Controller Synthesis for Infinitesimally Shape-Similar Formations

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.