Reformulating Kalman Filter Based Optimal Dynamic Coverage Control

Abstract

Our objective in this paper is to examine the problem formulation of one particular published result, make logical extensions, and consider the question of whether we should obtain solutions under such a formulation, or pursue alternative formulations. The problem considered in “A Kalman Filter-Based Control Strategy for Dynamic Coverage Control” by I. I. Hussein is for a network of mobile sensors with limited range to traverse and estimate a spatially-decoupled scalar field. In that paper the optimal trajectories are generated by an online procedure that minimizes the trace of the instantaneous covariance of the estimation error obtained from Kalman Filtering, using a finite set of admissible control inputs. We extend the formulation by observing that the procedure can be performed offline, that the cost function can be defined over a finite horizon, and that the set of control inputs can be a continuum. We illustrate, with simple examples, the kind of solutions that can be obtained using dynamic programming, and ask the question “Is this the type of trajectories that we want?” Alternative formulations are suggested and are left for future work.