Active Mapping via Gradient Ascent Optimization of Shannon Mutual Information over Continuous SE(3) Trajectories

TL;DR

This paper introduces a differentiable approximation of Shannon mutual information for active mapping, enabling gradient ascent optimization over continuous SE(3) trajectories to improve sensing strategies in 2D and 3D environments.

Contribution

It presents a novel differentiable formulation of mutual information that allows continuous optimization of sensor trajectories, overcoming non-differentiability issues of traditional ray-tracing methods.

Findings

More informative sensing trajectories generated

Avoids occlusions and collisions effectively

Validated in simulated and real-world experiments

Abstract

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.