Impact of Leadership and Mobility on ConsensusBuilding in Sensor Networks Introducing leadership and mobility is known to benefit wireless sensor networks in terms of consensusbuilding and collective decisionmaking. However, these benefits are neither analytically proven nor quantified in the literature. This paper fills this gap by investigating the mobility dynamics in wireless sensor networks analytically. The results of the analytical investigation are presented as a set of theorems and their proofs. This paper also establishes a natural synergy between the leaderfollower model and its bipartite graph representation. It demonstrates the advantages of the leaderfollower model for consensusbuilding over others in terms of improved convergence rate. It presents a strategy for choosing leaders from among the agents participating in the consensusbuilding process using the wellknown graphcoloring solution. Then, it shows how the leaderfollower model helps improve the convergence rate of consensusbuilding. Finally, it shows that the convergence rate of the consensusbuilding process can be further improved by making the leaders mobile.

Distributed leader following of an active leader for linear heterogeneous multiagent systems Abstract   This paper considers a leaderfollowing problem for a group of heterogeneous linear time invariant (LTI) followers that are interacting over a directed acyclic graph. Only a subset of the followers has access to the state of the leader in specific sampling times. The dynamics of the leader that generates its sampled states is unknown to the followers. For interaction topologies in which the leader is a global sink in the graph, we propose a distributed algorithm that allows the followers to arrive at the sampled state of the leader by the time the next sample arrives. Our algorithm is a practical solution for a leaderfollowing problem when there is no information available about the state of the leader except its instantaneous value at the sampling times. Our algorithm also allows the followers to track the sampled state of the leader with a locally chosen offset that can be timevarying. When the followers are mobile agents whose state or part of their state is their position vector, the offset mechanism can be used to enable the followers to form a transnational invariant formation about the sampled state of the leader. We prove that the control input of the followers to take them from one sampled state to the next one is minimum energy. We also show in case of the homogeneous followers, after the first sampling epoch the states and inputs of all the followers are synchronized with each other. Numerical examples demonstrate our results.