  In this work, we consider the problem of autonomous exploration in search of
targets while respecting a fixed energy budget. The robot is equipped with an
incremental-resolution symbolic perception module wherein the perception of
targets in the environment improves as the robot's distance from targets
decreases. We assume no prior information about the total number of targets,
their locations as well as their possible distribution within the environment.
This work proposes a novel decision-making framework for the resulting
constrained sequential decision-making problem by first converting it into a
reward maximization problem on a product graph computed offline. It is then
solved online as a Mixed-Integer Linear Program (MILP) where the knowledge
about the environment is updated at each step, combining automata-based and
MILP-based techniques. We demonstrate the efficacy of our approach with the
help of a case study and present empirical evaluation in terms of expected
regret. Furthermore, the runtime performance shows that online planning can be
efficiently performed for moderately-sized grid environments.
