Relative Angle Measurements Based Shape-Similar Formation for Mobile Robots with Input Time-Delay

Rui Luo, Zhinan Peng, Jiangping Hu, Bijoy Kumar Ghosh

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


This paper focuses on the infinitesimally shape-similar formation problem for a group of robots subject to input time delay. We assume that each robot is only equipped with bearing sensors. For the implementation of infinitesimally shape- similar motion, the shape-similarity matrix (SSM) is introduced by using bearing angle measurement (BAM). It is shown that the SSM only can maintain the angle-consistent but not keeping shape of formation along trajectories. Further, some conditions of selecting angles are given to guarantee the shape-preservation of formation on the basis of angle-consistent. To apply the above results, an optimization formation task is established for a group of robots with single integrator dynamics subject to input time-delay. This task aims at maintaining shape of formation as well as achieving position tracking. Then a shape-similar-based optimal controller is obtained by using Lagrangian multiplier method. Finally, a simulation scenario on a quadrilateral formation of four robots is carried out to demonstrate the proposed shape-similar based approaches.

Original languageEnglish
Title of host publicationProceedings of the 39th Chinese Control Conference, CCC 2020
EditorsJun Fu, Jian Sun
PublisherIEEE Computer Society
Number of pages6
ISBN (Electronic)9789881563903
StatePublished - Jul 2020
Event39th Chinese Control Conference, CCC 2020 - Shenyang, China
Duration: Jul 27 2020Jul 29 2020

Publication series

NameChinese Control Conference, CCC
ISSN (Print)1934-1768
ISSN (Electronic)2161-2927


Conference39th Chinese Control Conference, CCC 2020


  • Bearing angle measurement
  • Infinitesimally shape-similar formation
  • Input time delay
  • Shape-similar matrix


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