Fully Actuated System with an Unknown State: A Bearing-Only Circumnavigation Case

This paper provides an example of fully actuated system (FAS) with an unknown state. This example is from the one-agent one-stationary-target bearing-only circumnavigation problem in the multi-agent system research area. The goal of the bearing-only circumnavigation problem is to design an algorithm for the agent to move around the target with bearing-only measurements which can be regarded as the unit vector pointing from the agent to the target in a mathematical view. In this example, the control matrix contains the unknown state. The unknown state is estimated by an estimator, which is used to replace the unknown state in the control matrix for controller design. Rigorous convergence analysis is provided. Two simulations are conducted. Besides the stationary target case, the simulation section also contains a slowly moving target case.