  We provide the first step toward developing a hierarchical control-estimation
framework to actively plan robot trajectories for anomaly detection in confined
spaces. The space is represented globally using a directed region graph, where
a region is a landmark that needs to be visited (inspected). We devise a fast
mixing Markov chain to find an ergodic route that traverses this graph so that
the region visitation frequency is proportional to its anomaly detection
uncertainty, while satisfying the edge directionality (region transition)
constraint(s). Preliminary simulation results show fast convergence to the
ergodic solution and confident estimation of the presence of anomalies in the
inspected regions.
