Infinitesimal Shape-Similarity for Characterization and Control of Bearing-Only Multirobot Formations

When organizing robots into formations, the interplay between the underlying network topology of the team and the sensing and communication modalities available to the individual robots has a fundamental effect on what types of formations are possible. The purpose of this article is to characterize the available motions of formations in which relative angles between robots equipped with bearing-only sensors are maintained. First, infinitesimal shape-similarity, a property of frameworks for which maintaining certain angles between robots ensures that the formation is invariant to translation, rotation, and uniform scaling, is examined; the shape-similarity matrix is redeveloped, and results on its nullspace are presented. Second, triangulations, a class of frameworks, are shown to be infinitesimally shape-similar. Finally, the coupling between network topology and robot capabilities is examined through the design of a decentralized heterogeneous formation-control strategy for a class of triangulations in which all robots are equipped with bearing-only sensors and a single robot can measure distances; the formation-control strategy is demonstrated on a team of differential-drive robots.