Coverage control for heterogeneous mobile sensor networks on a circle

The coverage control problem for a network of heterogeneous mobile sensors with first-order dynamics is addressed in this paper. The goal of the problem is to minimize a coverage cost function which is defined to be the largest arrival time from the mobile sensor network to the points on a circle. The heterogeneity of the network is considered in terms of different maximum velocities of the mobile sensors, which in turn imposes different constraints on the sensors' control inputs. A necessary and sufficient condition for the global minimization of the coverage cost function is firstly derived via a partition of the circle. Then, a distributed coverage control scheme with input saturation is developed to drive the sensors to the optimal configuration such that the necessary and sufficient condition is satisfied. Under the distributed coverage control scheme, the mobile sensors' spatial order on the circle is preserved throughout the network's evolution and thus collision between mobile sensors is avoided. Finally, simulation results are presented to illustrate the effectiveness of the proposed distributed control scheme.