Optimal Trajectories of Mobile Remote Sensors for Parameter Estimation in Distributed Cyber-Physical Systems

In this paper, we present a method to obtain the optimal trajectories of a team of robots monitoring a distributed parameter system located in a different domain. The mobile robots are equipped with remote sensors capable of measuring the considered system's state from a separate space. The purpose of trajectory planning of the team of robots is to obtain measurements so as to estimate the parameters of the considered system. From a given set of partial differential equation the dynamics of the distributed system's behavior, the optimal path and steering of the team of mobile nodes is obtained by minimizing the D-optimality criteria associated with the expected accuracy of the obtained parameter values. From this original problem, an optimal control problem is derived with the advantage of being solvable by readily available commercial softwares. The method is illustrated on a diffusive distributed systems.