Bearing-Only-Based Formation Circumnavigation Guided by Multiple Unknown Targets

In this paper, we consider the problem of the formation circumnavigation on an ellipse guided by multiple unknown targets in two-dimensional space, where each agent only employ bearing measurement without knowing any target's position and velocity. A geometric center estimator is first established, only needing to use local information in gain design rather than any specific initialization. In the gain design, neither is the global information of some variables from all agents needed, nor is the gain needed to be designed large enough. Instead of designing corresponding controllers respectively, a unified circumnavigation controller is designed for the two cases of the stationary targets and the dynamic targets. The exponential stability of the whole algorithm is proved for the two cases. The conditions of some parameters in the circumnavigation controller are strictly derived. These conditions are very weak, and there exist a weak condition in which the controller can be simultaneously applied to the two cases. Finally, a series of simulations are conducted to verify the correctness of the algorithm.