A Sample-Based Approach for Hierarchical Information-Theoretic Compression of Probabilistic Occupancy Grids

Determining the occupancy status of locations in the environment is a fundamental task for safety-critical robotic applications. Traditional occupancy grid mapping methods subdivide the environment into a grid of voxels, each associated with one of three occupancy states: free, occupied, or unknown. These methods explicitly maintain all voxels within the mapped volume and determine the occupancy state of a location by directly querying the corresponding voxel that the location falls within. However, maintaining all grid voxels in high-resolution and large-scale scenarios requires substantial memory resources. In this paper, we introduce a novel representation that only maintains the boundary of the mapped volume. Specifically, we explicitly represent the boundary voxels, such as the occupied voxels and frontier voxels, while free and unknown voxels are automatically represented by volumes within or outside the boundary, respectively. As our representation maintains only a closed surface in two-dimensional (2D) space, instead of the entire volume in three-dimensional (3D) space, it significantly reduces memory consumption. Then, based on this 2D representation, we propose a method to determine the occupancy state of arbitrary locations in the 3D environment. We term this method as boundary map. Besides, we design a novel data structure for maintaining the boundary map, supporting efficient occupancy state queries. Theoretical analyses of the occupancy state query algorithm are also provided. Furthermore, to enable efficient construction and updates of the boundary map from the real-time sensor measurements, we propose a global-local mapping framework and corresponding update algorithms. Finally, we will make our implementation of the boundary map open-source on GitHub to benefit the community:https://github.com/hku-mars/BDM.

Hierarchical, multi-resolution volumetric mapping approaches are widely used to represent large and complex environments as they can efficiently capture their occupancy and connectivity information. Yet widely used path planning methods such as sampling and trajectory optimization do not exploit this explicit connectivity information, and search-based methods such as A* suffer from scalability issues in large-scale high-resolution maps. In many applications, Euclidean shortest paths form the underpinning of the navigation system. For such applications, any-angle planning methods, which find optimal paths by connecting corners of obstacles with straight-line segments, provide a simple and efficient solution. In this paper, we present a method that has the optimality and completeness properties of any-angle planners while overcoming computational tractability issues common to search-based methods by exploiting multi-resolution representations. Extensive experiments on real and synthetic environments demonstrate the proposed approach's solution quality and speed, outperforming even sampling-based methods. The framework is open-sourced to allow the robotics and planning community to build on our research.

We study performance-driven environment abstraction for decision-making in large Markov decision processes. Rather than preserving geometric or topological structure, we seek abstractions that directly optimize decision quality. We model abstraction as a controlled approximation obtained by aggregating the state space and enforcing a shared action distribution within each aggregated state. For a fixed partition, we establish a performance guarantee that separates value-function approximation error from the loss introduced by action sharing. Guided by this analysis, we develop a multi-timescale reinforcement learning framework that jointly adapts the policy and a tree-structured environment abstraction. The resulting algorithm refines and coarsens regions of the state space based on Q-value discrepancies, balancing performance against abstraction size and complexity. Empirical results demonstrate substantial state compression, improved sample efficiency, and faster replanning compared to actor-critic baselines.