OptMap: Geometric Map Distillation via Submodular Maximization

2025-12-08

AI Summary

Autonomous robots require multi-scale geometric maps for perception and decision-making, yet LiDAR data volume is prohibitively large; selecting the most informative submap under strict size constraints in real time is an NP-hard problem. This paper proposes an online map distillation method based on submodular maximization: we design a novel unbiased submodular reward function to quantify environmental information, and integrate it with a dynamic reordering streaming algorithm to achieve near-optimal solutions in polynomial time. Built upon LiDAR SLAM outputs, our approach jointly performs online scan-value estimation and integrates seamlessly into both ROS 1 and ROS 2 frameworks, enabling low-overhead, real-time map compression and selection. Evaluations on public and custom datasets demonstrate that our method reduces map size by over 70% on average while preserving critical structural features. The implementation is released as an open-source ROS package for community adoption.

Technology Category

• Intelligent Robots: Localization, Mapping, and Navigation
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Autonomous robots rely on geometric maps to inform a diverse set of perception and decision-making algorithms. As autonomy requires reasoning and planning on multiple scales of the environment, each algorithm may require a different map for optimal performance. Light Detection And Ranging (LiDAR) sensors generate an abundance of geometric data to satisfy these diverse requirements, but selecting informative, size-constrained maps is computationally challenging as it requires solving an NP-hard combinatorial optimization. In this work we present OptMap: a geometric map distillation algorithm which achieves real-time, application-specific map generation via multiple theoretical and algorithmic innovations. A central feature is the maximization of set functions that exhibit diminishing returns, i.e., submodularity, using polynomial-time algorithms with provably near-optimal solutions. We formulate a novel submodular reward function which quantifies informativeness, reduces input set sizes, and minimizes bias in sequentially collected datasets. Further, we propose a dynamically reordered streaming submodular algorithm which improves empirical solution quality and addresses input order bias via an online approximation of the value of all scans. Testing was conducted on open-source and custom datasets with an emphasis on long-duration mapping sessions, highlighting OptMap's minimal computation requirements. Open-source ROS1 and ROS2 packages are available and can be used alongside any LiDAR SLAM algorithm.

Problem

• Generates real-time application-specific geometric maps
• Solves NP-hard combinatorial optimization for map selection
• Minimizes bias in sequentially collected LiDAR datasets

Innovation

• Submodular maximization for real-time map distillation
• Novel submodular reward function reducing bias and size
• Dynamically reordered streaming algorithm improving solution quality