Periodic sensing trajectory generation for persistent monitoring

This paper presents periodic trajectory optimization method for a mobile sensor performing persistent monitoring to maintain the uncertainty in the environment at the minimum. The uncertain environment is represented by a set of deterministic spatial basis function with the stochastic temporal dynamic coefficients. An optimal control problem is formulated to determine the optimal periodic trajectory of the sensor and the uncertainty state as well as the initial condition and the period. The path induces the periodic Riccati equation and is proven to lead an arbitrary initial uncertainty state to the optimized periodic trajectory. It is also shown that the resulting optimal periodic solution can be used to develop a subopitmal filtering mechanism for the mobile sensor. A simple synthetic example is presented for preliminary demonstration the validity of the proposed methodology, producing physically meaningful sensing trajectories.