Handbook of discrete and computational geometry
Brief paper: Interconnection topologies for multi-agent coordination under leader-follower framework
Automatica (Journal of IFAC)
Decentralized cohesive motion control of multi-agent formation in 3-dimensional space
AICI'10 Proceedings of the 2010 international conference on Artificial intelligence and computational intelligence: Part I
Nonlinear maneuvering control of rigid formations of fixedwing UAVs
AIS'11 Proceedings of the Second international conference on Autonomous and intelligent systems
Global stabilization of rigid formations in the plane
Automatica (Journal of IFAC)
Leader-follower formation via complex Laplacian
Automatica (Journal of IFAC)
| Hi-index | 22.15 |
In this paper, we generalize the notion of persistence, which has been originally introduced for two-dimensional formations, to R^d for d=3, seeking to provide a theoretical framework for real world applications, which often are in three-dimensional space as opposed to the plane. Persistence captures the desirable property that a formation moves as a cohesive whole when certain agents maintain their distances from certain other agents. We verify that many of the properties of rigid and/or persistent formations established in R^2 are also valid for higher dimensions. Analysing the closed subgraphs and directed paths in persistent graphs, we derive some further properties of persistent formations. We also provide an easily checkable necessary condition for persistence. We then turn our attention to consider some practical issues raised in multi-agent formation control in three-dimensional space. We display a new phenomenon, not present in R^2, whereby subsets of agents can behave in a problematic way. When this behaviour is precluded, we say that the graph depicting the multi-agent formation has structural persistence. In real deployment of controlled multi-agent systems, formations with underlying structurally persistent graphs are of interest. We analyse the characteristics of structurally persistent graphs and provide a streamlined test for structural persistence. We study the connections between the allocation of degrees of freedom (DOFs) across agents and the characteristics of persistence and/or structural persistence of a directed graph. We also show how to transfer DOFs among agents, when the formation changes with new agent(s) added, to preserve persistence and/or structural persistence.