Dynamic Networked Coverage of Time-Varying Environments in the Presence of Fading Communication Channels

Abstract

In this paper, we study the problem of dynamic coverage of a set of points of interest (POIs) in a time-varying environment. We consider the scenario where a physical quantity is constantly growing at certain rates at the POIs. A number of mobile agents are then deployed to periodically cover (sense or service) the POIs and keep the physical quantity under control bounded at all the POIs. We assume a communication-constrained operation, where the mobile agents need to communicate to a fixed remote station over realistic wireless links to complete their coverage task. We then propose novel mixed-integer linear programs (MILPs) to design periodic trajectories and TX power policies for the mobile agents that minimize the total energy (the summation of motion and communication energy) consumption of the mobile agents in each period, while 1) guaranteeing the boundedness of the quantity of interest at all the POIs, and 2) meeting the constraints on the connectivity of the mobile agents, the frequency of covering the POIs, and the total energy budget of the mobile agents. We furthermore provide a probabilistic analysis of the problem. Our results show the superior performance of the proposed framework for dynamic coverage in realistic fading environments.

Sensor allocation with guaranteed exponential stability for linear multi-rate sampled-data systems

“…From the convex optimization literature (e.g., [16]) we know that the norm function is convex, the pointwise minimum of a set of linear functions is concave, and the subtraction of a concave function from a convex function is convex. Therefore, the inequalities in (14) are convex. 1520 M. MOARREF AND L. RODRIGUES…”

“…Consider the linear multi-rate sampled-data system defined in (1) and (9) under Assumptions 1 and 2. Given positive scalars˛andˇ, there exists a partition of the state vector among sensors, parametrized by a matrix L, that guarantees global uniform exponential stability with a decay rate greater than˛=2, if there exist positive-definite matrices P , R 0 , and X , symmetric matrices R i , i 2 I, and matrices N and N , with appropriate dimensions, satisfying conditions (4), (5), (14), and 2…”

“…According to (14), the entries of matrix variables R i , i 2 I, are bounded by an arbitrary positive scalarˇ. When solving Problem 1 in an optimization software, we assign the biggest acceptable number by the software toˇ.…”

“…Sensor allocation algorithms usually involve solving nonlinear mixed-integer problems. Although mixed-integer programs are NP-hard, there has been great effort in the literature to make sensor allocation algorithms more tractable and computationally attractive by eliminating any form of nonlinearity from the mixed-integer program (see [14] and the references therein).The main contributions of this paper are twofold. First, we propose sufficient Krasovskii-based conditions to partition the state vector among sensors, such that exponential stability of the multirate sampled-data system is guaranteed.…”

Path planning for cooperative routing of air-ground vehicles

“…Cooperative control and path planning for a team of vehicles (UAVs or UAVs together with ground vehicles) has been a problem of interest and has received wide attention during the past decade (see [4]- [10]). The problem of communication-constrained vehicle routing for a team of vehicles has been addressed in [11]- [14]. More specifically, authors in [11] study the problem of deploying a team of mobile agents to periodically monitor several points of interest.…”