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arxiv: 1907.09574 · v1 · pith:ZNFIRQ5Anew · submitted 2019-07-22 · 💻 cs.RO

LEGO: Leveraging Experience in Roadmap Generation for Sampling-Based Planning

Rahul Kumar , Aditya Mandalika , Sanjiban Choudhury , Siddhartha S. Srinivasa This is my paper

Pith reviewed 2026-05-24 17:45 UTC · model grok-4.3

classification 💻 cs.RO
keywords sampling-based motion planningroadmap generationconditional variational auto-encoderbottleneck regionsprior experiencemotion planningsparse roadmaps
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The pith

LEGO trains CVAEs on bottleneck samples from prior paths to generate sparse effective roadmaps for sampling-based motion planning.

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

The paper addresses the challenge of using past planning experience to build roadmaps that are both sparse for fast search and positioned to connect low-cost feasible paths. Standard CVAE training on full shortest paths can fail with complex obstacles or when test environments differ from training data. LEGO instead selects training targets only from bottleneck regions that uniform sampling struggles to hit and ensures those points are spread across diverse areas. The authors formally define these two selection criteria and prove performance guarantees for the resulting roadmaps. Experiments across planning problems, including robot arm tasks, show gains over both heuristic and learned baselines.

Core claim

LEGO trains the CVAE with target samples drawn exclusively from bottleneck regions along near-optimal paths that are otherwise difficult to sample uniformly, while also ensuring the samples are distributed across diverse regions to maximize the chance a feasible path exists. These properties are formally defined, and performance guarantees are proved for the algorithm that uses them.

What carries the argument

Two explicit criteria for choosing CVAE target samples: membership in bottleneck regions of near-optimal paths, plus spread across diverse regions.

If this is right

  • Roadmaps produced by LEGO are sparser yet more likely to contain low-cost feasible paths than those trained on complete shortest paths.
  • Formal performance guarantees apply once the two selection criteria are satisfied.
  • Significant improvements appear on robot-arm and other motion-planning benchmarks relative to both heuristics and prior learned methods.
  • The approach mitigates failures that occur with complex obstacle layouts or train-test mismatch.

Where Pith is reading between the lines

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

  • If bottleneck extraction from the prior data set is noisy, the training targets lose their intended advantage over uniform sampling.
  • The reported gains may shrink when test environments introduce obstacle configurations far outside the training distribution.
  • The same bottleneck-plus-diversity filter could be applied to improve other learned samplers beyond CVAEs.

Load-bearing premise

The prior dataset supplies shortest-path solutions from which bottleneck regions can be extracted reliably, and the learned distribution generalizes to test scenes whose obstacles may differ from training.

What would settle it

A held-out environment in which a LEGO-generated roadmap finds no feasible path within the allotted samples while a uniform sampler or a shortest-path-trained CVAE succeeds.

Figures

Figures reproduced from arXiv: 1907.09574 by Aditya Mandalika, Rahul Kumar, Sanjiban Choudhury, Siddhartha S. Srinivasa.

Figure 1
Figure 1. Figure 1: Comparison of roadmaps generated from (a) uniform Halton sequence [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The LEGO framework for training a CVAE to predict a roadmap. (a) The training process for learning a generative sampling distribution using a CVAE. The input is a pair of candidate samples and feature vector. (b) At test time, the model is sampled to get vertices which are then composed with a constant sparse graph to get a final roadmap. We present an algorithmic framework, Leveraging Experience with Grap… view at source ↗
Figure 3
Figure 3. Figure 3: (a) The training input generated by SHORTESTPATH. (b) Failure of SHORTESTPATH model to route through gaps (c) Another failure of the model due to unexpected obstacles (d) The training input generated by LEGO. Diverse shortest paths are generated followed by extraction of bottleneck nodes. A. General Train and Test Procedure To summarize, the overall training framework is as follows: 1) Load a database of p… view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of samples (distribution illustrated as heatmap) generated [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of samples (green) generated by all baseline algorithms on a 2D problem, planning from start (blue) to goal (red). [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparisons of SHORTESTPATH against LEGO on different problem domains. In each problem domain (column), success rate (top), normalized path lengths (middle) and solutions determined on the roadmaps constructed using samples generated by the two samplers (bottom) are shown. 250 500 750 1000 1250 Number of Samples 0.2 0.4 0.6 0.8 1.0 Success Rate Halton ShortestPath LEGO (a) Corrupted Environment 1 250 500 7… view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of samplers on corrupted environments, i.e., different [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: A simple illustration of the CVAE framework setup for training with [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Samples generated by CVAE trained with different latent variable [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 12
Figure 12. Figure 12: Environments sampled in R3 to train the CVAE. c) Snake Robot Planning: For R 5 , the training procedure was similar to that in the R 2 problems. The training procedure for the robot in R 9 consisted of a Gdense with 6000 samples which was used to plan for 20 planning problems in each of 20 randomly generated 2D environments [PITH_FULL_IMAGE:figures/full_fig_p012_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Environments sampled in R9 to train the CVAE. d) Manipulator Arm Planning: The training data consisted of 20 random environments where the obstacles in the environment were arbitrarily repositioned. In each of the randomly generated environment, 50 planning problems were considered as an input to the train the CVAE model [PITH_FULL_IMAGE:figures/full_fig_p012_13.png] view at source ↗
Figure 11
Figure 11. Figure 11: Environments sampled in R2 to train the CVAE. b) N-Link Arm Planning: The training procedure for the robot in R 3 , R 5 consisted of a Gdense with 6000 samples which was used to plan for 20 planning problems in each of 20 randomly generated 2D environments [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 16
Figure 16. Figure 16: Performance of LEGO on different roadmaps. The parameter p denotes the ratio of Halton samples to learned samples in the roadmap). R 9 problems. Not however, that this sparse roadmap contains both the learned samples as well as samples generated from Halton sequence. While the learned samples are concentrated near the bottleneck regions and along diverse paths, Halton samples ensure the coverage over the … view at source ↗
Figure 17
Figure 17. Figure 17: Samples generated by LEGO for manipulator arm planning. The blue dots represent the end effector positions corresponding to the samples [PITH_FULL_IMAGE:figures/full_fig_p013_17.png] view at source ↗
Figure 15
Figure 15. Figure 15: Comparison of SHORTESTPATH against BOTTLENECKNODE (top row) and DIVERSEPATHSET (bottom row) on success rate (left column) and normalized path length (right column). C. Roadmap Construction To evaluate the performance of LEGO, we construct sparse roadmaps, Gsparse. The sparse graph consisted of 200 samples in R 2 , R 5 problems and 300 samples in case of R 7 , R 8 and 200 400 600 800 1000 1200 Number of Sa… view at source ↗
read the original abstract

We consider the problem of leveraging prior experience to generate roadmaps in sampling-based motion planning. A desirable roadmap is one that is sparse, allowing for fast search, with nodes spread out at key locations such that a low-cost feasible path exists. An increasingly popular approach is to learn a distribution of nodes that would produce such a roadmap. State-of-the-art is to train a conditional variational auto-encoder (CVAE) on the prior dataset with the shortest paths as target input. While this is quite effective on many problems, we show it can fail in the face of complex obstacle configurations or mismatch between training and testing. We present an algorithm LEGO that addresses these issues by training the CVAE with target samples that satisfy two important criteria. Firstly, these samples belong only to bottleneck regions along near-optimal paths that are otherwise difficult-to-sample with a uniform sampler. Secondly, these samples are spread out across diverse regions to maximize the likelihood of a feasible path existing. We formally define these properties and prove performance guarantees for LEGO. We extensively evaluate LEGO on a range of planning problems, including robot arm planning, and report significant gains over heuristics as well as learned baselines.

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

1 major / 0 minor

Summary. The paper introduces LEGO, an algorithm for leveraging prior experience to generate roadmaps in sampling-based motion planning. It trains a CVAE on target samples from bottleneck regions along near-optimal paths (hard for uniform sampling) that are also diverse, formally defines these properties, proves performance guarantees, and reports significant empirical gains over heuristics and learned baselines on problems including robot arm planning.

Significance. If the formal definitions, performance guarantees, and empirical gains hold under distribution shift, LEGO could provide a more reliable method than standard CVAE training for producing sparse, effective roadmaps from prior data, addressing documented failure modes in complex or mismatched environments.

major comments (1)
  1. [Abstract and performance guarantees] Abstract and performance guarantees section: the two criteria (bottleneck samples on near-optimal paths + diversity) are claimed to address mismatch between training and testing environments, but the guarantees appear conditioned only on the prior dataset providing reliable shortest-path solutions; no formal analysis or bounds are provided for generalization when obstacle configurations differ between train and test, which the abstract identifies as a failure mode for the baseline CVAE.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback. We address the major comment below and will make corresponding revisions to clarify the scope of our claims and guarantees.

read point-by-point responses

  1. Referee: [Abstract and performance guarantees] Abstract and performance guarantees section: the two criteria (bottleneck samples on near-optimal paths + diversity) are claimed to address mismatch between training and testing environments, but the guarantees appear conditioned only on the prior dataset providing reliable shortest-path solutions; no formal analysis or bounds are provided for generalization when obstacle configurations differ between train and test, which the abstract identifies as a failure mode for the baseline CVAE.

    Authors: We agree with the observation. The formal performance guarantees are conditioned on the prior dataset containing reliable near-optimal paths; they establish that the two criteria produce roadmaps with the desired sparsity and coverage properties under that assumption. The abstract's statement that the criteria address mismatch is supported by the empirical results (including on problems with complex obstacles and train-test differences), but we do not provide formal generalization bounds for arbitrary changes in obstacle configurations. We will revise the abstract to more precisely distinguish the theoretical guarantees from the empirical benefits under mismatch, and we will add a paragraph in the discussion section explicitly acknowledging this limitation of the analysis. revision: yes

Circularity Check

0 steps flagged

No circularity detected; derivation relies on external prior data and formal proofs

full rationale

The abstract and provided text describe training a CVAE on an external prior dataset of shortest paths, with target samples selected according to explicitly defined criteria (bottleneck regions and diversity). The paper claims to formally define these properties and prove performance guarantees, but no equations, self-citations, or reductions are visible that make any prediction equivalent to its inputs by construction. The central claims depend on the independent prior dataset and stated proofs rather than tautological fitting or self-referential definitions, rendering the derivation self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that shortest paths in the training set can be used to identify bottleneck regions and that the resulting CVAE distribution transfers to new scenes.

axioms (1)
  • domain assumption Shortest paths in the prior dataset identify bottleneck regions that are difficult for uniform sampling.
    Invoked when defining the target samples for CVAE training.

pith-pipeline@v0.9.0 · 5745 in / 1073 out tokens · 23441 ms · 2026-05-24T17:45:02.702590+00:00 · methodology

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Reference graph

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