Leader-Tracking in a Shape-Preserving Formation With Bearing-Only Measurements

This paper studies the problem of shape-preserving formation control for multi-agent systems where only bearing measurements are available. Most existing methods to solve the problems assume that accurate global or local position measurements of agents are available, or use estimators to get these information without analysis of estimators' effects on the closed loop system stability. In this work, we propose a framework integrating an estimator to get relative positions using bearing-only measurements and an estimator-based controller to achieve tracking a pair of leaders in a formation with a preserved shape. The estimator is designed by exploiting orthogonality to cope with the high non-linearity of bearing measurements, based on which the controller is designed with the estimated relative positions. With rigorous theoretical analysis of the closed-loop system, we characterize the leaders which can be tracked by followers in a shape-preserving formation using bearing-only measurements, and the asymptotic stability of the closed-loop system can be guaranteed. Simulations testify the effectiveness of the proposed framework.