[Paper Review] Partially Observable Markov Decision Processes (POMDPs) and Robotics

Hanna Kurniawati|arXiv (Cornell University)|Jul 15, 2021

Reinforcement Learning in Robotics77 references4 citations

TL;DR

This paper reviews the application of Partially Observable Markov Decision Processes (POMDPs) in robotics, highlighting how sampling-based approximate solvers have overcome POMDPs' historical computational intractability. It demonstrates that these methods now enable robust, real-time decision-making in uncertain, partially observable environments—making POMDPs practical for complex robotics tasks such as navigation, manipulation, and human-robot collaboration.

ABSTRACT

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.

Motivation & Objective

• Address the long-standing challenge of computational intractability in POMDPs, which previously hindered their use in robotics.
• Explain how sampling-based approximate solvers have significantly improved scalability and practicality of POMDPs for real-world robotics problems.
• Review key computational issues—such as large state, observation, and action spaces, long planning horizons, and complex dynamics—that impede POMDP deployment.
• Present practical implementation strategies and software tools that enable integration of POMDPs into robotics systems.
• Illustrate the synergy between POMDPs and reinforcement learning, particularly in model-based Bayesian RL and deep learning approaches.

Proposed method

• Formulate robotics planning problems under uncertainty as POMDPs using a 6-tuple: $\langle\mathcal{S}, \mathcal{A}, \mathcal{O}, T, Z, R\rangle$, where $\mathcal{S}$, $\mathcal{A}$, and $\mathcal{O}$ represent state, action, and observation spaces.
• Represent the robot’s belief state as a probability distribution over possible states, enabling decision-making under partial observability.
• Employ sampling-based approximate solvers (e.g., Monte Carlo tree search, point-based methods) to compute near-optimal policies efficiently, avoiding exact computation.
• Use belief space planning to compute actions that balance information gathering and goal achievement, leveraging stochastic models of actions and observations.
• Integrate POMDPs with reinforcement learning by modeling unknown transition and reward functions as partially observed parameters, enabling online belief updates.
• Apply deep learning techniques to embed POMDP structure into neural networks, combining model-based and model-free learning for improved policy generalization.

Experimental results

Research questions

• RQ1 How can POMDPs be effectively applied to real-world robotics problems despite their high computational complexity?
• RQ2 What computational challenges—such as large state and observation spaces—limit the scalability of POMDPs in robotics?
• RQ3 To what extent do sampling-based solvers improve the practicality of POMDPs for real-time robotic decision-making?
• RQ4 How do POMDPs naturally balance information gathering and task execution in uncertain environments?
• RQ5 What is the relationship between POMDPs and modern reinforcement learning, particularly in model-based and deep learning frameworks?

Key findings

• Sampling-based POMDP solvers now enable computation of high-quality policies within reasonable time, making POMDPs practical for real-world robotics applications.
• POMDPs significantly improve system robustness in uncertain environments, such as underwater navigation, object manipulation with partial knowledge, and human-robot collaboration.
• The integration of POMDPs with reinforcement learning allows agents to learn both task performance and model uncertainty simultaneously, improving adaptability.
• Deep learning methods that embed POMDP structure into neural networks achieve better generalization than purely model-free approaches.
• Open-source software tools and belief space planning interfaces now support deployment of POMDPs in robotics stacks, easing practical adoption.
• Despite remaining scalability challenges, current methods are sufficient to enhance robustness in a wide range of robotics problems, including long-horizon and complex dynamics scenarios.