Synchronized and Balanced Collective Formations in Multi-Agent Systems
Multi-agent systems possess improved robustness properties over single agent systems, and hence, are more desirable for various engineering applications, where it is required for the multiple agents to move in a formation. These applications include, but are not limited to, tracking, surveillance, reconnaissance, environmental monitoring, searching, sensing and data collection. Motivated by these applications, various collective motions of multiple vehicles have been explored in the literature. This thesis studies a particular type of collective motion in multi-agent systems where the heading angles of the agents are either in synchronized or in balanced formation. These formations are characterized by the motion of the collective centroid of the group of agents, and serve as motion primitives to achieve general tracking patterns. Synchronization is achieved when the agents and their centroid move in a common direction. A complementary notion of synchronization is balancing, in which the position of the centroid remains stationary. In the existing literature, the problems of achieving synchronization and balancing in a multi-agent system have been studied under the assumption that the agents are coupled through controller gains that are identical or homogeneous. In this thesis, it is assumed that the controller gains are heterogeneously distributed, that is, they are not necessarily the same for each agent. This addresses a practical scenario where the gains may vary nominally due to minor implementation errors or drastically due to major faults or errors. The thesis first discusses synchronization and balancing of agents while allowing them to move either along straight line paths or around individual circular orbits. Conditions, under which heterogeneous controller gains result in synchronized or balanced formation, are derived. The effect of heterogeneous gains is analyzed on the common velocity direction at which the system of agents synchronizes, and on the location of the collective centroid about which balanced formation stabilizes. It is shown that heterogeneity in controller gains generalizes synchronized and balanced performances of a multi-agent system scenario. Next, we discuss synchronization and balancing of agents on a common circular orbit of prescribed radius and fixed center. Two cases, when the controller gains are bounded and when the control efforts are bounded, are also studied. In addition, all-to-all interaction and limited interaction among agents are also addressed in this thesis.