Control of Formations with Non-rigid and Hybrid Graphs

This thesis studies the problem of control of multi-agent formations, of which the interaction architectures can be modeled by undirected and directed graphs or a mixture of the two (hybrid graphs). The algorithms proposed in this thesis can be applied to control the architectures of multi-agent systems or sensor networks, and the developed control laws can be employed in the autonomous agents of various types within multi-agent systems. This thesis discusses two major issues. The first tackles formations with undirected and directed underlying graphs, more specifically, the problems of rigidity restoration and persistence verification for multi-agent formations are studied. The second discusses the control of formations with both undirected and directed interaction architectures (hybrid formations) by distance-based control methods. The main contributions of this thesis are: definition of spindle agent and basic graphs for non-rigid undirected graphs, development of new operations for the constructions of undirected and directed graphs, design of graph rigidity restoration strategy by merging two or more non-rigid graphs, development of new persistence analysis strategy for arbitrary directed graphs, definition and investigation of hybrid formations and the underlying hybrid graphs, verification of persistence and minimal persistence for hybrid graphs, as well as the control of persistent hybrid formations by distance-based approaches