GVD-TG: Topological Graph based on Fast Hierarchical GVD Sampling for Robot Exploration

TL;DR

The paper tackles real-time autonomous exploration by leveraging topological maps built from Generalized Voronoi Diagrams (GVD). It introduces a hierarchical GVD sampling framework augmented with a coverage map to balance global efficiency and local detail, alongside denoising to reduce spurious nodes. A connectivity-constrained mean shift clustering with KD-tree acceleration and a double-layer switch mechanism ensures reachable topological nodes and robust map connectivity, while morphology-based frontier detection and a lightweight cost function enable real-time viewpoint selection. Experimental results in simulation and real-world tests show complete exploration success with substantial reductions in exploration time and minimal backtracking, validating the method's practicality in unknown, obstacle-rich environments.

Abstract

Topological maps are more suitable than metric maps for robotic exploration tasks. However, real-time updating of accurate and detail-rich environmental topological maps remains a challenge. This paper presents a topological map updating method based on the Generalized Voronoi Diagram (GVD). First, the newly observed areas are denoised to avoid low-efficiency GVD nodes misleading the topological structure. Subsequently, a multi-granularity hierarchical GVD generation method is designed to control the sampling granularity at both global and local levels. This not only ensures the accuracy of the topological structure but also enhances the ability to capture detail features, reduces the probability of path backtracking, and ensures no overlap between GVDs through the maintenance of a coverage map, thereby improving GVD utilization efficiency. Second, a node clustering method with connectivity constraints and a connectivity method based on a switching mechanism are designed to avoid the generation of unreachable nodes and erroneous nodes caused by obstacle attraction. A special cache structure is used to store all connectivity information, thereby improving exploration efficiency. Finally, to address the issue of frontiers misjudgment caused by obstacles within the scope of GVD units, a frontiers extraction method based on morphological dilation is designed to effectively ensure the reachability of frontiers. On this basis, a lightweight cost function is used to assess and switch to the next viewpoint in real time. This allows the robot to quickly adjust its strategy when signs of path backtracking appear, thereby escaping the predicament and increasing exploration flexibility. And the performance of system for exploration task is verified through comparative tests with SOTA methods.

Figures (16)

• Figure 1: To balance the detail of grid maps and the efficiency of topological maps, we propose an exploration framework based on dynamic hierarchical GVD, which avoids path backtracking and improves exploration efficiency by maintaining accurate topological details in real time.
• Figure 2: Pipeline.
• Figure 3: In case 1, LiDAR beams passing through narrow structures create isolated free regions (yellow) separated by large unknown areas (gray). In case 2, limited scanning frequency causes gaps between consecutive frames to be misclassified as unknown space. Both cases produce undersized GVD cells that reduce feature extraction efficiency. With map denoising, fewer GVD nodes are needed to capture environmental topology, significantly improving task performance.
• Figure 4: (a) and (b) illustrate how the sampling density of conventional Voronoi diagrams affects the partitioning of functional regions, while (c) is the regional division effect under high-density GVD sampling. In contrast, (d) shows that our hierarchical sampling strategy achieves broader area coverage with significantly fewer GVD nodes, thereby improving topological accuracy while minimizing computational time.
• Figure 5: Mean shift based on connectivity constraints. In case 1 and case 2, the red dots are topological nodes and the gray dots are GVD nodes. The correct situation should be that the GVD nodes in each color area are clustered into one topological node. Error situation in case1 using traditional mean shift: The topological node generated by the clustering of two GVD nodes is generated on an obstacle. Error situation in case2 using traditional mean shift: The original correct topological nodes in the GVD areas of yellow and skin color were attracted to the pink area by crossing boundaries.