Target Localization and Circumnavigation With Integral Action in R²

Prior results on target localization and circumnavigation with bearing measurements in
$\mathbb {R}^{2}$
are extended with integral action, resulting in a control system that is robust to bounded load disturbances on the control inputs. Such disturbances may arise in practice due to modeling errors and need to be considered to ensure small tracking errors. The control inputs are modeled as the system velocities in the bearing and orthogonal bearing directions, facilitating an implementation on both aerial and ground vehicles. This is demonstrated in a simulation example, followed by an experimental application with ground-based vehicle circumnavigation, highlighting the performance and importance of using the proposed controllers.