Random disambiguation paths for traversing a mapped hazard field

We consider the problem of safely and swiftly navigating through a spatial arrangement of potential hazard detections in which each detection has associated with it a probability that the detection is indeed a true hazard. When in close proximity to a detection, we assume the ability – for a cost – to determine whether or not the hazard is real. Our approach to this problem involves a new object, the random disambiguation path (RDP), which is a curve-valued random variable parametrized by a binary tree with particular properties. We prove an admissibility result showing that there is positive probability that the use of an RDP reduces the expected traversal length compared to the conventional shortest zero-risk path, and we introduce a practically computable additive-constant approximation to the optimal RDP. The theoretical considerations are complemented by simulation and example.