NAMOUnc: Uncertain Navigation Among Obstacles

• NAMOUnc is an uncertainty-aware framework that represents navigational decisions with interval-valued time costs for both bypassing and removal of movable obstacles.
• It integrates four key uncertainty sources—observation, model, action, and blockage—to dynamically guide decision-making in cluttered scenarios.
• Empirical results in simulation and real-world tests show that NAMOUnc balances success rate and efficiency, outperforming traditional deterministic planners in mixed environments.

Searching arXiv for the exact term and related papers to ground the article in current sources. NAMOUnc most directly denotes “Navigation Among Movable Obstacles with Decision Making on Uncertainty Interval”, a robotic navigation-and-manipulation framework for cluttered environments containing movable obstacles (MOs). Its defining premise is that the canonical NAMO decision—whether to bypass an obstacle or remove it—should be made explicitly under uncertainty, with both options represented as time cost intervals rather than deterministic scalars. In the formulation introduced on arXiv, NAMOUnc jointly optimizes success rate (SR) and goal-reaching time while incorporating observation uncertainty, model uncertainty, action uncertainty, and blockage uncertainty from partial observability (Zhang et al., 16 Sep 2025).

1. Problem setting and conceptual scope

Classical Navigation Among Movable Obstacles (NAMO) considers a robot that must reach a goal in a workspace containing static obstacles and MOs. If the shortest path is blocked by an MO, the robot can either plan a detour or manipulate the obstacle to a stock region and then continue. In the problem formulation associated with NAMOUnc, many prior NAMO methods assume a known static map or a fully observable world, treat manipulation as necessary or central, and focus primarily on feasibility or success rate rather than cost. NAMOUnc is motivated by the observation that manipulation is often optional, detours frequently exist, and removal can be both costly and failure-prone (Zhang et al., 16 Sep 2025).

The framework isolates four uncertainty sources. Observation uncertainty arises from sensor noise in MO detection and robot pose uncertainty from localization, yielding uncertain MO pose estimates and collision risk. Model uncertainty enters through approximate predictors for bypass and removal time. Action uncertainty reflects the fact that loading or transporting an MO can fail, and that SR varies by obstacle and situation. Blockage uncertainty from partial observability arises because the prior map contains only static obstacles while MOs are discovered online, so unseen areas may contain additional blockers (Zhang et al., 16 Sep 2025).

This makes NAMOUnc an explicitly decision-theoretic extension of NAMO rather than a purely geometric planner. The central claim is not that all blocked paths should trigger manipulation, nor that safe navigation is achieved by always detouring. Instead, the framework compares uncertain bypass and removal strategies via interval-valued operational costs. A plausible implication is that NAMOUnc treats obstacle interaction as a contingent control decision conditioned on both geometric structure and uncertainty quantification.

2. State representation and uncertainty-aware cost modeling

The formal setting uses robot pose $X_r = (x_r, y_r, \theta_r)$, uncertain MO poses $X_{MO}^i$, waypoint sequences $pt_i = (p_i, \alpha_i)$, and actions comprising navigation along a trajectory or removal of an MO to a stock region (Zhang et al., 16 Sep 2025).

For observation uncertainty, the relative MO measurement from the camera is $Y^i = (d^i, \phi^i)$ with covariance $\Sigma_Y$, and the robot pose carries covariance $\Sigma_r$. The global MO pose is

$$X_{MO}^i = \begin{pmatrix} x_r + d^i \cos(\theta_r + \phi^i) \ y_r + d^i \sin(\theta_r + \phi^i) \end{pmatrix},$$

with covariance

$$\Sigma_{MO}^i = J_r \Sigma_r J_r^T + J_y \Sigma_Y J_y^T,$$

where $J_r = \frac{\partial X_{MO}^i}{\partial X_r}$ and $J_y = \frac{\partial X_{MO}^i}{\partial Y^i}$. Multiple measurements of the same MO are fused with a Kalman filter. With confidence level $X_{MO}^i$0, the MO belief region is modeled as an ellipse derived from $X_{MO}^i$1, inflated by the MO’s physical radius; any path intersecting this region is treated as collision-prone and triggers a decision between bypass and removal (Zhang et al., 16 Sep 2025).

For bypass-time estimation, NAMOUnc extracts three trajectory features from the waypoint sequence. The feature vector is $X_{MO}^i$2, where $X_{MO}^i$3 is total path length, the smoothness term is

$X_{MO}^i$4

and the direction-change variance is

$X_{MO}^i$5

A Gaussian Linear Regressor (GLR) predicts $X_{MO}^i$6 and $X_{MO}^i$7, giving the bypass navigation interval

$X_{MO}^i$8

under the stated $X_{MO}^i$9 confidence assumption. If no detour path exists, $pt_i = (p_i, \alpha_i)$0 (Zhang et al., 16 Sep 2025).

Removal cost is modeled under action uncertainty. Let $pt_i = (p_i, \alpha_i)$1 be the time to successfully remove one MO, $pt_i = (p_i, \alpha_i)$2 the manipulation SR, and $pt_i = (p_i, \alpha_i)$3 the maximum number of removal attempts before fallback to bypass. The expected removal cost is

$pt_i = (p_i, \alpha_i)$4

The first term accounts for success on attempt $pt_i = (p_i, \alpha_i)$5; the second accounts for failure in all $pt_i = (p_i, \alpha_i)$6 attempts followed by bypass. SR is itself uncertain and updated online via a Beta distribution. After $pt_i = (p_i, \alpha_i)$7 advance trials, with $pt_i = (p_i, \alpha_i)$8 successes and $pt_i = (p_i, \alpha_i)$9 failures, the prior is $Y^i = (d^i, \phi^i)$0. After $Y^i = (d^i, \phi^i)$1 operational trials with $Y^i = (d^i, \phi^i)$2 successes and $Y^i = (d^i, \phi^i)$3 failures, the posterior becomes $Y^i = (d^i, \phi^i)$4. Using the confidence interval induced by $Y^i = (d^i, \phi^i)$5, NAMOUnc obtains a removal cost interval $Y^i = (d^i, \phi^i)$6 (Zhang et al., 16 Sep 2025).

Blockage uncertainty is modeled for unseen corridors. At waypoint $Y^i = (d^i, \phi^i)$7, the corridor width is $Y^i = (d^i, \phi^i)$8, the robot radius is $Y^i = (d^i, \phi^i)$9, the MO diameter is Gaussian $\Sigma_Y$0, and the MO center-wall distance is uniform,

$\Sigma_Y$1

The deterministic blockage condition is written as

$\Sigma_Y$2

Marginalizing over $\Sigma_Y$3 yields the piecewise form

$\Sigma_Y$4

Then

$\Sigma_Y$5

approximated by sampling. With obstacle appearance parameter $\Sigma_Y$6 over free area $\Sigma_Y$7,

$\Sigma_Y$8

and the blockage probability at $\Sigma_Y$9 is

$\Sigma_r$0

For a trajectory $\Sigma_r$1,

$\Sigma_r$2

and the corresponding blockage-cost interval is

$\Sigma_r$3

The key structural point is that both navigation and manipulation are lifted to interval-valued costs in the same uncertainty calculus (Zhang et al., 16 Sep 2025).

3. Decision rule, planning pipeline, and execution stack

NAMOUnc constructs two strategy-level intervals. For bypass,

$\Sigma_r$4

and for removal,

$\Sigma_r$5

Interval addition is performed by summing lower bounds and upper bounds separately. The framework then applies the Laplace criterion, assuming the realized cost is uniformly distributed over the interval $\Sigma_r$6. The resulting utility is

$\Sigma_r$7

so strategy selection reduces to comparing $\Sigma_r$8 and $\Sigma_r$9, and choosing the lower-utility interval (Zhang et al., 16 Sep 2025).

Operationally, the decision loop is: plan a shortest path on the prior static map; detect whether an uncertain MO blocks the path; construct bypass and removal options; estimate navigation, removal, and blockage intervals for each option; compare them with the Laplace rule; and execute the lower-cost strategy. The procedure is deterministic once the intervals have been estimated, but its inputs are probabilistic and updated online. In particular, the Beta-posterior SR update makes repeated manipulation failures directly alter later bypass-versus-removal decisions (Zhang et al., 16 Sep 2025).

The implementation uses ROS Noetic with MoveBase. The global planner is A* on a static map with MOs and uncertainty ellipses temporarily inserted as obstacles. The local planner is TEB (Timed Elastic Band). Localization is performed by AMCL using LiDAR, and the prior static map is generated with GMapping. For MO detection, the system uses a camera and ArUco markers to reduce classification uncertainty. The real robot platform is a Clearpath Jackal with arm, LiDAR, and RealSense camera; simulation uses a simple room in PyBullet and a large warehouse in Gazebo. The GLR component is implemented in PyTorch and trained on approximately $$X_{MO}^i = \begin{pmatrix} x_r + d^i \cos(\theta_r + \phi^i) \ y_r + d^i \sin(\theta_r + \phi^i) \end{pmatrix},$$0 trajectory segments, with evaluation on $$X_{MO}^i = \begin{pmatrix} x_r + d^i \cos(\theta_r + \phi^i) \ y_r + d^i \sin(\theta_r + \phi^i) \end{pmatrix},$$1 test trajectories. Experiments were run on an Intel i7-12700H, 16GB RAM platform (Zhang et al., 16 Sep 2025).

This architecture makes NAMOUnc neither a pure motion planner nor a pure manipulation policy. It is a hybrid navigation-manipulation stack in which uncertainty estimates are propagated upward into a decision layer. A plausible implication is that its practical novelty lies less in any single planner component than in the interval-valued coupling of perception, navigation cost prediction, manipulation SR estimation, and partial-observability risk.

4. Empirical behavior in simulation and physical deployment

The empirical program comprises two simulation environments and a real-world warehouse-like setup. In simulation, the room environment isolates specific uncertainties with a single MO blocking the only path, while the warehouse environment introduces a larger map with multiple MOs placed in regions such as $$X_{MO}^i = \begin{pmatrix} x_r + d^i \cos(\theta_r + \phi^i) \ y_r + d^i \sin(\theta_r + \phi^i) \end{pmatrix},$$2, $$X_{MO}^i = \begin{pmatrix} x_r + d^i \cos(\theta_r + \phi^i) \ y_r + d^i \sin(\theta_r + \phi^i) \end{pmatrix},$$3, and $$X_{MO}^i = \begin{pmatrix} x_r + d^i \cos(\theta_r + \phi^i) \ y_r + d^i \sin(\theta_r + \phi^i) \end{pmatrix},$$4. The reported metrics are running time and failures, with a timeout at $$X_{MO}^i = \begin{pmatrix} x_r + d^i \cos(\theta_r + \phi^i) \ y_r + d^i \sin(\theta_r + \phi^i) \end{pmatrix},$$5 s (Zhang et al., 16 Sep 2025).

For bypass-time regression, NAMOUnc compares three estimators: an average speed method, a trapezoid method, and the proposed GLR. On the $$X_{MO}^i = \begin{pmatrix} x_r + d^i \cos(\theta_r + \phi^i) \ y_r + d^i \sin(\theta_r + \phi^i) \end{pmatrix},$$6 train/test split, the GLR attains a median absolute error of 1.59 s, versus 3.43 s for average speed and 3.31 s for the trapezoid method. Its interquartile range is 0.69 s, compared with 1.35 s and 1.91 s respectively. The reported interpretation is that GLR captures the influence of curvature and smoothness more effectively than simple kinematic heuristics (Zhang et al., 16 Sep 2025).

The action-uncertainty ablation compares a version with the action-uncertainty module and one without it. Two MO classes are evaluated: an easy MO with SR approximately $$X_{MO}^i = \begin{pmatrix} x_r + d^i \cos(\theta_r + \phi^i) \ y_r + d^i \sin(\theta_r + \phi^i) \end{pmatrix},$$7, and a hard MO with SR approximately $$X_{MO}^i = \begin{pmatrix} x_r + d^i \cos(\theta_r + \phi^i) \ y_r + d^i \sin(\theta_r + \phi^i) \end{pmatrix},$$8. For the easy MO, the variant without action uncertainty can be faster because it removes a blocker directly; the uncertainty-aware version may inspect alternative regions first. For the hard MO, the uncertainty-aware version bypasses all MOs because the removal interval becomes unfavorable, while the variant without action uncertainty repeatedly attempts removal and exhibits large time and variability. The reported IQRs are 2.53 s versus 6.16 s for the easy case and 1.35 s versus 34.14 s for the hard case. Under unbiased SR estimates, the uncertainty-aware variant yields 91.04 s average running time versus 110.48 s without the module; under biased SR estimates, it still reports 108.66 s versus 110.48 s (Zhang et al., 16 Sep 2025).

The blockage-uncertainty module is evaluated in environments AB and ABE, where ABE contains an extra MO at region $$X_{MO}^i = \begin{pmatrix} x_r + d^i \cos(\theta_r + \phi^i) \ y_r + d^i \sin(\theta_r + \phi^i) \end{pmatrix},$$9 along a bypass. In AB, where no surprise MO appears on the detour, the version without blockage modeling is faster: 67.04 s versus 77.77 s. In ABE, the situation reverses: the version without blockage uncertainty incurs 141.02 s because it bypasses $$\Sigma_{MO}^i = J_r \Sigma_r J_r^T + J_y \Sigma_Y J_y^T,$$0, is later blocked at $$\Sigma_{MO}^i = J_r \Sigma_r J_r^T + J_y \Sigma_Y J_y^T,$$1, and is forced into multiple removals; the uncertainty-aware version instead removes $$\Sigma_{MO}^i = J_r \Sigma_r J_r^T + J_y \Sigma_Y J_y^T,$$2 earlier and reports 90.08 s. Overall, the blockage-aware variant gives 83.92 s versus 104.03 s (Zhang et al., 16 Sep 2025).

The broader simulation comparison includes Priority bypass, Priority removal, Random choice, LaMB, and NAMOUnc. In the room scenario, where the only path is blocked, bypass-only methods such as A* fail, whereas NAMOUnc and priority removal succeed with similar times of approximately 79–78 s. In the warehouse scenario, NAMOUnc and TEB have comparable average times, but TEB exhibits failure cases visible as $$\Sigma_{MO}^i = J_r \Sigma_r J_r^T + J_y \Sigma_Y J_y^T,$$3 s outliers while NAMOUnc has no failures. The reported conclusion is that NAMOUnc achieves a favorable trade-off between efficiency and completeness (Zhang et al., 16 Sep 2025).

Real-world trials use five runs per condition in three layouts: ABC, BC, and AB. The average times are:

• ABC: TEB 300.00 s, Priority removal 96.33 s, Random 115.34 s, NAMOUnc 137.69 s.
• BC: TEB 46.66 s, Priority removal 94.78 s, Random 72.73 s, NAMOUnc 50.41 s.
• AB: TEB 61.11 s, Priority removal 97.94 s, Random 107.44 s, NAMOUnc 72.56 s.

The overall averages are 135.93 s for TEB, 96.35 s for Priority removal, 98.50 s for Random, and 86.88 s for NAMOUnc. The reported interpretation is that NAMOUnc is not best in every single configuration, but gives the best average performance across mixed scenarios because it succeeds in the all-blocked case while remaining competitive in layouts where bypass remains feasible (Zhang et al., 16 Sep 2025).

5. Assumptions, limitations, and position within NAMO research

NAMOUnc assumes that observation noise is approximately Gaussian in the pose covariance model, MO diameters are Gaussian, MO positions are uniform over free space for blockage estimation, and interval-valued costs are uniformly distributed when the Laplace criterion is applied. It further assumes availability of a prior static map, a robot capable of reliable manipulation, and an environment that is primarily 2D with static walls and floor-level obstacles (Zhang et al., 16 Sep 2025).

The reported limitations are correspondingly concrete. Scalability may become problematic in very large environments because blockage probabilities must be computed along longer trajectories and because repeated SR learning accumulates overhead. The uncertainty models are deliberately simplified; real observation errors may be non-Gaussian or multimodal, and action failures may depend on obstacle-specific properties such as shape and friction. The use of ArUco markers reduces classification uncertainty in a way that may not generalize to unlabeled environments. The stock-region predictor and removal-time model are learned from limited data and may not transfer to substantially different domains (Zhang et al., 16 Sep 2025).

Within the broader literature, NAMOUnc is placed at the intersection of classical NAMO methods such as Stilman and Kuffner’s work, RNAMO, and LaMB, and more general task and motion planning under uncertainty. Its distinctiveness lies in five features explicitly highlighted in the source material: interval-valued time costs for both bypass and removal, joint optimization of SR and time rather than SR alone, a formal blockage-probability model for unseen space based on corridor width and object size, integration of four uncertainty modules, and strategy selection via the Laplace criterion (Zhang et al., 16 Sep 2025).

A recurrent misconception in NAMO is that manipulation should be privileged whenever an MO blocks the nominal shortest path. The formulation behind NAMOUnc rejects that assumption: removal is only one branch in an interval-based comparison, and can become dominated by bypass when SR is low or repeated failures are likely. The converse misconception—that reliable navigation is achieved by always detouring—is also contradicted by the blockage-uncertainty experiments, where narrow unseen corridors can make early removal preferable. This suggests a broader methodological point: NAMOUnc reframes blockage handling as an uncertainty-aware operational trade-off rather than a fixed policy.

6. Nomenclature and cross-domain uses of the label

As a bibliographic matter, the exact string “NAMOUnc” appears as the title of the robotics paper “NAMOUnc: Navigation Among Movable Obstacles with Decision Making on Uncertainty Interval” (Zhang et al., 16 Sep 2025). That usage is the direct and explicit referent of the term in the current arXiv record.

A secondary, more speculative use appears in the medical-imaging paper “Nodule-Aligned Latent Space Learning with LLM-Driven Multimodal Diffusion for Lung Nodule Progression Prediction”, where the detailed notes state that a concept like “NAMOUnc” would naturally refer to an uncertainty-aware extension of NAMD (Nodule-Aligned Multimodal Diffusion). In that context, the proposed interpretation is “Nodule-Aligned Multimodal diffusion with Uncertainty modeling”, built on sampling-based uncertainty, aligned latent geometry, and malignancy-risk estimation for lung nodules (Song et al., 16 Mar 2026).

Another unrelated paper, “Cooperation in NOMA Networks Under Limited User-to-User Communications”, concerns cooperative non-orthogonal multiple access with an amplify-and-forward relay; in the attached explanatory material, “NAMOUnc” is used parenthetically as a label for that walkthrough, but the paper itself is a communications-theoretic analysis of outage probability and throughput rather than a robotics NAMO framework (Tran et al., 2018).

The result is a mild nomenclatural ambiguity across domains. In technical usage, however, NAMOUnc is most concretely established as the robotics framework for uncertainty-aware Navigation Among Movable Obstacles (Zhang et al., 16 Sep 2025).