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

Active Exploration and Mapping via Iterative Covariance Regulation over Continuous $SE(3)$ Trajectories