  The problem of active mapping aims to plan an informative sequence of sensing
views given a limited budget such as distance traveled. This paper consider
active occupancy grid mapping using a range sensor, such as LiDAR or depth
camera. State-of-the-art methods optimize information-theoretic measures
relating the occupancy grid probabilities with the range sensor measurements.
The non-smooth nature of ray-tracing within a grid representation makes the
objective function non-differentiable, forcing existing methods to search over
a discrete space of candidate trajectories. This work proposes a differentiable
approximation of the Shannon mutual information between a grid map and
ray-based observations that enables gradient ascent optimization in the
continuous space of SE(3) sensor poses. Our gradient-based formulation leads to
more informative sensing trajectories, while avoiding occlusions and
collisions. The proposed method is demonstrated in simulated and real-world
experiments in 2-D and 3-D environments.
