Coverage Control Using Directional Nonlinear Dynamic Sensors with Non-smooth Sensing Range

Abstract

This paper investigates control design for the coverage problem using mobile sensors, which have nonlinear dynamics with non-smooth directional sensing ranges. Different from the standard gradient based optimization technique to find the optimal coverage problem in literature, new control methodology is needed to compute the gradient of non-smooth cost function and ensure the convergence. In this approach, the boundaries of sensing range are approximated by smooth sigmoid functions, leading to an approximation of the coverage cost function. With this approximation, an innovative non-smooth gradient-based coverage controller is designed for mobile sensors with nonlinear unicycle dynamics. Our work shows that once the initial state of sensors is within the set where the gradient of the approximated cost function is well-defined, the state of sensors will stay in this set and will converge to an invariant set, which contains all critical points (or optimal solutions) of the coverage problem. Simulation results verify the effectiveness of the proposed coverage control approach.