Infinitesimally shape-similar motions using relative angle measurements

摘要

This paper revisits the formation control problem, whereby a team of mobile robots assemble and maintain a desired geometric shape. However, the types of shapes that are realizable by a given robot team depends directly on the sensing modalities of the individual robots. For example, rigidity-based approaches make use of distance measurements, and the idea is to restrict the motion of the robots so that all inter-robot distances are maintained, thereby ensuring purely rigid motion. Rather than distances, we notice that for certain sensor classes, such as monocular pinhole cameras, only relative angle measurements are available. To this end, we introduce the notion of shape-similar motions, which constitutes a class of angle preserving motions that also preserve the shape of the formation in the sense that rigid motions as well as uniform scalings are permissible. We construct the shape-similarity matrix, whose null-space captures angle preserving motions, and show that by restricting the dimension of the null-space, we can guarantee that motions of the formation preserve the shape. Lastly, we implement a shape-similar controller on a team of differential drive mobile robots.