Optimal path planning for uncertain exploration

Exploration always occurs in the presence of uncertainty. In this paper, we consider path planning for autonomous vehicles equipped with range-based sensors and traveling in an uncertain area. The mission of the vehicles is to explore a set of objects of interest while reducing uncertainty in object position, visibility and state. A connection is shown between the Kalman filter (used to reduce uncertainty) and the so-called Shannon model for exploration through the use of a range-based covariance. This connection is exploited to estimate states and to travel between objects of interest. A bound on the covariance error and several illustrative examples are provided.