The persistent coverage control problem is formulated based on cell discretisation of two-dimensional mission space and time-increasing cell ages. A new performance function is defined to represent the coverage level of the mission space, and time behaviour is evaluated by the probabilistic method based on the detection model of agents. For comparison, persistent coverage controllers are designed by a target-based approach and a reactive approach. Both controllers are designed in a distributed manner using Voronoi tessellation and Delaunay graph-based local information sharing. Numerical simulation is performed to analyse the evaluated mean age of cells and evaluated coverage level over time for the designed persistent coverage controllers. The differences between the evaluation model and simulation situation are discussed.

This paper addresses a problem of complete sensing coverage in 3D environments. We propose a distributed random algorithm to drive mobile robotic sensors on the vertices of a truncated octahedral grid for complete sensing coverage of a bounded 3D area. Furthermore, we develop a distributed algorithm for the self-deployment of mobile sensors to form a desired 3D geometric shape on the vertices of the truncated octahedral grid. These algorithms are developed based on some consensus rules that only rely on local information. The proposed algorithms utilize 3D grids for the coverage task. Several simulations are conducted to illustrate the validity of the proposed distributed sensing coverage and formation building algorithms for a mobile robotic sensor network. Also, we give mathematically rigorous proof of the convergence with probability 1 of our proposed algorithms.

A distributed coverage control scheme based on the state space model predictive control, which is known as receding horizon control (RHC) for decoupled systems, is presented. An optimal control problem is formulated for a set of decoupled robotic systems where a cost function couples the dynamical behavior of the robots. The coupling is described through a connected graph using a Voronoi diagram, where each robot is a node and the cost and constraints of the optimization problem associated with each robot are a function of its state and of the states of its neighbors. The complexity of the problem is addressed by breaking a centralized receding horizon controller into distinct RHC controllers of smaller sizes. Each RHC controller is associated with a different node and it computes the local control inputs based only on the position of the robot and that of its neighbors. The stability of the distributed scheme is analyzed and its properties compared with the linear quadratic regulator (LQR) design which has been proposed in the literature. Moreover, the proposed coverage algorithm is also applied to deploy a group of mobile robots in a desired formation pattern. The simulation results are used to illustrate the good performance of the proposed coverage control scheme.