Planning Persistent Monitoring Trajectories in Spatiotemporal Fields using Kinodynamic RRT*

This paper proposes a sampling based kinodynamic planning technique for planning persistent monitoring trajectories for a sensing robot in a spatiotemporal environmental field. The robot uses a Kalman-Bucy filter to estimate the spatiotemporal field. Since the error covariance matrix of the Kalman-Bucy filter evolves according to the nonlinear Riccati differential equation, this requires planning a trajectory under a difficult differential constraint. The paper adapts kinodynamic RRT* to deal with this differential constraint. By properly choosing the state space, the sampling space, the stopping criterion, and a approximate procedure for the optimal steering of RRT*, the proposed algorithm finds trajectory for the robot that tries to minimize a metric on the error covariance matrix of the field estimate. Numerical simulations and experimental trials with an m3pi robot demonstrate the effectiveness of the algorithm.