Kernel design for coordination of autonomous, time-varying multi-agent configurations

The coordination of agents in an autonomous system can greatly increase its ability to perform missions in a wide array of applications including distributed computing, coordination of mobile autonomous agents, and cooperative sensing. To expand the functionality of these systems to a wider array of applications, a need exists for coordinated control algorithms driving the system of nodes or agents to any prescribed state configuration in both time and space using only information passed between communicating agents. Using tools from graph theory, this paper derives a graph transformation method that maps the kernel of a graph's Laplacian matrix to any desired state configuration vector while retaining inter-agent communication characteristics of the graph. Using the transformation, this paper derives a theoretically-justified, decentralized control algorithm driving kinematic agents to any relative time-varying state configuration. Theoretical results are illustrated with numerical examples including load distribution in a computing network and surveillance of a moving target with kinematic agents.