A class of bounded distributed controllers for connectivity preservation of unicycles

This paper is concerned with the connectivity preservation of a group of nonholonomic agents using a novel distributed control scheme. The proposed controllers are bounded, and are capable of maintaining the connectivity of those pairs of agents which are initially within the connectivity range. This means that if the underlying network of agents is initially connected, it will remain connected at all times. The main idea is to design the controller in such a way that when an agent is about to lose connectivity with a neighbor, the lowest-order derivative of the agent´s position that is neither zero nor perpendicular to the edge connecting the agent to the corresponding neighbor makes an acute angle with this edge, forcing it to shrink. The results are first developed for a static information flow graph and are then extended to the case of dynamic edge addition. The control laws are derived based on a set of potential functions which are smooth, resulting in bounded control inputs. The effectiveness of the proposed control scheme is illustrated by a consensus example.