Sampling-based incremental information gathering with applications to robotic exploration and environmental monitoring

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.