Ergodic exploration has spawned a lot of interest in mobile robotics due to its ability to design time trajectories that match desired spatial coverage statistics. However, current ergodic approaches are for continuous spaces, which require detailed sensory information at each point and can lead to fractal-like trajectories that cannot be tracked easily. This paper presents a new ergodic approach for graph-based discretization of continuous spaces. It also introduces a new time-discounted ergodicity metric, wherein early visitations of information-rich nodes are weighted more than late visitations. A Markov chain synthesized using a convex program is shown to converge more rapidly to time-discounted ergodicity than the traditional fastest mixing Markov chain. The resultant ergodic traversal method is used within a hierarchical framework for active inspection of confined spaces with the goal of detecting anomalies robustly using SLAM-driven Bayesian hypothesis testing. Both simulation and physical experiments on a ground robot show the advantages of this framework over greedy and random exploration methods for left-behind foreign object debris detection in a ballast tank.

翻译：遍历性探索因其能够设计出与期望空间覆盖统计相匹配的时间轨迹，在移动机器人领域引起了广泛关注。然而，现有的遍历性方法主要针对连续空间，这类方法需要在每个点获取详细的传感信息，且可能产生难以跟踪的分形轨迹。本文提出了一种新的遍历性方法，用于连续空间的图基离散化。同时引入了一种新的时间折扣遍历性度量，其中对信息丰富节点的早期访问赋予比晚期访问更高的权重。通过凸规划合成的马尔可夫链被证明比传统的最快混合马尔可夫链能更快地收敛到时间折扣遍历性。所得到的遍历性遍历方法被用于分层框架中，以实现对受限空间的主动巡检，其目标是通过SLAM驱动的贝叶斯假设检验鲁棒地检测异常。在压载舱遗留异物碎片检测的仿真和地面机器人物理实验中，该框架相较于贪婪探索和随机探索方法均展现出显著优势。