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

• Published in: Chinese Control Conference pp. 4819 - 4824
• Main Authors: Luo, Rui, Peng, Zhinan, Hu, Jiangping, Ghosh, Bijoy Kumar
• Format: Conference Proceeding
• Language: English
• Published: Technical Committee on Control Theory, Chinese Association of Automation 01.07.2020
• Subjects: Bearing angle measurement; Delay effects; Infinitesimally shape-similar formation; Input time delay; Mobile robots; Robot sensing systems; Shape; Shape-similar matrix; Task analysis; Trajectory
• ISSN: 1934-1768
• DOI: 10.23919/CCC50068.2020.9189040

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.