Heterogeneous interaction modalities for shape-similar formations

Abstract

Formation control of multi-robot teams is fundamentally influenced by the available sensing and communication capabilities of individual robots. The significance of these capabilities manifests in the network topology induced by interaction modalities present in the team, which may include maintenance of relative distances, bearings, or angles in the formation. To understand this significance and aid in design of effective control strategies, this thesis investigates the interplay between network topology and heterogeneous interaction modalities present in multi-robot formations. With regard to this investigation, each chapter of this thesis addresses a series of research questions that motivate and drive the results. The thesis begins by considering formations in which the relative angles between robots are maintained. To characterize such formations, infinitesimal shape-similarity is developed to describe frameworks in which angle maintenance renders the framework invariant to infinitesimal translations, rotations, and uniform scaling. After developing tools for assessing frameworks for this property, design of formation controllers for infinitesimally shape-similar frameworks reveals the sensing and communication requirements on the robots executing them. To explore relaxations of these requirements, a bearing-only self-assembly mechanism for a class of infinitesimally shape-similar frameworks is designed, and a formation-control strategy is developed to leverage a single distance measurement, suggesting that heterogeneity may be exploited at large. To relate heterogeneous distance, bearing, and angle constraints, the relationships between infinitesimal rigidity, bearing-rigidity, and shape-similarity are examined, espousing the coupling of network topology and interaction modalities in a team. The motions of formations specified by heterogeneous constraints are then characterized, and formation-control strategies are developed. Ultimately, this thesis demonstrates that the coupling of the network topology and heterogeneous interaction modalities of multi-robot teams should be accounted for explicitly to assess the tradeoffs between connectivity and information access in achieving effective formation control.