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 closed-form 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.