  We consider a path-planning scenario for a mobile robot traveling in a
configuration space with obstacles under the presence of stochastic
disturbances. A novel path length metric is proposed on the uncertain
configuration space and then integrated with the existing RRT* algorithm. The
metric is a weighted sum of two terms which capture both the Euclidean distance
traveled by the robot and the perception cost, i.e., the amount of information
the robot must perceive about the environment to follow the path safely. The
continuity of the path length function with respect to the topology of the
total variation metric is shown and the optimality of the Rationally
Inattentive RRT* algorithm is discussed. Three numerical studies are presented
which display the utility of the new algorithm.
