  This paper develops \emph{iterative Covariance Regulation} (iCR), a novel
method for active exploration and mapping for a mobile robot equipped with
on-board sensors. The problem is posed as optimal control over the $SE(3)$ pose
kinematics of the robot to minimize the differential entropy of the map
conditioned the potential sensor observations. We introduce a differentiable
field of view formulation, and derive iCR via the gradient descent method to
iteratively update an open-loop control sequence in continuous space so that
the covariance of the map estimate is minimized. We demonstrate autonomous
exploration and uncertainty reduction in simulated occupancy grid environments.
