Source-linked AI summary
Partially Observable Markov Decision Processes (POMDPs) and Robotics
Hanna Kurniawati
TL;DR
Robotics needs reliable decisions despite nondeterministic actions and partially observable states, but exact POMDP optimization is computationally intractable. This paper reviews POMDPs, sampling-based approximate solvers, the computational issues they address, and robotics implementation lessons. The review concludes that approximate methods can improve robustness for many realistic robotics problems within reasonable computational resources, although scalability issues remain.
Problem
Exact POMDP solutions are computationally intractable, making traditionally high-complexity methods impractical for many realistic robotics problems.
Method
The paper reviews POMDP formulation, sampling-based approximate solving methods, the computational issues they alleviate, and implementation lessons from robotics applications.
Results
Sampling-based approximate solvers compute good, non-optimal policies that substantially improve robotics robustness within reasonable computational resources.
Takeaways & Limitations
POMDPs are practical for a variety of realistic robotics problems, despite some remaining scalability issues.
Takeaways & Limitations
The review is not exhaustive and omits policy-search approaches, Gaussian-belief methods, and broader belief-space extensions beyond selected examples.
Abstract
from arXiv · showhide
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.
1 Introduction
POMDPs provide a principled framework for robust robotic decision-making under nondeterministic effects and partial observability, but exact optimization was long considered impractical. Sampling-based advances now compute sufficiently good strategies within reasonable resources, making POMDPs practical for many realistic robotics problems.
- Motivation and framework: POMDPs model nondeterministic actions and partially observable states using beliefs, enabling action strategies that balance information gathering with goal attainment.Beliefs represent probability distributions over possible states rather than a single known state.
- Computational challenge: Exact optimal POMDP solutions are computationally intractable, and earlier solvers required many hours even for benchmark problems with fewer than 30 states.This computational burden was considered grossly insufficient for realistic robotics problems.
- Sampling-based progress: Sampling-based methods compute non-optimal but often sufficient action strategies that substantially improve robustness within reasonable computational resources.These advances have accumulated over the past two decades.
- Paper scope: The paper reviews POMDP models, sampling-based methods, computational issues they alleviate, robotics implementations, and connections to motion planning and machine learning.The review spans both algorithmic advances and lessons related to robotics applications.
2 The Problem and POMDP Formulation
POMDPs represent sequential robotic decision-making when actions have uncertain effects and observations do not reveal the exact state. The formulation combines states, actions, observations, transitions, observations, and rewards with belief updates and value-based policy optimization, while supporting several planning objectives and finite or continuous variants.
- Problem setting: POMDPs represent sequential decisions in which action outcomes are nondeterministic and observations may leave multiple states indistinguishable.Robotics examples include underwater navigation, manipulation, and human-robot collaboration.
- POMDP model: A POMDP is defined by the six-tuple ⟨S, A, O, T, Z, R⟩, comprising state, action, observation, transition, observation, and reward components.The transition function gives the probability of reaching a subsequent state after an action, while the observation function models measurement and perception uncertainty.
- Agent operation: At each step, the agent uses a belief over hidden states to choose an action, receives an observation, and updates its belief about the resulting state.The agent’s actual state remains hidden, while observations may reveal information about it.
- Objectives and solution: Solving a POMDP seeks a policy mapping beliefs to actions that maximizes an objective based commonly in robotics on expected total discounted reward.The infinite-horizon formulation uses a discount factor and a stationary optimal policy; finite-horizon value functions are non-stationary.
- Objectives and solution: Goal-POMDPs use action costs to reach a target belief concentrated on goal states and are equivalent to expected-total-discounted-reward POMDPs.The paper focuses on expected total discounted reward and generally assumes discrete, finite state, action, and observation spaces unless stated otherwise.
3 Sampling-Based Approximate POMDP Solvers
Sampling-based approximate solvers make POMDP planning more practical by trading exact optimality for scalable computation over representative beliefs and, in some methods, sampled actions or histories.
- POMDP solving is PSPACE-hard, and high computational complexity made exact-policy methods impractical for realistic robotics problems.Earlier benchmark problems typically had fewer than 30 states, yet the best algorithms could require many hours.
- A breakthrough solver computed good policies for an 870-state problem, extending practical solving beyond the under-30-state benchmarks common at the time.Point-Based Value Iteration achieved this result in approximately 50 hours.
- Sampling-based solvers relax optimality and estimate values only for representative beliefs reachable from a given initial belief, substantially reducing computational complexity.Their general workflow iteratively samples beliefs, estimates their values, updates the policy, and stops according to available planning time or bound convergence.
- Later offline solvers improved scalability further: HSVI2 solved Tag better than PBVI in 2 hours versus 50 hours, while SARSOP achieved a better Tag policy in 6 seconds.HSVI2 and SARSOP were also demonstrated on problems exceeding 15K states and 1K observations, and SARSOP on RockSample(10,10) with over 100K states.
- Online solvers compute only the best action from the current belief before execution, reducing memory requirements compared with offline policy construction.POMCP represents beliefs with particles in a history tree and uses forward simulations to estimate action values.
4 Applying POMDPs to Physical Robots
POMDPs have been applied to physical-robot planning and control as solving capabilities became scalable enough for realistic applications. The section also discusses software tools, implementation strategies, and modeling concerns relevant to deployment.
- POMDPs have been applied to planning and control in physical robots, including a demonstration lasting 7 consecutive days at 7 hours per day.
- Open-source tools implement approximate POMDP solvers such as Perseus, HSVI, SARSOP, DESPOT, and ABT.Examples include Symbolic Perseus, ZMDP, APPL Toolkit, APPL-online, and TAPIR.
- OPPT eases interfacing POMDP models with ROS through parameter files for robot motion planning or plugins for general transition, observation, and reward functions.
- Sequential online implementations can delay execution because belief updates and action computation are often expensive.
- Parallelizing belief updates with action computation can reduce delays by starting computation when action execution begins.The section gives Sequential-Importance-Resampling particle filtering as an example of computation that can begin immediately after action selection.
- POMDP models require careful transition, observation, and reward-function design, using conservative estimates, learned data, or combinations of both.
5 Discussion
The discussion situates sampling-based POMDP progress alongside motion planning and learning. It also describes POMDPs as a model-based Bayesian reinforcement-learning representation and notes newer neural approaches for incompletely known models.
- 5.1 Comparison to Sampling-Based Motion Planning: The techniques that made POMDPs practical in robotics are described as closely resembling the key techniques and progressions of motion planning.
- POMDPs represent model-based Bayesian reinforcement learning by modeling uncertainty over unknown transition and reward functions as probability distributions.
- In this representation, partially observed parameters of transition and reward distributions are updated as the agent receives observations.
- Solving the resulting POMDP balances information-gathering actions against other task actions.
- Deep-learning approaches include model-free methods that learn policies or value functions directly and structure-embedded methods reported to achieve better generalization.
6 Conclusion
The conclusion presents sampling-based methods as the basis for making POMDPs useful in realistic robotics despite computational difficulty. It emphasizes remaining scalability issues alongside practical robustness gains and available software support.
- POMDPs model planning under non-deterministic actions and partial observability, but finding their optimal solutions is computationally intractable.
- Sampling-based methods compute good approximate solutions within reasonable computational resources and significantly improve robotics-system robustness.
- Five major scalability issues are large state, observation, and action spaces, long planning horizons, and complex dynamics.
- Open-source implementations and interfaces to typical robotics software ease the application of POMDPs to robotics problems.
- Although some scalability issues remain, existing methods are efficient enough to improve robustness across many robotics problems.