Variable-Resolution Virtual Maps for Autonomous Exploration with Unmanned Surface Vehicles (USVs)

Autonomous exploration by unmanned surface vehicles (USVs) in near-shore waters requires reliable localisation and consistent mapping over extended areas, but this is challenged by GNSS degradation, environment-induced localisation uncertainty, and limited on-board computation. Virtual map-based methods explicitly model localisation and mapping uncertainty by tightly coupling factor-graph SLAM with a map uncertainty criterion. However, their storage and computational costs scale poorly with fixed-resolution workspace discretisations, leading to inefficiency in large near-shore environments. Moreover, overvaluing feature-sparse open-water regions can increase the risk of SLAM failure as a result of imbalance between exploration and exploitation. To address these limitations, we propose a Variable-Resolution Virtual Map (VRVM), a computationally efficient method for representing map uncertainty using bivariate Gaussian virtual landmarks placed in the cells of an adaptive quadtree. The adaptive quadtree enables an area-weighted uncertainty representation that keeps coarse, far-field virtual landmarks deliberately uncertain while allocating higher resolution to information-dense regions, and reduces the sensitivity of the map valuation to local refinements of the tree. An expectation-maximisation (EM) planner is adopted to evaluate pose and map uncertainty along frontiers using the VRVM, balancing exploration and exploitation. We evaluate VRVM against several state-of-the-art exploration algorithms in the VRX Gazebo simulator, using a realistic marina environment across different testing scenarios with an increasing level of exploration difficulty. The results indicate that our method offers safer behaviour and better utilisation of on-board computation in GNSS-degraded near-shore environments.