  In this article, we propose a sampling-based motion planning algorithm
equipped with an information-theoretic convergence criterion for incremental
informative motion planning. The proposed approach allows dense map
representations and incorporates the full state uncertainty into the planning
process. The problem is formulated as a constrained maximization problem. Our
approach is built on rapidly-exploring information gathering algorithms and
benefits from advantages of sampling-based optimal motion planning algorithms.
We propose two information functions and their variants for fast and online
computations. We prove an information-theoretic convergence for an entire
exploration and information gathering mission based on the least upper bound of
the average map entropy. A natural automatic stopping criterion for
information-driven motion control results from the convergence analysis. We
demonstrate the performance of the proposed algorithms using three scenarios:
comparison of the proposed information functions and sensor configuration
selection, robotic exploration in unknown environments, and a wireless signal
strength monitoring task in a lake from a publicly available dataset collected
using an autonomous surface vehicle.
