A variational approach to trajectory planning for persistent monitoring of spatiotemporal fields

This paper considers the problem of planning a trajectory for a sensing robot to best estimate a time-changing scalar field in its environment. We model the field as a linear combination of basis functions with time-varying weights. The robot uses a Kalman-like filter to maintain an estimate of the field, and to compute the error covariance of the estimate. The goal is to find a trajectory for the sensing robot that minimizes a cost metric on the error covariance and the control effort expended by the robot. Pontryagin´s Minimum Principle is used to find a set of differential equations that must be satisfied by the optimal trajectory. A numerical solver is used to find a trajectory satisfying these equations to give persistent monitoring trajectories.