Aided optimal search: Data-driven target pursuit from on-demand delayed binary observations

We consider the following search problem: an autonomous robot (the searcher) needs to locate and reach a target moving in a field scattered with Unattended Ground Sensors (UGS). The searcher has very limited information about the target: (i) it has an initial distribution (the prior) describing the probability of the target being at a given location at the initial time, and (ii) it can interrogate nearby sensors; each sensor records a binary measurement, describing whether or not the target passed in the proximity of the sensor at some point in time. Then the goal for the searcher is to estimate the trajectory of the target, and plan a maneuver that allows reducing the uncertainty about the current target state. We refer to this problem as aided optimal search, in that the search process is aided by an external infrastructure (the ground sensors). The paper adopts a Dynamic Data-Driven Appplications Systems (DDDAS) paradigm, in which the data collected by the searcher is used to update the belief on the trajectory of the target, and the searcher actively steers the measurement process to improve its knowledge about the location of the target. In particular, we make two main contributions. The first regards the target trajectory estimation. We show how to perform optimal Bayesian inference from binary measurements using a Gaussian Mixture Model (GMM). One of the main insights is that parameterizing the GMM in the information filter (inverse covariance) form allows huge computational savings: the information matrix of each mixture component is a very sparse (block-tridiagonal) matrix, which allows us to deal with a GMM with thousands of components in a fraction of a second. The second contribution regards planning: we propose a Mixed-Integer Programming (MIP) approach to plan the optimal searcher path, which minimizes the uncertainty about the position of the target. The key idea here is the use of sampling to decouple the complexity of the MIP from the length of the trajectory of the target. We demonstrate the proposed strategy in extensive simulations, reporting statistics about success rate and computational time for different scenarios and target motion models. The proposed search strategy largely outperforms greedy strategies (e.g., visiting the most likely target position).