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.

The interplay between network topology and the interaction modalities of a multi-robot team fundamentally impact the types of formations that can be achieved. To explore the trade-offs between network structure and the sensing and communication capabilities of individual robots, this paper applies controller synthesis to formation control of infinitesimally shape-similar frameworks, for which maintaining the relative angles between robots ensures invariance of the framework to translation, rotation, and uniform scaling. Beginning with the development of a controller for the sole purpose of maintaining the formation, the controller-synthesis approach is introduced as a mechanism for incorporating user- designated objectives while ensuring that the formation is maintained. Both centralized and decentralized formulations of the synthesized controller are presented, the resulting sensing and communication requirements are discussed, and the method is demonstrated on a team of differential-drive robots.

The sensing modalities available to individual agents in a multi-robot team have a significant effect on what the team can accomplish. Previous work on infinitesimal shape-similarity has shown that maintaining relative angles between robots equipped with bearing-only sensors can render a formation of these robots invariant to translation, rotation, and uniform scaling; however, previous work has not proposed decentralized control strategies for exploiting this invariance. To address this deficiency, this paper proposes a decentralized formation control strategy for assembled triangulations, a class of infinitesimally shape-similar formations. Heterogeneous in terms of sensing and control, a decentralized formation control strategy is developed in which one robot sets the position of the formation, a robot capable of measuring bearings and distances controls the scale and heading, and the remaining robots maintain the assembled triangulation. The asymptotic controllers that compose the formation control strategy of this work are implemented on a team of differential-drive robots.

Formation control strategies are fundamentally impacted by the sensing modalities present in the multi-robot team. Infinitesimal shape-similarity describes frameworks for which maintaining the relative angles between robots in formation also maintains the shape up to translation, rotation, and uniform scaling; however, ensuring invariance of the formation to these motions requires that the robots measure a sufficient number of angles, which means that the topology of the frame-work must be carefully designed. In this paper, we investigate the self-assembly of a class of infinitesimally shape-similar frameworks by robots equipped with bearing-only sensors. To accomplish self-assembly, we introduce a rank condition on the shape-similarity matrix for analyzing frameworks; we then use this rank condition to show that triangulations are infinitesimally shape-similar. A graph grammar is presented to assemble triangulations, and a controller is designed to achieve self-assembly of a team of differential-drive robots.

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.