Belief-Space Planning

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10 papers in the last four weeks, against 2 the four weeks before. 0.1% of all new papers.

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Latest papers 47

Jun 17, 2026cs.AI

Generative-Model Predictive Planning for Navigation in Partially Observable Environments

Navigation in partially observable environments presents a significant challenge for autonomous agents, requiring effective decision-making with limited sensory information in unknown environments. Belief-based methods, particularly those using neural networks to approximate the belief space, often fail to capture the inherent multimodality of belief spaces, especially in high-dimensional cases with perceptual aliasing. While generative models present a compelling alternative, they typically require substantial data or expert demonstrations and lack explicit mechanisms for long-term planning. In this paper, we introduce BeliefDiffusion, a novel framework that combines the benefits of both generation and planning. BeliefDiffusion leverages diffusion models to explicitly characterize multimodal belief distributions and utilizes Model Predictive Control (MPC) to simultaneously plan ahead. It consists of two steps: (1) Imagining plausible environment configurations based on observation history and (2) Planning efficient navigation strategies across an aggregated configurations. Through extensive experiments in synthetic map environments, we demonstrate that BeliefDiffusion significantly outperforms both model-free reinforcement learning baselines and other generative approaches in navigation success rate and path efficiency. Our results validate that explicitly incorporating multimodal belief representations into planning enables more robust navigation in partially observable settings.

Thomas Quilter, Yifan Zhu, Guorui Quan +2

Department of Computer Science Aalto University Espoo, Finland

Belief-Space Planning Diffusion-Based Planning Robot Navigation Partially Observable Markov Decision Processes

Jun 14, 2026cs.RO

PO-PDDL: Learning Symbolic POMDPs from Visual Demonstrations for Robot Planning Under Uncertainty

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.

Wenjing Tang, Xuanjin Jin, Yuan Liu +3

Shanghai Jiao Tong University · Shanghai Innovation Institute

Belief-Space Planning Symbolic Planning Robot Task Planning Learning from Demonstration Partially Observable Markov Decision Processes

Jun 9, 2026cs.AI

Belief-Space Control for Personalized Cancer Treatment via Active Inference

Cancer treatment is at the core a sequential decision-making problem with partial observability, latent patient heterogeneity, and explicit constraints on the budget for medical measurements. Unlike standard Reinforcement Learning (RL) approaches that control state trajectories, cancer treatments permanently modify patients' transition dynamics, changing how states evolve over time. We model cancer treatment as a belief-space planning problem using active inference, deriving an expected free-energy objective that unifies goal-directed control and information acquisition under measurement budgets without. We implement this framework using real clinical cancer data from the AACR Project GENIE Biopharma Collaborative dataset. Results on clinical data demonstrate a simultaneous patient categorization and high treatment efficacy, under real measurement and treatment constraints.

Deniz Sargun, H. Bugra Tulay, C. Emre Koksal

Amazon.com Inc. Palo Alto, CA · HP Inc. Denver, CO · The Ohio State University Columbus, OH

Belief-Space Planning Healthcare Active Inference Cost-Aware Inference Clinical Decision-Making Oncology

Jun 3, 2026cs.RO

Think Fast and Far: Long-Horizon Online POMDP Planning via Rapid State Sampling

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}.

Yuanchu Liang, Edward Kim, J. Arden Knoll +4

Australian National University, Canberra ACT 2601, Australia. · Rice University, Houston TX 77005, USA.

Belief-Space Planning Partially Observable Markov Decision Processes

May 29, 2026cs.CL

PatchWorld: Gradient-Free Optimization of Executable World Models

Text-agent environments are typically modeled as partially observable Markov decision processes (POMDPs), assuming that the simulator's latent state and transition dynamics are hidden from the agent. Yet little work has examined whether executable code can be induced to serve as a world model for prediction and planning under partial observability. We introduce PatchWorld, a gradient-free framework that turns offline trajectories into executable Python world models through counterexample-guided code repair. Instead of predicting the next observation with a black-box model, PatchWorld induces symbolic belief-state programs whose action updates can be inspected, replayed, and locally patched. Across seven AgentGym environments, PatchWorld-Simple achieves the highest code-based planning score among evaluated methods, reaching 76.4% macro success in live one-step lookahead while invoking no LLM calls inside the world-model prediction module itself. We further find that a human-specified residual-memory bias improves surface observation fidelity but weakens decision utility. This exposes a tradeoff in executable world models, since improving observation fidelity can come at the expense of action-discriminative dynamics, and vice versa. Code is available at https://github.com/HKBU-KnowComp/PatchWorld.

Jiaxin Bai, Yue Guo, Yifei Dong +13

1Hong Kong Baptist University · 2Independent Researcher · 3HKUST +4

Belief-Space Planning World Model Learning World Models World Model-Based Planning Program Synthesis Model-Based Planning

May 27, 2026cs.RO

Integrated Exploration-Aware UAV Route Optimization and Path Planning

Uncrewed aerial vehicles (UAVs) are increasingly used for exploration-driven monitoring in hazardous environments such as disaster zones, contaminated sites, wildfire areas, and damaged infrastructure, where limited flight endurance must be allocated between visiting reported locations and gathering new information. In these settings, prior information regarding hazards is often incomplete, spatially imprecise, and subject to change during execution. For example, initial reports may identify a region where a hazard is likely to exist, but the actual hazard may be displaced, partially observed, or entirely unreported. We present an integrated exploration-aware UAV route optimization and path planning framework for hazard monitoring under uncertain and evolving prior information. The environment is represented as a spatial risk map, where each location has an associated belief of hazardous conditions. Reported hazards are modeled as uncertain regions of interest (ROIs) rather than confirmed target locations, requiring the UAV to inspect reported areas while also using its limited flight endurance to explore informative regions. The proposed method solves a vehicle routing problem over reported ROIs, augments the route with auxiliary pseudo-nodes to improve spatial coverage, allocates the remaining flight distance budget across route segments, and optimizes dynamically feasible B-spline trajectories for local exploration. During execution, UAV measurements update a grid-based belief map, and the remaining trajectory is replanned when new information and the remaining budget justify adaptation. Across 48 scenario configurations, online replanning improves average KL reduction by 15.9% over the offline optimized planner and 48.6% over straight-line traversal.

Jimin Choi, Grant Stagg, Cameron K. Peterson +1

Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109, USA · Department of Electrical Engineering, Brigham Young University, Provo, UT 84602, USA · Department of Aerospace Engineering, Department of Civil and Environmental Engineering, and Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI 48109, USA

Belief-Space Planning Trajectory Optimization Informative Path Planning UAV Navigation Vehicle Routing UAV Trajectory Optimization+1

May 21, 2026cs.RO

Higher Order Reasoning for Collaborative Communicationless Mobile Robot Operations

In communicationless environments, multi-robot systems must operate without the constant information exchange that many coordination strategies typically assume. This paper presents a novel dynamic epistemic planning framework that enables implicit coordination and long horizon planning through higher-order reasoning among robots. With our approach, robots form and propagate higher-order belief particles, update world beliefs using Bayesian inference, and select actions via a behavior tree that anticipates teammates' likely decisions. A temporally aware Model Predictive Path Integral (MPPI) controller integrates this reasoning into low-level execution, allowing robots to plan intercepts and adapt trajectories under partial observability. The proposed framework is evaluated in both simulations and physical experiments, where it consistently reduces task completion time compared to a first-order baseline, demonstrating that epistemic logic can serve as a robust foundation for resilient coordination in communication-restricted domains.

Jonathan Reasoner, Nicola Bezzo

Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA 22904, USA

Belief-Space Planning Multi-Robot Motion Planning Multi-Robot Coordination Multi-Agent Reasoning

May 13, 2026cs.AI

Ego2World: Compiling Egocentric Cooking Videos into Executable Worlds for Belief-State Planning

Embodied agents in household environments must plan under partial observation: they need to remember objects, track state changes, and recover when actions fail. Existing benchmarks only partially test this ability. Egocentric video datasets capture realistic human activities but remain passive, while interactive simulators support execution but rely on synthetic scenes and hand-crafted dynamics, introducing a sim-to-real gap and often assuming fully observable state. We introduce Ego2World, an executable benchmark that turns egocentric cooking videos into executable symbolic worlds governed by graph-transition rules. Built on HD-EPIC, Ego2World derives reusable transition rules from video annotations and executes them in a hidden symbolic world graph. During evaluation, the simulator maintains the hidden world graph, while the agent plans over its own partial belief graph using only local observations and execution feedback. This separation forces agents to update memory and replan without observing the true world state. Experiments show that action-overlap scores overestimate physical-state success, and that persistent belief memory improves task completion while reducing repeated visual exploration -- suggesting that belief maintenance should be a first-class target of embodied-agent evaluation.

Qinchuan Cheng, Zhantao Gong, Pengzhan Sun +3

Xi’an Jiaotong University · Nankai University · National University of Singapore +1

Belief-Space Planning Long-Horizon Agent Evaluation AI Agent Benchmarks

May 12, 2026cs.RO

Multistep Belief Space Dynamics Learning For Risk-Aware Control

As autonomous vehicles move from a simplified research setting to practical use, there exists a large gap between the dynamic behavior of a human driving and an autonomous system. Risk-aware behavior needs to naturally develop in order to scale to the demands of the real world. A major issue for risk-aware planning and control has been predicting how dynamical uncertainty evolves through time and optimizing plans that account for this without being overly conservative. Here, we present a learning framework to predict distributional dynamics that can be optimized in real time for Model Predictive Control (MPC). We explore the importance of structure when learning distributional dynamics for use in MPC. A rigorous ablation study is conducted on a large dataset of real world off-road driving that shows the impact of deviations from our proposed structure. Furthermore, we deploy our learned model and planning stack on a full sized vehicle in challenging off-road conditions. Our planning architecture is able to naturally regulate the speed of the vehicle based on the environment and consistently demonstrates intelligent behavior over miles of diverse terrain.

Jason Gibson, Bogdan Vlahov, Patrick Spieler +1

Georgia Institute of Technology, Atlanta GA 30313 USA · California Institute of Technology, Pasadena, CA 91125, USA

Belief-Space Planning Autonomous Driving Model Predictive Control

May 12, 2026cs.LO

Ensuring Logic in the Fog: Sound POMDP Synthesis with LTL Objectives

Synthesising autonomous agents that can navigate uncertain environments while adhering to complex temporal constraints remains a fundamental challenge. While Linear Temporal Logic (LTL) provides a rigorous language for specifying such tasks, the inherent undecidability of qualitatively verifying LTL satisfaction in partially observable Markov decision processes renders quantitative synthesis difficult, especially when designing reliable reward signals for approximate solvers. In this paper, we bridge this gap with a novel, sound reward-shaping mechanism that dynamically generates belief-dependent rewards grounded in certified LTL satisfaction. By integrating this mechanism into an enhanced Monte Carlo Planning framework, we empower agents to navigate the `fog' of partial observability with a search process focused on maximising verifiable success. Our experiments demonstrate that this approach not only thrives in scenarios where existing solvers fail but also maintains effectiveness and scalability across diverse benchmark domains.

Can Zhou, Yulong Gao, Pian Yu

Imperial College London, United Kingdom · University College London, United Kingdom

Belief-Space Planning Reward Shaping Monte Carlo Tree Search Partially Observable Markov Decision Processes

May 9, 2026cs.RO

Terminal Matters: Kinodynamic Planning with a Terminal Cost and Learned Uncertainty in Belief State-Cost Space

In many real-world robotic tasks, robots must generate dynamically feasible motions that reliably reach desired goals even under uncertainty. Yet existing sampling-based kinodynamic planners typically optimize accumulated trajectory costs and treat goal reaching as a feasibility check, rather than explicitly optimizing terminal-state quality, such as goal preference or goal-reaching reliability. In this work, we introduce a terminal-cost formulation for kinodynamic planning that allows terminal-state quality to be optimized alongside accumulated trajectory cost. We prove that AO-RRT, an asymptotically optimal kinodynamic planner, preserves its asymptotic optimality under this augmented objective. We further extend the formulation to belief space and prove that minimizing the Wasserstein distance between the terminal belief and the goal improves a lower bound on the probability of reaching the goal region. The resulting planner, KiTe, uses this terminal-cost objective to encode goal preferences and improve reliability under uncertainty. To support systems without analytical uncertainty models, we learn dynamics and process uncertainty directly from data and integrate the learned belief dynamics into planning. Experiments on Flappy Bird, Car Parking, and Planar Pushing show that KiTe consistently improves goal-reaching success under uncertainty. Real-world Planar Pushing experiments further demonstrate that KiTe can plan effectively with learned dynamics and uncertainty. Source code is available at https://github.com/elpis-lab/KiTe.

Zhuoyun Zhong, Seyedali Golestaneh, Constantinos Chamzas

All authors are affiliated with the Department of Robotics Engineering, Worcester Polytechnic Institute (WPI), Worcester, MA 01609, USA

Belief-Space Planning Trajectory Optimization Kinodynamic Motion Planning Trajectory Generation Motion Planning Sampling-Based Motion Planning

May 8, 2026cs.AI

Multi-Environment POMDPs with Finite-Horizon Objectives

Partially Observable Markov Decision Processes (POMDPs) are systems in which one agent interacts with a stochastic environment, and receives only partial information about the current state. In a multi-environment POMDP (MEPOMDP), the initial state is unknown, and assumed to be adversarially chosen. In this work we focus on computing the optimal value and policy in MEPOMDPs with finite-horizon objectives. That problem is known to be PSPACE-complete in POMDPs. Our main results are as follows: (1) we establish that it is also PSPACE-complete in the more general setting of MEPOMDPs; (2) we present a practical algorithm and evaluate it on classical benchmarks, significantly outperforming the only previously known algorithm.

Léonard Brice, Filip Cano, Krishnendu Chatterjee +2

Institute of Science and Technology Austria

Belief-Space Planning Markov Models Partially Observable Markov Decision Processes

May 3, 2026cs.RO

Optimizing Trajectory-Trees in Belief Space: An Application from Model Predictive Control to Task and Motion Planning

This paper explores the benefits of computing arborescent trajectories (trajectory-trees) instead of commonly used sequential trajectories for partially observable robotic planning problems. In such environments, a robot infers knowledge from observations, and the optimal course of action depends on these observations. \revise{Trajectory-trees, optimized in belief space, naturally capture this dependency by branching where the belief state is expected to evolve into multiple distinct scenarios, such as upon receiving an observation. Unlike sequential trajectories, which model a single forward evolution of the system, trajectory-trees capture multiple possible contingencies.} First, we focus on Model Predictive Control (MPC) and demonstrate the benefits of planning tree-like trajectories. We formulate the control problem as the optimization of a tree with a single branching (PO-MPC). This improves performance by reducing control costs through more informed planning. To satisfy the real-time constraints of MPC, we develop an optimization algorithm called Distributed Augmented Lagrangian (D-AuLa), which leverages the decomposability of the PO-MPC formulation to parallelize and accelerate the optimization. We apply the method to both linear and non-linear MPC problems using autonomous driving examples. Second, we address Task And Motion Planning (TAMP), and introduce a planner (PO-LGP) reasoning on decision trees at task level, and trajectory-trees at motion-planning level. This approach builds upon the Logic-Geometric-Programming Framework (LGP) and extends it to partially observable problems. The experiments show the method's applicability to problems with a small belief state size, and scales to larger problems by optimizing explorative policies, which are used as macro-actions in an overarching task plan.

Camille Phiquepal, Marc Toussaint

Learning and Intelligent Systems Lab (LIS), TU Berlin, Germany

Belief-Space Planning Model Predictive Control Motion Planning Optimal Control

Apr 28, 2026cs.AI

Distill-Belief: Closed-Loop Inverse Source Localization and Characterization in Physical Fields

{Closed-loop inverse source localization and characterization (ISLC) requires a mobile agent to select measurements that localize sources and infer latent field parameters under strict time constraints.} {The core challenge lies in the belief-space objective: valid uncertainty estimation requires expensive Bayesian inference, whereas using fast learned belief model leads to reward hacking, in which the policy exploits approximation errors rather than actually reducing uncertainty.} {We propose \textbf{Distill-Belief}, a teacher--student framework that decouples correctness from efficiency. A Bayes-correct particle-filter teacher maintains the posterior and supplies a dense information-gain signal, while a compact student distills the posterior into belief statistics for control and an uncertainty certificate for stopping. At deployment, only the student is used, yielding constant per-step cost.} {Experiments on seven field modalities and two stress tests show that Distill-Belief consistently reduces sensing cost and improves success, posterior contraction, and estimation accuracy over baselines, while mitigating reward hacking.}

Yiwei Shi, Zixing Song, Mengyue Yang +2

SEMT, University of Bristol, Bristol, UK · LUCAS, Loughborough University, Loughborough, UK

Belief-Space Planning Reward Hacking Active Sensing Inverse Problems

Apr 28, 2026cs.RO

Variational Neural Belief Parameterizations for Robust Dexterous Grasping under Multimodal Uncertainty

Contact variability, sensing uncertainty, and external disturbances make grasp execution stochastic. Expected-quality objectives ignore tail outcomes and often select grasps that fail under adverse contact realizations. Risk-sensitive POMDPs address this failure mode, but many use particle-filter beliefs that scale poorly, obstruct gradient-based optimization, and estimate Conditional Value-at-Risk (CVaR) with high-variance approximations. We instead formulate grasp acquisition as variational inference over latent contact parameters and object pose, representing the belief with a differentiable Gaussian mixture. We use Gumbel-Softmax component selection and location-scale reparameterization to express samples as smooth functions of the belief parameters, enabling pathwise gradients through a differentiable CVaR surrogate for direct optimization of tail robustness. In simulation, our variational neural belief improves robust grasp success under contact-parameter uncertainty and exogenous force perturbations while reducing planning time by roughly an order of magnitude relative to particle-filter model-predictive control. On a serial-chain robot arm with a multifingered hand, we validate grasp-and-lift success under object-pose uncertainty against a Gaussian baseline. Both methods succeed on the tested perturbations, but our controller terminates in fewer steps and less wall-clock time while achieving a higher tactile grasp-quality proxy. Our learned belief also calibrates risk more accurately, keeping mean absolute calibration error below 0.14 across tested simulation regimes, compared with 0.58 for a Cross-Entropy Method planner.

Clinton Enwerem, Shreya Kalyanaraman, John S. Baras +1

Belief-Space Planning Stochastic Optimization Robotic Grasping Variational Inference Decision-Making under Uncertainty

Apr 27, 2026math.OC

Dual Control of Linear Systems from Bilinear Observations with Belief Space Model Predictive Control

We study finite-horizon quadratic control of linear systems with bilinear observations, in which the control input affects not only the state dynamics but also the partial observations of the state. In this setting, the separation principle can fail because control inputs influence the future quality of state estimates. State estimation requires an input-dependent Kalman filter whose gain and error covariance evolve as functions of the control inputs. To address this challenge, we propose a belief-space model predictive control (

\texttt{B-MPC}

) method that plans directly over both the estimated state and its error covariance. In particular,

\texttt{B-MPC}

plans with a deterministic surrogate of the belief evolution defined by the input-dependent Kalman filter. Through numerical experiments in two synthetic settings, we show that

\texttt{B-MPC}

can outperform both the separation-principle controller and its MPC variant in favorable regimes, and that these gains are accompanied by lower estimation covariance and more uncertainty-aware action choices.

Daniel Cao, Beixi Du, Andrew Lowitt +3

Cornell

Belief-Space Planning Model Predictive Control

Apr 4, 2026eess.SY

Risk-Constrained Belief-Space Optimization for Safe Control under Latent Uncertainty

Many safety-critical control systems operate under latent uncertainty that sensors cannot resolve at decision time. Such uncertainty, arising from unknown physical properties, disturbances, or unobserved geometry, affects dynamics, task feasibility, and safety margins. Standard methods optimize expected performance and offer limited protection against rare but severe outcomes, while robust formulations treat uncertainty conservatively without exploiting its probabilistic structure. We consider systems with measured state and an unknown, time-invariant parameter represented by a belief distribution. We propose a risk-sensitive belief-space Model Predictive Path Integral (MPPI) controller that plans under this belief, regularizes performance using Conditional Value-at-Risk (CVaR), and imposes a CVaR constraint on a trajectory safety margin over the horizon. For the exact risk-constrained formulation underlying this controller, we establish three properties: (1) the CVaR constraint implies a probabilistic safety guarantee, (2) the controller recovers the risk-neutral optimum as the objective risk weight tends to zero, and (3) a union-bound argument extends the per-horizon guarantee to cumulative safety over repeated solves. In contact-rich MuJoCo simulations of vision-guided dexterous stowing, where a manipulator inserts a grasped object into an occupied slot with pose uncertainty exceeding prescribed lateral clearance requirements, our method achieves 82% success with zero contact violations at high risk aversion, compared with 55% and 50% for a risk-neutral configuration and a chance-constrained baseline, both of which incur nonzero exterior contact forces. Project page: https://clintonenwerem.com/belief-cvar-mppi/.

Clinton Enwerem, John S. Baras, Calin Belta

Institute for Systems Research, University of Maryland, College Park, MD, USA

Belief-Space Planning Safety-Critical Control MPPI Control Conditional Value-at-Risk