  Efficient robotic exploration of unknown, sensor limited,
global-information-deficient environments poses unique challenges to path
planning algorithms. In these difficult environments, no deterministic
guarantees on path completion and mission success can be made in general.
Integrated Exploration (IE), which strives to combine localization and
exploration, must be solved in order to create an autonomous robotic system
capable of long term operation in new and challenging environments. This paper
formulates a probabilistic framework which allows the creation of exploration
algorithms providing probabilistic guarantees of success. A novel connection is
made between the Hamiltonian Path Problem and exploration. The Guaranteed
Probabilistic Information Explorer (G-PIE) is developed for the IE problem,
providing a probabilistic guarantee on path completion, and asymptotic
optimality of exploration. A receding horizon formulation, dubbed RH-PIE, is
presented which addresses the exponential complexity present in G-PIE. Finally,
RH-PIE planner is verified via autonomous, hardware-in-the-loop experiments.
