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

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.