This paper presents a control-theoretic approach for trajectory optimization of mobile robots suitable for environmental monitoring. The method is based on the optimization of the Constructability Gramian in order to maximize the information collected while traversing a state trajectory. The maximization of the collected information is combined with energy constraints to define an optimization-based controller that achieves persistent environmental monitoring. The results of its application to the estimation of the concentration of a diffusing gas using a mobile robot are shown in simulation.