%0 Journal Article %T Sampling %A Gamini Dissanayake %A Jaime Valls Miro %A Maani Ghaffari Jadidi %J The International Journal of Robotics Research %@ 1741-3176 %D 2019 %R 10.1177/0278364919844575 %X 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 the 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 %K Motion and path planning %K planning under uncertainty %K belief space planning %K field robotics %K robotic information gathering %K environmental monitoring %K robotic exploration %K Gaussian processes %K mutual information %U https://journals.sagepub.com/doi/full/10.1177/0278364919844575