POMDP-based Object Search with Growing State Space and Hybrid Action Domain
Authors: Yongbo Chen, Hesheng Wang, Shoudong Huang, Hanna Kurniawati
Abstract
Efficiently locating target objects in complex indoor environments with diverse furniture, such as shelves, tables, and beds, is a significant challenge for mobile robots. This difficulty arises from factors like localization errors, limited fields of view, and visual occlusion. We address this by framing the object-search task as a highdimensional Partially Observable Markov Decision Process (POMDP) with a growing state space and hybrid (continuous and discrete) action spaces in 3D environments. Based on a meticulously designed perception module, a novel online POMDP solver named the growing neural process filtered k-center clustering tree (GNPF-kCT) is proposed to tackle this problem. Optimal actions are selected using Monte Carlo Tree Search (MCTS) with belief tree reuse for growing state space, a neural process network to filter useless primitive actions, and k-center clustering hypersphere discretization for efficient refinement of high-dimensional action spaces. A modified upper-confidence bound (UCB), informed by belief differences and action value functions within cells of estimated diameters, guides MCTS expansion. Theoretical analysis validates the convergence and performance potential of our method. To address scenarios with limited information or rewards, we also introduce a guessed target object with a grid-world model as a key strategy to enhance search efficiency. Extensive Gazebo simulations with Fetch and Stretch robots demonstrate faster and more reliable target localization than POMDP-based baselines and state-of-the-art (SOTA) non-POMDP-based solvers, especially large language model (LLM) based methods, in object search under the same computational constraints and perception systems. Real-world tests in office environments confirm the practical applicability of our approach. Project page: https://sites.google.com/view/gnpfkct.
Multi-object search in unknown household environments requires planning under extensive uncertainty - from unknown object locations to cluttered spaces with unobserved obstacles. POMDPs offer a principled framework for such problems but remain intractable in large domains. We propose Inter-POMDP, a novel interleaved POMDP planning algorithm that decomposes this challenge into two interacting levels: a high-level POUCT planner reasons over object distributions using LLM-informed histogram beliefs, while a low-level motion planner models navigation uncertainty with obstacle-aware particle beliefs as domain knowledge to guide high-level POUCT. This interleaved design balances planning quality and efficiency despite the large search space across unknown multi-room environments. Both simulation and real-world experiments show that our Inter-POMDP algorithm reduces collision counts by up to 63%, navigation steps by up to 35%, and detection counts by up to 32% compared with baseline methods. Full videos are https://sites.google.com/view/inter-pomdp
Partially Observable Markov Decision Processes (POMDPs) are a general and principled framework for motion planning under uncertainty. Despite tremendous improvement in the scalability of POMDP solvers, long-horizon POMDPs remain difficult to solve. To alleviate the difficulty, this paper proposes a new approximate online POMDP solver, called Reference-Based Online POMDP Planning via Rapid State Space Sampling (ROP-RAS3). ROP-RAS3 uses novel extremely fast sampling-based motion planning techniques to sample the state space and generate a diverse set of macro actions online, which are then used to bias belief-space sampling and infer high-quality policies without requiring exhaustive enumeration of the action space -- a fundamental constraint for modern online POMDP solvers. ROP-RAS3 converges to a near-optimal reference-based solution at a rate that depends on the number of sampled actions, rather than the size of the action space. ROP-RAS3 is evaluated on various long-horizon POMDPs with up to 3000 lookahead steps and 35-dimensional state spaces, where the state, action and observation spaces can be continuous, discrete, or a hybrid of discrete and continuous. Although the reference-based optimal solution may not be the same as the optimal POMDP solution, empirical results indicate that in all of these problems, in terms of success rate, ROP-RAS3 outperforms other state-of-the-art methods by up to multiple folds. We also demonstrate the capability of our approach on a physical robot demonstration. This work extends the theory and empirical results of our ISRR24 paper. Code can be found at \texttt{https://github.com/RDLLab/ROPRAS3}.
Online planning under uncertainty remains a fundamental challenge for robotic systems operating in partially observable environments with high-dimensional state spaces. While sampling-based POMDP solvers enable approximate decision-making in large or continuous domains, their performance degrades as belief dimensionality increases due to the high variance inherent in Monte Carlo-based estimation. In this work, we extend the Rao-Blackwellized online POMDP (RB-POMDP) framework to improve its generalizability in high-dimensional settings through hybrid continuous-discrete belief representations. By analytically propagating uncertainty associated with marginalized state components during tree-based planning, the proposed approach reduces sampling-induced variance in value estimation. We demonstrate the effectiveness of this framework in a robotic search-and-rescue task by integrating it with FastSLAM 2.0. Experimental results show that the proposed planner achieves higher cumulative rewards using significantly fewer particles and planning simulations than purely sampling-based methods under equivalent computational budgets. These results suggest that structured high-dimensional robotic problems admitting tractable sufficient statistics can be effectively leveraged within the RB-POMDP framework for computationally feasible online decision-making.