Routing problems such as Hamiltonian Path Problem (HPP), seeks a path to visit all the vertices in a graph while minimizing the path cost. This paper studies a variant, HPP with Probabilistic Terminals (HPP-PT), where each vertex has a probability representing the likelihood that the robot's path terminates there, and the objective is to minimize the expected path cost. HPP-PT arises in target object search, where a mobile robot must visit all candidate locations to find an object, and prior knowledge of the object's location is expressed as vertex probabilities. While routing problems have been studied for decades, few of them consider uncertainty as required in this work. The challenge lies not only in optimally ordering the vertices, as in standard HPP, but also in handling history dependency: the expected path cost depends on the order in which vertices were previously visited. This makes many existing methods inefficient or inapplicable. To address the challenge, we propose a search-based approach RPT* with solution optimality guarantees, which leverages dynamic programming in a new state space to bypass the history dependency and novel heuristics to speed up the computation. Building on RPT*, we design a Hierarchical Autonomous Target Search (HATS) system that combines RPT* with either Bayesian filtering for lifelong target search with noisy sensors, or autonomous exploration to find targets in unknown environments. Experiments in both simulation and real robot show that our approach can naturally balance between exploitation and exploration, thereby finding targets more quickly on average than baseline methods.

翻译：路由问题如哈密顿路径问题（HPP）旨在寻找访问图中所有顶点且最小化路径成本的路径。本文研究其变体——带概率终端的哈密顿路径问题（HPP-PT），其中每个顶点具有一个概率，表示机器人路径在该处终止的可能性，目标是最小化期望路径成本。HPP-PT 产生于目标物体搜索场景，移动机器人需遍历所有候选位置以寻找物体，而关于物体位置的先验知识以顶点概率形式表达。尽管路由问题已被研究数十年，但少有工作考虑如本文所需的不确定性。其挑战不仅在于如标准 HPP 般优化顶点访问顺序，还在于处理历史依赖性：期望路径成本取决于先前访问顶点的顺序。这使得许多现有方法效率低下或不适用。为应对这一挑战，我们提出一种基于搜索的方法 RPT*，该方法具有解的最优性保证，通过在新状态空间中利用动态规划规避历史依赖性，并采用新颖启发式策略加速计算。基于 RPT*，我们设计了分层自主目标搜索系统，该系统将 RPT* 与贝叶斯滤波（用于带噪声传感器的终身目标搜索）或自主探索（用于未知环境中的目标搜寻）相结合。仿真与真实机器人实验表明，我们的方法能自然平衡利用与探索，从而在平均意义上比基线方法更快地找到目标。