A spatiotemporal optimal stopping problem for mission monitoring with stationary viewpoints

We consider an optimal stopping formulation of the mission monitoring problem, where a monitor vehicle must remain in close proximity to an autonomous robot that stochastically follows a pre-planned trajectory. This problem arises when autonomous underwater vehicles are monitored by surface vessels, and in a diverse range of other scenarios. The key problem characteristics we consider are that the monitor must remain stationary while observing the robot, and that the robot motion is modelled in general as a stochastic process. We propose a resolution-complete algorithm for this problem that runs in polynomial time. The algorithm is based on a sweepplane approach and generates a motion plan that maximises the expected observation time. A variety of stochastic models may be used to represent the expected robot trajectory. We present results drawn from real AUV trajectories and Monte Carlo simulations that validate the correctness of our algorithm and its feasibility in practice.