Localization and circumnavigation of a group of targets by a single agent using bearing measurements

This paper considers the problem of localization and circumnavigation by a single agent of a group of targets which are either stationary or moving slowly with unknown speed. The system inputs include the agent´s position and the bearing angles of the targets. There are two modes of signal reception for the agent: continuous and segmented. With continuous signal reception, the agent is able to receive bearing information from all targets at the same time. With segmented reception, bearing information is only received from one target at a time. The concept of a virtual center or target for the agent to circle around is introduced as well as a method of calculating it. An estimator is proposed, initially for the continuous reception case with stationary targets, to localize the virtual center as well as a control law that forces the agent to move on a circular trajectory around the virtual center such that both the estimator and the control system convergence to the correct trajectory are exponentially stable. Then the case where signal is received by the agent in a segmented manner is studied in the same way. The algorithms can be used when the targets are not stationary, and simulations show that the algorithms remain useful when the targets do not move very fast.