LEGS-POMDP: Language and Gesture-Guided Object Search in Partially Observable Environments

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.

Real-world robot task planning must operate under both stochastic action execution and partial observability, yet constructing Partially Observable Markov Decision Process (POMDP) models for real robotics domains remains difficult and labor-intensive. We introduce PO-PDDL, a symbolic formulation of POMDPs that preserves the relational structure and LLM-friendly syntax of the Planning Domain Definition Language (PDDL), while explicitly modeling partial observability, stochasticity, and beliefs. Building on this formulation, we propose a demonstration-driven pipeline for learning PO-PDDL models. The proposed method reconstructs latent symbolic state trajectories from real-robot execution videos, identifies partial observability via inconsistencies between inferred states and visual observations, and learns stochastic transition and observation models accordingly. The resulting PO-PDDL domains are reusable across tasks and enable online belief-space planning under both perception and execution uncertainty. Experiments on real-world long-horizon manipulation tasks show that our method consistently outperforms existing PDDL and POMDP model-learning approaches, achieving robust task planning under uncertainty with significantly lower planning cost.

Language-guided object retrieval under partial observability requires deciding whether to gather more evidence, interact with the scene, grasp a candidate, or abstain. We present a closed-loop framework that coordinates these decisions for retrieving a target specified in relation to a reference container. The framework maintains a persistent joint belief over target identity, container relation, and presence through tracked-object, unobserved-target, and target-absent hypotheses. View-conditioned categorical VLM observations update this belief; conformal grasp eligibility and robot feasibility govern commitment, while finite-horizon belief-space planning selects information-gathering actions. Across five different scenarios, our proposed method succeeds in 19/25 simulation episodes versus 12/25 for the best-performing task-adapted baseline and is the only evaluated policy to achieve at least one success in each scenario. Ablations show that cross-view memory improves success under partial occlusion, while the full system does not consistently outperform simplified variants. Real-robot trials demonstrate closed-loop re-observation and autonomous recovery from injected grasp failures, while injected viewpoint failures end in false defer. Experimental results demonstrate the feasibility of coordinating evidence gathering and selective grasp commitment within a unified framework for retrieval under partial observability.