Coverage Control under Connectivity Constraints

In this paper, centralized and decentralized laws for the coverage problem under connectivity constraints are proposed. We formulated the problem as a continuous optimization task with the inequality constraint that algebraic connectivity must not be less than a small positive number, and solved the problem based on the active set method. This formulation can cause agents to be trapped in undesired local minima; to address this, we added the squared distance between the centroid of the coverage area and that of the agent system to the objective function of the coverage control. To derive the decentralized law, we employed an average consensus estimator that determines the algebraic connectivity and system centroid. When the algebraic connectivity is greater than the threshold, the proposed control laws allow agents to advance along the direction of steepest descent of the objective function. Once the connectivity is equal to the threshold, agents maintain the connectivity while decreasing the objective function by moving along the projection vector of the steepest descent in the direction in which the connectivity is constant. Simulation results confirmed the effectiveness of our proposed laws.