Robotic exploration in large-scale environments is computationally demanding due to the high overhead of processing extensive frontiers. This article presents an OctoMap-based frontier exploration algorithm with predictable, asymptotically bounded performance. Unlike conventional methods whose complexity scales with environment size, our approach maintains a complexity of $\mathcal{O}(|\mathcal{F}|)$, where $|\mathcal{F}|$ is the number of frontiers. This is achieved through strategic forward and inverse sensor modeling, which enables approximate yet efficient frontier detection and maintenance. To further enhance performance, we integrate a Bayesian regressor to estimate information gain, circumventing the need to explicitly count unknown voxels when prioritizing viewpoints. Simulations show the proposed method is more computationally efficient than the existing OctoMap-based methods and achieves computational efficiency comparable to baselines that are independent of OctoMap. Specifically, the Bayesian-enhanced framework achieves up to a $54\%$ improvement in total exploration time compared to standard deterministic frontier-based baselines across varying spatial scales, while guaranteeing task completion. Real-world experiments confirm the computational bounds as well as the effectiveness of the proposed enhancement.

翻译：大规模环境中的机器人探索因处理大量前沿区域的高计算开销而具有挑战性。本文提出一种基于OctoMap的前沿探索算法，具有可预测的渐近有界性能。与复杂度随环境规模扩展的传统方法不同，本方法维持$\mathcal{O}(|\mathcal{F}|)$的复杂度，其中$|\mathcal{F}|$表示前沿区域的数量。这一特性通过战略性的正向和逆向传感器建模实现，能够以近似方式高效检测和维护前沿区域。为提升性能，我们集成贝叶斯回归器估计信息增益，从而避免在视点优先级排序时显式计数未知体素。仿真表明，所提方法比现有基于OctoMap的方法计算效率更高，且与不依赖OctoMap的基线方法计算效率相当。具体而言，贝叶斯增强框架在不同空间尺度下，相比标准确定性前沿基线方法最高可提升$54\%$的总探索时间，同时保证任务完成度。实际实验验证了计算边界和所提增强方法的有效性。