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

arXiv: https://arxiv.org/abs/2204.07623 · HTML: https://mlsanity.com/paper/2204.07623/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Apr 2022.

## Built on by (most cited first, 3 of 3)

- [Deep Reinforcement Learning-based Large-scale Robot Exploration](https://mlsanity.com/paper/2403.10833/) (2024)
- [Policy Learning for Active Target Tracking over Continuous SE(3) Trajectories](https://mlsanity.com/paper/2212.01498/) (2022)
- [HEADER: Hierarchical Robot Exploration via Attention-Based Deep Reinforcement Learning with Expert-Guided Reward](https://mlsanity.com/paper/2510.15679/) (2025)

## Abstract (arXiv)

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.