OptMap: Geometric Map Distillation via Submodular Maximization

TL;DR

OptMap is an efficient algorithm for online geometric map distillation that uses submodular maximization to generate application-specific maps from LiDAR data, reducing computational costs.

Contribution

It introduces a novel submodular reward function and a streaming algorithm for real-time, application-specific map generation in autonomous robotics.

Findings

Achieves near-optimal map selection with polynomial-time algorithms.

Reduces input set sizes while maintaining informativeness.

Demonstrates minimal computation requirements in long-duration mapping.

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, each algorithm may require a different map for optimal performance. LiDAR sensors generate an abundance of geometric data (up to 50 MB per second) to satisfy these diverse requirements. However, the point-based operations required to process perception data are both memory and computationally expensive. Such operations can be bypassed via learned representations that encode similarity, but selecting informative, size-constrained maps remains an NP-hard combinatorial problem. In this work we present OptMap: a geometric map distillation algorithm which achieves online, 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 solution bias. 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. OptMap's practical value is then illustrated through its application to online geometric change detection. Open-source ROS1 and ROS2 packages are available and can be used alongside any LiDAR odometry algorithm.