On trajectory optimization for active sensing in Gaussian process models

We consider the problem of optimizing the trajectory of a mobile sensor with perfect localization whose task is to estimate a stochastic, perhaps multidimensional field modeling the environment. When the estimator is the Kalman filter, and for certain classes of objective functions capturing the informativeness of the sensor paths, the sensor trajectory optimization problem is a deterministic optimal control problem. This estimation problem arises in many applications besides the field estimation problem, such as active mapping with mobile robots. The main difficulties in solving this problem are computational, since the Gaussian process of interest is usually high dimensional. We review some recent work on this problem and propose a suboptimal non-greedy trajectory optimization scheme with a manageable computational cost, at least in static field models based on sparse graphical models.