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

Abstract

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.

Energetics in robotic flight at small scales

“…3 Consider for instance recent developments in LiDARs, which are critical for mapping, localization and autonomous navigation and obstacle avoidance. 4 More about energy-aware trajectory generation follows in §3. 5 A list of symbols used in this review is provided in appendix A.…”

“…Indeed, it is plausible that overactuation may actually help design more energy-efficient trajectories to be tracked by the vehicle in forward flight. 4…”

“…Some key examples include robotic first responders [1], aerial manipulation [2], cooperative construction [3], radiation detection [4] and intelligence, surveillance and reconnaissance. Bioinspired aerial robots [5,6] can help study the trade-offs in avian and insect flight.…”

Navigation Functions With Time-Varying Destination Manifolds in Star Worlds

“…Known heuristics are (re)introduced to tackle the time-varying nature of the workspace: virtual forces [38]-see [39], [40] for leader-following problems-which inevitably give rise to local minima [41], [42]; fuzzy logic [43], [44], or search-based methods [45], which come at the expense of completeness. Provably correct (local minima-free) potential fields have been constructed using fast marching methods [46] and sampling-computational complexity issues here persisting-and with navigation functions on sphere worlds only, for the case of a moving destination [47]. Local potential-based methods [48], [49] have also tackled cases of moving destinations, but without consideration to collision avoidance.…”

“…2) and star-to-sphere (Fig. 3b) transformations of the standard navigation function framework remain diffeomorphic when applied to the time-varying destination manifold case of [47], thereby extending the aforementioned approach to star worlds, including forests of stars. Time-varying destination functions in sphere worlds [47] are first reviewed in §II, and together with some necessary notation, the new obstacle representation approach is introduced.…”