Path Planning With Spatiotemporal Optimal Stopping for Stochastic Mission Monitoring

We consider an optimal stopping formulation of the mission monitoring problem, in which a monitor vehicle must remain in close proximity to an autonomous robot that stochastically follows a predicted trajectory. This problem arises in a diverse range of scenarios, such as autonomous underwater vehicles supervised by surface vessels, pedestrians monitored by aerial vehicles, and animals monitored by agricultural robots. The key problem characteristics we consider are that the monitor must remain stationary while observing the robot, robot motion is modeled in general as a stochastic process, and observations are modeled as a spatial probability distribution. We propose a resolution-complete algorithm that runs in a polynomial time. The algorithm is based on a sweep-plane approach and generates a motion plan that maximizes the expected observation time and value. A variety of stochastic models may be used to represent the robot trajectory. We present results with data drawn from real AUV missions, a real pedestrian trajectory dataset and Monte Carlo simulations. Our results demonstrate the performance and behavior of our algorithm, and relevance to a variety of applications.