Simultaneous Estimation of Position and Orientation for Multi-Robot Systems without Compass

Abstract

This paper investigates the posture localization problem (simultaneously estimating the positions and orientations) for multi-robot systems with relative position measurements in their own local frames. It is assumed that none of the robots has access to a compass and knows the difference of its local frame relative to the global frame. Under such a setup, this paper shows that the solvability of the posture localization problem is equivalent to the joint localizability of estimating only positions, and moreover, it is also equivalent to a very simple graphical condition that each connected component contains at least two anchors. In addition, this paper explores self-localizable, jointly localizable, and unlocalizable conditions and provides a classification algorithm in a self-evaluation manner. Finally, corresponding to different categories of robots, heterogeneous distributed iteration algorithms are presented, which can globally asymptotically solve for true positions and orientations simultaneously. Simulation validates the proposed distributed algorithms.