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arxiv: 2604.14026 · v1 · submitted 2026-04-15 · 💻 cs.RO

Scale-Invariant Sampling in Multi-Arm Bandit Motion Planning for Object Extraction

Servet B. Bayraktar , Andreas Orthey , Marc Toussaint This is my paper

Pith reviewed 2026-05-10 13:02 UTC · model grok-4.3

classification 💻 cs.RO
keywords scale-invariant samplingobject extractionmotion planningdisassemblyMAB-RRTnarrow passagesPCA directionssampling strategies
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The pith

Scale-invariant sampling boosts object extraction success rates by an order of magnitude in most tested scenarios.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that a scale-invariant sampling strategy can overcome the collision bottleneck in sampling-based planners for tight object extraction tasks such as removing bolts or pins from narrow spaces. It does so by running a grow-shrink search to locate high-entropy scales in configuration space and then applying principal components analysis to extract useful motion directions from those scales. The resulting sampler is placed inside a multi-arm bandit RRT planner and compared against uniform, obstacle-based, narrow-passage, mate-vector, physics-based, and disassembly BFS baselines on eight 3D scenarios. The experiments show success rates rise by roughly a factor of ten on seven of the eight cases, making general-purpose extraction feasible where conventional sampling fails almost every time.

Core claim

A scale-invariant sampling strategy that first uses a grow-shrink search to identify high-entropy scales and then applies PCA to select principal directions for extraction motions, when embedded in an MAB-RRT planner, raises success rates by one order of magnitude over uniform sampling, obstacle-based sampling, narrow-passage sampling, mate vectors, physics-based planning, and disassembly breadth-first search on seven of eight challenging 3D object extraction scenarios involving bolts, gears, rods, pins, and sockets.

What carries the argument

scale-invariant sampling that combines grow-shrink search for high-entropy scales with PCA for direction selection inside an MAB-RRT planner

If this is right

  • Disassembly tasks with millimeter-scale clearances become solvable by general planners without custom per-object tuning.
  • Sampling effort concentrates on scales that actually produce collision-free extraction trajectories rather than wasting samples on irrelevant resolutions.
  • Multi-arm bandit RRT planners gain a practical way to handle narrow passages that defeat uniform and local sampling heuristics.
  • The same scale-finding step can be reused across different object geometries such as bolts, gears, rods, and sockets.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The grow-shrink plus PCA pattern may transfer to other narrow-passage problems such as assembly sequencing or navigation through cluttered environments.
  • Entropy-driven scale selection could reduce dependence on physics simulation inside disassembly planners by focusing samples before contact is modeled.
  • Extending the search to dynamic or higher-dimensional configuration spaces might reveal whether the identified scales remain stable under added degrees of freedom.

Load-bearing premise

The grow-shrink search reliably identifies high-entropy scales that generalize across scenarios and the PCA directions correspond to useful object extraction motions without additional tuning.

What would settle it

Running the same eight scenarios with the grow-shrink and PCA components disabled and finding no meaningful difference in success rates from the listed baseline strategies would falsify the central claim.

Figures

Figures reproduced from arXiv: 2604.14026 by Andreas Orthey, Marc Toussaint, Servet B. Bayraktar.

Figure 1
Figure 1. Figure 1: Overview about scale-invariant sampling in MAB-RRT. As input, we use a start configuration xstart and a goal region Xgoal. We then search for a high-information entropy scale and initialize the multi-arm bandit with this scale. We then start a MAB￾RRT loop, where an arm is chose, the chosen sampler is used for one RRT update step, and the arm reward is updated. This loop continues until a termination condi… view at source ↗
Figure 2
Figure 2. Figure 2: Visualization of scale-invariant sampling in tunnel passages of different sizes (5 units, 10 units, and 15 units). Final burn-in radius is shown as , and path are shown depending on the type of active sampler: uniform, positive principal component, and negative principal component. Start is marked with , goal with . Valid samples are shown as uniform, positive principal component, negative principal compon… view at source ↗
Figure 3
Figure 3. Figure 3: Environment Comparison: Start vs. End states for selected environments. Each pair shows the initial (left) and final (right) configuration. radius r0 = 1.0, min radius rmin = 1e−6, max radius rmax = 25.0, batch size b = 64, growth factor g = exp (−0.7), shrink factor s = exp (0.9), max steps S = 50, and validity rates αmin = 0.1 and αmax = 0.5. For the Multi-arm bandit, we use a sliding window of Nsliding-… view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of success rate using planners MAB-RRT (ours), RRT + Bridge Sampling [24], RRT + Gaussian Sampling [8], RRT + Obstacle Sam￾pling [2], MateVec-TRRT [17], BK-RRT [55,52], BFS [52], [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Final sampling results across environments (radius set to 1e-6 vs. 25.0). Final radius from grow-shrink shown as , initial radius as . Tree edges shown as . Valid samples: uniform, positive principal component, negative principal component, scale-invariant sampler. Start marked with , goal with . To show the results, we plot the success rate from zero to one hundred per￾cent over time in log scale, as show… view at source ↗
Figure 6
Figure 6. Figure 6: T-Bolt Experiment: MAB dynamics during planning. (a) UCB scores adjust dynamically as the planner gathers reward information. (b) Rapid reward accumulation for cylinder arms indicates their effectiveness in generating valid samples within the narrow passage, while the uniform arm’s reward surges once free space is reached. Uniform, PCA positive, PCA negative. 4.2 Robustness of Scale-Invariant Sampling Anot… view at source ↗
read the original abstract

Object extraction tasks often occur in disassembly problems, where bolts, screws, or pins have to be removed from tight, narrow spaces. In such problems, the distance to the environment is often on the millimeter scale. Sampling-based planners can solve such problems and provide completeness guarantees. However, sampling becomes a bottleneck, since almost all motions will result in collisions with the environment. To overcome this problem, we propose a novel scale-invariant sampling strategy which explores the configuration space using a grow-shrink search to find useful, high-entropy sampling scales. Once a useful sampling scale has been found, our framework exploits this scale by using a principal components analysis (PCA) to find useful directions for object extraction. We embed this sampler into a multi-arm bandit rapidly-exploring random tree (MAB-RRT) planner and test it on eight challenging 3D object extraction scenarios, involving bolts, gears, rods, pins, and sockets. To evaluate our framework, we compare it with classical sampling strategies like uniform sampling, obstacle-based sampling, and narrow-passage sampling, and with modern strategies like mate vectors, physics-based planning, and disassembly breadth first search. Our experiments show that scale-invariant sampling improves success rate by one order of magnitude on 7 out of 8 scenarios. This demonstrates that scale-invariant sampling is an important concept for general purpose object extraction in disassembly tasks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript introduces a scale-invariant sampling approach for sampling-based motion planning in tight object extraction scenarios. It employs a grow-shrink search to identify high-entropy scales in configuration space, followed by PCA to extract principal directions for biased sampling within an MAB-RRT planner. Through experiments on eight 3D scenarios involving bolts, gears, rods, pins, and sockets, the method is shown to outperform classical (uniform, obstacle-based, narrow-passage) and modern (mate vectors, physics-based, disassembly BFS) sampling strategies, achieving up to an order of magnitude higher success rates on seven of the eight test cases.

Significance. The proposed integration of grow-shrink scale search with PCA-based directional sampling in a multi-armed bandit RRT framework addresses a key challenge in narrow-passage motion planning for object extraction. If the reported gains are statistically robust and the method generalizes without extensive tuning, it could advance practical robotics applications in disassembly and maintenance tasks. The empirical comparison to multiple baselines is a strength, but the absence of detailed methodology for scale selection and statistical validation reduces the current significance.

major comments (3)
  1. [Experimental Results] Experimental Results section: The central claim of an order-of-magnitude success-rate improvement on 7 out of 8 scenarios is presented without reporting the number of independent trials, statistical significance tests (e.g., p-values), error bars, or raw success-rate values per scenario and baseline. This information is load-bearing for verifying the empirical contribution.
  2. [Method] Grow-shrink search description: No details are provided on the explored scale range, the precise entropy metric or threshold used to declare a scale 'high-entropy', the search termination criteria, or whether these hyperparameters remain fixed across all eight scenarios. This directly affects the reproducibility and generalization of the scale-invariant claim.
  3. [Method] PCA integration in MAB-RRT: The paper does not specify how many principal components are retained, the exact mechanism by which these directions bias the sampling distribution, or any validation that the top eigenvectors align with feasible extraction trajectories rather than irrelevant variance (e.g., rotation about an axis). This is necessary to substantiate that the PCA step produces useful directions without per-scenario retuning.
minor comments (2)
  1. [Abstract] Abstract: The term 'mate vectors' is used without definition or citation; a brief explanation or reference would improve clarity for readers unfamiliar with the baseline.
  2. [Throughout] Notation and terminology: Ensure consistent capitalization and phrasing for 'scale-invariant sampling' and 'MAB-RRT' throughout the text and figures.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We appreciate the referee's comments, which highlight important aspects for improving the manuscript's clarity and rigor. Below we provide point-by-point responses to the major comments.

read point-by-point responses

  1. Referee: [Experimental Results] Experimental Results section: The central claim of an order-of-magnitude success-rate improvement on 7 out of 8 scenarios is presented without reporting the number of independent trials, statistical significance tests (e.g., p-values), error bars, or raw success-rate values per scenario and baseline. This information is load-bearing for verifying the empirical contribution.

    Authors: We agree that these details are necessary to fully support the empirical claims. We will revise the Experimental Results section to include the number of independent trials, error bars on the success rates, the raw success-rate values for each scenario and method, and results from statistical significance tests such as p-values from appropriate non-parametric tests. revision: yes

  2. Referee: [Method] Grow-shrink search description: No details are provided on the explored scale range, the precise entropy metric or threshold used to declare a scale 'high-entropy', the search termination criteria, or whether these hyperparameters remain fixed across all eight scenarios. This directly affects the reproducibility and generalization of the scale-invariant claim.

    Authors: We will augment the description of the grow-shrink search to include the explored scale range, the entropy metric and threshold for high-entropy scales, the search termination criteria, and note that these parameters were held constant across the eight scenarios. revision: yes

  3. Referee: [Method] PCA integration in MAB-RRT: The paper does not specify how many principal components are retained, the exact mechanism by which these directions bias the sampling distribution, or any validation that the top eigenvectors align with feasible extraction trajectories rather than irrelevant variance (e.g., rotation about an axis). This is necessary to substantiate that the PCA step produces useful directions without per-scenario retuning.

    Authors: We will clarify the PCA integration by specifying the number of principal components retained, detailing how the principal directions are used to bias the sampling distribution in the MAB-RRT, and providing evidence or discussion that these directions align with feasible extraction trajectories. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical evaluation of algorithmic sampler against external baselines

full rationale

The paper describes an algorithmic pipeline (grow-shrink search for high-entropy scale followed by PCA for biased directions inside MAB-RRT) and reports success-rate improvements from direct experiments on eight scenarios versus independent baselines (uniform, obstacle-based, narrow-passage, mate-vector, physics-based, and BFS disassembly). No equations, predictions, or first-principles claims are presented that reduce by construction to fitted parameters, self-definitions, or self-citations internal to the work. The reported order-of-magnitude gains are measured outcomes, not tautological outputs of the method's own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The approach assumes configuration-space sampling can be made scale-invariant through iterative search and that principal components capture extraction-relevant directions; no explicit free parameters or invented entities are named in the abstract.

axioms (2)
  • domain assumption Grow-shrink search will locate high-entropy sampling scales that improve exploration in narrow passages.
    Invoked to justify the core sampling strategy for object extraction tasks.
  • domain assumption PCA on samples at the chosen scale yields directions useful for extraction motions.
    Central to exploiting the found scale for planning.

pith-pipeline@v0.9.0 · 5551 in / 1350 out tokens · 49569 ms · 2026-05-10T13:02:21.270872+00:00 · methodology

discussion (0)

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