Convergence analysis for a class of bounded distributed connectivity preserving consensus algorithms for unicycles

This paper presents a class of bounded connectivity preserving consensus control algorithms for a team of unicycles. The control law is based on some analytic potential functions, ensuring the boundedness of the control signal. It is assumed that the information flow graph is an undirected static tree. A detailed convergence analysis for the designed controllers is subsequently presented. The growth of the radius of the smallest circle centered at a fix point which contains all agents is shown to be bounded by a decaying exponential function. This result is used to show the boundedness of the trajectories of the agents. Some important properties of positive limit sets of nonlinear systems are then used to prove the convergence of the agents to consensus, under the proposed controllers. Simulations demonstrate the effectiveness of the proposed connectivity preserving control law.