Planning periodic persistent monitoring trajectories for sensing robots in Gaussian Random Fields

This paper considers the problem of planning a trajectory for a sensing robot to best estimate a time-changing Gaussian Random Field in its environment. The robot uses a Kalman filter to maintain an estimate of the field value, and to compute the error covariance matrix of the estimate. A new randomized path planning algorithm is proposed to find a periodic trajectory for the sensing robot that tries to minimize the largest eigenvalue of the error covariance matrix over an infinite horizon. The algorithm is proven to find the minimum infinite horizon cost cycle in a graph, which grows by successively adding random points. The algorithm leverages recently developed methods for periodic Riccati recursions to efficiently compute the infinite horizon cost of the cycles, and it uses the monotonicity property of the Riccati recursion to efficiently compare the cost of different cycles without explicitly computing their costs. The performance of the algorithm is demonstrated in numerical simulations.