  This paper considers the problem of safely coordinating a team of
sensor-equipped robots to reduce uncertainty about a dynamical process, where
the objective trades off information gain and energy cost. Optimizing this
trade-off is desirable, but leads to a non-monotone objective function in the
set of robot trajectories. Therefore, common multi-robot planners based on
coordinate descent lose their performance guarantees. Furthermore, methods that
handle non-monotonicity lose their performance guarantees when subject to
inter-robot collision avoidance constraints. As it is desirable to retain both
the performance guarantee and safety guarantee, this work proposes a
hierarchical approach with a distributed planner that uses local search with a
worst-case performance guarantees and a decentralized controller based on
control barrier functions that ensures safety and encourages timely arrival at
sensing locations. Via extensive simulations, hardware-in-the-loop tests and
hardware experiments, we demonstrate that the proposed approach achieves a
better trade-off between sensing and energy cost than coordinate-descent-based
algorithms.
