected by a non-trivial network. We show that any undesired equilibrium is exponentially unstable if the frequencies satisfy a given bound. This property can also be interpreted as a robustness result for small model perturbations of the homogeneous case with zero frequencies. As such, the Lohe model is a good choice for control applications in swarm robotics.

Robust synchronization of heterogeneous robot swarms on the sphere / Markdahl, Johan; Proverbio, Daniele; Goncalves, Jorge. - (2020), pp. 5798-5803. (Intervento presentato al convegno CDC 2020 tenutosi a Jeju Island, South Korea nel 14th-18th December 2020) [10.1109/CDC42340.2020.9304268].

Robust synchronization of heterogeneous robot swarms on the sphere

Proverbio, Daniele
Secondo
;
2020-01-01

Abstract

Synchronization on the sphere is important to certain control applications in swarm robotics. Of recent interest is the Lohe model, which generalizes the Kuramoto model from the circle to the sphere. The Lohe model is mainly studied in mathematical physics as a toy model of quantum synchronization. The model makes few assumptions, wherefore it is well-suited to represent a swarm. Previous work on this model has focused on the cases of complete and acyclic networks or the homogeneous case where all oscillator frequencies are equal. This paper concerns the case of heterogeneous oscillators connected by a non-trivial network. We show that any undesired equilibrium is exponentially unstable if the frequencies satisfy a given bound. This property can also be interpreted as a robustness result for small model perturbations of the homogeneous case with zero frequencies. As such, the Lohe model is a good choice for control applications in swarm robotics.
2020
2020 59th IEEE Conference on Decision and Control (CDC)
Piscataway, NJ, USA
Institute of Electrical and Electronics Engineers Inc.
978-1-7281-7447-1
Markdahl, Johan; Proverbio, Daniele; Goncalves, Jorge
Robust synchronization of heterogeneous robot swarms on the sphere / Markdahl, Johan; Proverbio, Daniele; Goncalves, Jorge. - (2020), pp. 5798-5803. (Intervento presentato al convegno CDC 2020 tenutosi a Jeju Island, South Korea nel 14th-18th December 2020) [10.1109/CDC42340.2020.9304268].
File in questo prodotto:
File Dimensione Formato  
CDC_conf_synch.pdf

Solo gestori archivio

Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 337.04 kB
Formato Adobe PDF
337.04 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/397349
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 8
social impact