OptMap: Geometric Map Distillation via Submodular Maximization

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 submod-ular algorithm which improves empirical solution quality and addresses input order bias via an online approximation of the value of all scans. T esting 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. ODERN autonomous systems use a modular software architecture with separate algorithms for perceiving the environment, planning collision-free paths, estimating vehicle motion, and making higher-level decisions to complete their tasks. Many of these algorithms depend on geometric information about the environment to function properly. As a result, their performance and processing time can vary greatly depending on the quality of the geometric data. For example, trajectory planners use geometric maps to plan collision-free paths, but the density of geometric data is critical for balancing real-time replanning requirements against reliable collision detection. This trade-off is best served by dense geometric maps that specifically capture the intended trajectory corridor (Figure 1a). In contrast, localization entails aligning a source and reference point cloud, a process best served by using a sparse and global reference point could to minimize computation time while maximizing alignment accuracy (Figure 1b). Distribution Statement A: Approved for public release; distribution is unlimited. Map is dense while remaining efficient as only points near the intended trajectory are returned.