Optimal sequential inspection

In this paper, we consider a problem of sequential resource allocation. Such a problem arises in a simplified Intelligence, Surveillance and Reconnaissance (ISR) scenario where a Micro Air Vehicle (MAV) is tasked with search and classification in an environment with false targets. The MAV visits the objects of interest in a specified sequence for classification. A human operator aids classification of objects based on the images sent to him from the MAV and the operator may request that the object be revisited if he requires further information. Such a request is made at most once by the operator for each object. The information gained by the operator when any object is revisited is the same. There is a random delay in communicating his findings to the MAV and the probability density function of the delay is assumed known. The MAV has a finite fuel reserve and upon receiving the feedback from the operator, it must decide whether to revisit the object or whether to continue to the next object in the sequence. In every revisit, fuel is expended from the reserve and equals twice the delay plus a fixed fuel cost. The objective is to maximize the number of revisits so as to maximize the information gained about the objects, which enables them to be classified as targets or false targets. Using Stochastic Dynamic Programming, we show that there is a threshold delay for each object and it is optimal to revisit the object if the operator delay is smaller than the threshold and not to revisit otherwise.