Simultaneous localization and mapping (SLAM) is a foundational state estimation problem in robotics in which a robot accurately constructs a map of its environment while also localizing itself within this construction. We study the active SLAM problem through the lens of optimal stochastic control, thereby recasting it as a decision-making problem under partial information. After reviewing several commonly studied models, we present a general stochastic control formulation of active SLAM together with a rigorous treatment of motion, sensing, and map representation. We introduce a new exploration stage cost that encodes the geometry of the state when evaluating information-gathering actions. This formulation, constructed as a nonstandard partially observable Markov decision process (POMDP), is then analyzed to derive rigorously justified approximate solutions that are near-optimal. To enable this analysis, the associated regularity conditions are studied under general assumptions that apply to a wide range of robotics applications. For a particular case, we conduct an extensive numerical study in which standard learning algorithms are used to learn near-optimal policies.

翻译：同时定位与地图构建（SLAM）是机器人领域的一项基础状态估计问题，机器人需在精确构建环境地图的同时，在该构建中实现自身定位。我们从最优随机控制的视角研究主动SLAM问题，从而将其重新表述为一个部分信息下的决策问题。在回顾若干常见模型后，我们提出一种主动SLAM的通用随机控制公式，并对运动、感知与地图表示进行严格处理。我们引入一种新的探索阶段代价函数，该函数在评估信息采集动作时编码了状态的几何结构。这一公式被构建为非标准的部分可观测马尔可夫决策过程（POMDP），随后通过分析得出严格证明的近似解，这些解接近最优。为便于分析，我们在适用于广泛机器人应用的通用假设下研究了相关的正则性条件。针对特定案例，我们进行了大量数值研究，使用标准学习算法来学习接近最优的策略。