Adaptive Observer From Body-Frame Relative Position Measurements for Cooperative Localization

In this letter, we propose an observer scheme to estimate in a common frame the position and yaw orientation of a group of robots from body-frame relative position measurements. The state of the robots is represented by their position and yaw orientation. The graph representing the sensing interaction among the robots is directed and it is only required to be weakly connected in addition to satisfy certain persistency of excitation conditions. Our proposed observer scheme consists of three distinct components. Firstly, an adaptive observer is used to estimate the relative yaw corresponding to each persistently exciting edge. Subsequently, an observer is used to estimate the yaw orientation in a common frame based on these estimated relative yaws. Finally, a third observer is employed to estimate the positions in this common frame, using the estimated yaw orientations. The stability of the whole system is investigated and numerical simulations validate the theoretical findings.