  We propose a path planning methodology for a mobile robot navigating through
an obstacle-filled environment to generate a reference path that is traceable
with moderate sensing efforts. The desired reference path is characterized as
the shortest path in an obstacle-filled Gaussian belief manifold equipped with
a novel information-geometric distance function. The distance function we
introduce is shown to be an asymmetric quasi-pseudometric and can be
interpreted as the minimum information gain required to steer the Gaussian
belief. An RRT*-based numerical solution algorithm is presented to solve the
formulated shortest-path problem. To gain insight into the asymptotic
optimality of the proposed algorithm, we show that the considered path length
function is continuous with respect to the topology of total variation.
Simulation results demonstrate that the proposed method is effective in various
robot navigation scenarios to reduce sensing costs, such as the required
frequency of sensor measurements and the number of sensors that must be
operated simultaneously.
