  At the heart of path-planning methods for autonomous robotic exploration is a
heuristic which encourages exploring unknown regions of the environment. Such
heuristics are typically computed using frontier-based or information-theoretic
methods. Frontier-based methods define the information gain of an exploration
path as the number of boundary cells, or frontiers, which are visible from the
path. However, the discrete and non-differentiable nature of this measure of
information gain makes it difficult to optimize using gradient-based methods.
In contrast, information-theoretic methods define information gain as the
mutual information between the sensor's measurements and the explored map.
However, computation of the gradient of mutual information involves finite
differencing and is thus computationally expensive. This work proposes an
exploration planning framework that combines sampling-based path planning and
gradient-based path optimization. The main contribution of this framework is a
novel reformulation of information gain as a differentiable function. This
allows us to simultaneously optimize information gain with other differentiable
quality measures, such as smoothness. The proposed planning framework's
effectiveness is verified both in simulation and in hardware experiments using
a Turtlebot3 Burger robot.
