Planning under uncertainty is critical to robotics. The Partially Observable Markov Decision Process (POMDP) is a mathematical framework for such planning problems. It is powerful due to its careful quantification of the non-deterministic effects of actions and partial observability of the states. But precisely because of this, POMDP is notorious for its high computational complexity and deemed impractical for robotics. However, since early 2000, POMDPs solving capabilities have advanced tremendously, thanks to sampling-based approximate solvers. Although these solvers do not generate the optimal solution, they can compute good POMDP solutions that significantly improve the robustness of robotics systems within reasonable computational resources, thereby making POMDPs practical for many realistic robotics problems. This paper presents a review of POMDPs, emphasizing computational issues that have hindered its practicality in robotics and ideas in sampling-based solvers that have alleviated such difficulties, together with lessons learned from applying POMDPs to physical robots.

翻译：部分可观察的Markov 决策程序(POMDP)是解决此类规划问题的数学框架。它之所以强大,是因为它仔细量化了行动的非决定性影响和各州部分可观察性。但正因为如此,POMDP因其计算复杂性高而臭名昭著,而且被认为对机器人来说不切实际。然而,自2000年初以来,由于基于抽样的近似解决方案,POMDP解决能力取得了巨大进步。虽然这些解决方案没有产生最佳解决方案,但它们可以计算出良好的POMDP解决方案,大大改善机器人系统在合理计算资源范围内的稳健性,从而使POMDP对许多现实机器人问题具有实用性。本文回顾了POMDP,强调了妨碍其在机器人中的实用性和减轻此类困难的基于取样的解决方案中的想法的计算问题,以及从将POMDP应用于物理机器人中汲取的教训。