# Riemannian Optimization for Active Mapping with Robot Teams

arXiv: https://arxiv.org/abs/2404.18321 · HTML: https://mlsanity.com/paper/2404.18321/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Apr 2024.

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

- [An Overview of the Burer-Monteiro Method for Certifiable Robot Perception](https://mlsanity.com/paper/2410.00117/) (2024)
- [Scalable Multi-Robot Informative Path Planning for Target Mapping via Deep Reinforcement Learning](https://mlsanity.com/paper/2409.16967/) (2024)
- [Decentralized Online Riemannian Optimization for Strongly Geodesically Convex Functions](https://mlsanity.com/paper/2607.20316/) (2026)

## Abstract (arXiv)

Autonomous exploration of unknown environments using a team of mobile robots demands distributed perception and planning strategies to enable efficient and scalable performance. Ideally, each robot should update its map and plan its motion not only relying on its own observations, but also considering the observations of its peers. Centralized solutions to multi-robot coordination are susceptible to central node failure and require a sophisticated communication infrastructure for reliable operation. Current decentralized active mapping methods consider simplistic robot models with linear-Gaussian observations and Euclidean robot states. In this work, we present a distributed multi-robot mapping and planning method, called Riemannian Optimization for Active Mapping (ROAM). We formulate an optimization problem over a graph with node variables belonging to a Riemannian manifold and a consensus constraint requiring feasible solutions to agree on the node variables. We develop a distributed Riemannian optimization algorithm that relies only on one-hop communication to solve the problem with consensus and optimality guarantees. We show that multi-robot active mapping can be achieved via two applications of our distributed Riemannian optimization over different manifolds: distributed estimation of a 3-D semantic map and distributed planning of SE(3) trajectories that minimize map uncertainty. We demonstrate the performance of ROAM in simulation and real-world experiments using a team of robots with RGB-D cameras.