Constrained decision-making for low-count radiation detection by mobile sensors

This paper approaches from an optimal control perspective the problem of fixed-time detection of mobile radioactive sources in transit by means of a collection of mobile sensors. Under simplifying assumptions on the motion and geometry of the source, the sensors, and the surrounding environment, the optimal control problem admits an intuitive, analytic closedform solution. This solution is obtained thanks to analytic expressions for bounds on the probabilities of detection and false alarm for a Neyman-Pearson detection test. The intuition derived from this analytic solution supports the development of a motion control law that steers (suboptimally) the sensors to a given neighborhood of the suspected source, while navigating among stationary obstacles in their environment. This motion controller closes the loop at the acceleration level of a heterogeneous collection of sensor platforms. Experimental studies with these platforms corroborate the theoretical convergence results.