  Representation of a swarm of independent robotic agents under graph-theoretic
constructs allows for more formal analysis of convergence properties. We
consider the local and global convergence behavior of an N-member swarm of
agents in a modified consensus problem wherein the connectivity of agents is
governed by probabilistic functions. The addition of a random walk control
ensures Lyapunov stability of the swarm consensus. Simulation results are given
and planned experiments are described.
