Pith. sign in

REVIEW 3 major objections 4 minor 36 references

BridgeFlow: Fast and Robust SE(2)-Equivariant Motion Planning with Flow Matching

T0 review · 3 major / 4 minor · reviewed 2026-08-02 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This paper claims that exact SE(2)-equivariant motion planning can be achieved with a standard network by canonicalizing tasks into a unified reference frame, and that pairing a Brownian bridge prior with context-aware optimal transport mak

desk verdict Solid 2D flow-matching planner with a neat canonicalization proof, but the 7-DoF Franka generalization claim is not supported as written. read the letter →

arxiv 2607.14725 v1 pith:Z5XCQ6Y6 submitted 2026-07-16 cs.RO

Xinzhe Zhou , Xuyang Wang , Xiaoming Duan , Jianping He This is my paper
classification cs.RO
keywords motionplanningSE(2)-equivarianceflowmatchingBrownianbridgepriormini-batchoptimaltransportclassifier-freeguidancecanonicalizationgenerativetrajectoryprediction
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

BridgeFlow sets out to break the usual trade-off in learning-based motion planning between spatial generalization and inference speed. Instead of building equivariance into the network, it rotates and translates every task into a canonical frame—start at the origin, goal on the positive x-axis—runs a standard U-Net in that frame, and rotates the predicted velocities back, which the paper proves yields strict SE(2)-equivariance. It pairs this with a Brownian bridge prior that anchors trajectories at start and goal and context-aware mini-batch optimal transport that restricts pairings to identical tasks, straightening the learned flow field. Classifier-free guidance on occupancy maps bakes obstacle avoidance into the vector field. If these claims hold, a single network can plan collision-free trajectories in 2–5 integration steps and generalize zero-shot to rotated, translated, or entirely unseen environments, with reported gains of up to 15× inference speed and roughly 2× valid trajectory rate over baselines.

What carries the argument

The paper's load-bearing object is the task-centric canonicalization module: a deterministic map T_can(p)=R_−θ(p−s) that translates the start to the origin and rotates the start-goal vector onto the positive x-axis, with the inverse rotation applied after inference. The Brownian bridge prior p_info_i = μ_lin,i + σ_prior sqrt(γ_i(1−γ_i)) ε sets the variance to zero at both endpoints, making the prior itself SE(2)-equivariant and letting the network learn zero velocity at endpoints. Context-aware mini-batch optimal transport solves the assignment only within trajectories sharing the same task context, preventing cross-context pairings that would destabilize training. Classifier-free guidance w

What would settle it

Test the manipulator claim with a tabletop rotation that is not a multiple of 90°; if success/valid rates fall far below the reported ~80% when the table's absolute pose relative to the fixed robot base changes, the decoded trajectories are not strictly SE(2)-equivariant. Alternatively, set start equal to goal in the 2D task: the heading angle θ = atan2(g_y−s_y, g_x−s_x) is undefined, so the canonicalization must either fail or adopt an ad hoc convention, contradicting 'strict' equivariance.

Watch

Extended reading notes

Core claim

The central claim is Theorem 2: for any rigid transformation T ∈ SE(2), the learned vector field obeys v_θ(T(x_t), t | T(P)) = R_α v_θ(x_t, t | P) exactly, even though the backbone is a standard U-Net with no equivariant layers. The mechanism is a deterministic canonicalization operator that maps the start to the origin and the start-to-goal vector to the x-axis; because the Brownian bridge prior commutes with rigid transformations, the canonical inputs of a task and its transformed version coincide exactly, so the network produces the same canonical velocities and decanonicalization rotates them back. The paper further claims that combining this with a Brownian bridge prior and context-awar

Load-bearing premise

The framework's strict equivariance assumes the whole task is captured by start, goal, and occupancy map; in the manipulator experiment, where planning is described as happening in 7-DoF joint space, that assumption fails because rotating the workspace does not rotate the robot's joint limits or self-collision geometry, and even the 2D proof presumes start and goal are distinct.

Editorial extensions

If this is right

  • Exact SE(2)-equivariance becomes a preprocessing step rather than a network-design constraint, so any standard architecture can inherit spatial generalization.
  • The Brownian bridge prior and context-aware OT straighten the flow enough that 2–5 integration steps suffice, moving planning toward real-time control loop rates.
  • Because occupancy-map conditioning is baked in via classifier-free guidance, no costly cost-function gradients are needed at inference for obstacle avoidance.
  • Zero-shot transfer to rotated/translated task versions is claimed without augmentation, with the manipulator experiment reporting 80% valid trajectories on unseen SE(2) transfers versus roughly 20% for diffusion baselines.
  • Endpoint constraints are satisfied naturally: the bridge prior's zero variance at boundaries teaches the network a zero vector field there, so the ODE solver needs no endpoint in-painting.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: The same canonicalize-and-decanonicalize recipe should extend to SE(3), but only up to the residual symmetry around the start–goal axis; the clean cancellation in the 2D proof depends on the single heading angle, so an SE(3) version would need to address that leftover rotation.
  • Editorial inference: The manipulator experiment is best read as evidence of Cartesian/end-effector equivariance. For a fixed-base arm, rotating the tabletop does not rotate the robot's joint limits or self-collision geometry, so the official '7-DoF joint space' framing carries an extra assumption the paper does not state.
  • Editorial inference: A cleaner stress test of the core idea would be a free-floating mobile robot in the plane, where the robot's body itself transforms with SE(2); there the canonicalization claim would be exact and the speedup could be measured without the joint-space confound.
  • Editorial extension: Since the Brownian bridge prior and the occupancy-map guidance seem to reinforce each other, a natural variant is to condition the prior's noise scale on local obstacle density—an option the paper leaves untouched.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper proposes BridgeFlow, an SE(2)-equivariant flow-matching motion planner that combines a Brownian-bridge informative prior, context-aware mini-batch optimal transport, classifier-free guidance on occupancy maps, and a task-centric canonicalization module. The central theoretical claim is that the canonicalization module yields strict SE(2)-equivariance with a standard U-Net, avoiding expensive equivariant backbones, while the Brownian-bridge prior and context-aware OT straighten the flow for fast few-step inference. The method is evaluated on dense 2D point-mass environments and on a 7-DoF Franka manipulation task, reporting large speedups and improved valid rates over MPD and FlowMP baselines, plus zero-shot generalization to unseen spatial transformations and unseen environments.

Significance. If the claims hold, the paper makes a useful practical contribution: it shows that exact equivariance can be achieved by input canonicalization rather than by specialized network architectures, and that an informative prior paired with context-aware OT can accelerate flow-matching inference while improving trajectory validity. The proof of Theorem 2 is clean and the algebraic cancellation in Theorem 1 is internally consistent under the stated conditions. The 2D experimental results are promising and the idea of environment-aware CFG is well-motivated. However, the significance is substantially undercut by the 7-DoF Franka evaluation, whose SE(2)-equivariance premise is unsupported, and by the absence of any statistical characterization of the reported improvements.

major comments (3)
  1. [§IV-C, Table II] The Franka experiments are described as evaluating 'pure SE(2) rigid body transformations' of the training tasks, but the text explicitly states that planning occurs in '7-DoF joint space' (Sec. IV-C, RQ1). For a fixed-base manipulator, a joint configuration q∈R^7 has no natural SE(2) action: rotating/translating the tabletop changes Cartesian goal poses but not the robot's kinematic map, joint limits, or self-collision geometry. If the generated trajectories are instead Cartesian end-effector waypoints, the paper never says so, and SE(2) does not preserve joint-limit or collision feasibility. Therefore the abstract's claim of robust generalization on a 7-DoF manipulator under arbitrary spatial transformations is not supported by the experiments as presented. This is load-bearing and requires either a reworked evaluation in Cartesian workspace with explicit IK/feasibility handling, or re
  2. [§III-B2, Theorem 1] The 'exact reduction margin' is positive only under two unstated and unverified conditions: (i) the dataset-level symmetry assumption E[δ]=0 (the paper writes δ̄→0) and (ii) the imposed bound σ̄²<1. The first is dataset-dependent and not checked; the second is asserted without demonstrating that the chosen σ_prior satisfies it. Moreover, since the informative prior is constructed around μ_lin plus endpoint-anchored noise, the cost drop relative to a unit-variance Gaussian is partly baked into the definition. The theorem should be stated as a conditional inequality with explicit hypotheses, and those hypotheses should be verified in the experimental setup.
  3. [Tables I–III] All reported metrics are single-run point estimates. There are no standard deviations, no number of seeds, and no significance tests. This is particularly problematic for the central empirical claims, e.g., Table II's VR 80.0% vs 21.0% on unseen SE(2) transfers, or Table I's unseen-distribution VR 39.4% vs 29.9%. Without error bars or seed counts, the reader cannot assess whether the improvements are robust or within noise. Please report mean±std over at least 3 seeds and state the number of test contexts per setting.
minor comments (4)
  1. [§III-E, Theorem 2] The canonicalization operator and the proof require s≠g. If s=g, the heading angle θ is undefined and the canonical frame degenerates. The theorem statement should include this non-degeneracy condition. Also, for d=3, the notation T(p)=Rp+d with R∈SO(2) is ambiguous unless the rotation is embedded in the first two coordinates; this should be clarified, especially since the Franka experiments are explicitly 3D.
  2. [Table I] The 'MPD Prior' rows are reported in the table but never discussed in the text. This is a relevant comparison point—MPD Prior 15 steps has inference time 0.038s, which reduces the claimed 15× speedup to roughly 5×—and should either be analyzed or removed.
  3. [Algorithm 1] Line 15 returns 'L_FM/B', which appears to be a typo. It should return L_FM or a clearly defined loss variable.
  4. [§IV-B4] The claim that the network 'naturally learns that the vector field at these fixed endpoints must be exactly zero' is plausible because the regression target at boundary waypoints is zero for all t, but this is not a formal guarantee. The sentence should be softened to reflect that the training objective encourages this behavior.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's theoretical claims are constructive algebraic identities, not fitted predictions.

full rationale

The derivation chain in BridgeFlow is self-contained. Theorem 1 ('Transport Cost Reduction') is a direct computation: C_std - C_info = ||mu_lin||^2 + 2<mu_lin,E[delta]> + (1 - sigma_bar^2)D follows from the definitions of the two priors and the linear interpolation path; the positivity conclusion uses the stated assumptions sigma_bar^2<1 and s != g, and the symmetry assumption on obstacles. This is a theorem about the priors, not a parameter fitted to data and then relabeled as a prediction. Theorem 2 is a constructive equivariance guarantee: the canonicalization map T_can(p)=R_-theta(p-s) sends any SE(2)-transformed task back to the same canonical inputs, so any deterministic network produces the same canonical field, and decanonicalizing by R_theta gives exactly the required pushforward v_tilde = R_alpha v. Proposition 1 is the standard equivariance of an isotropic Gaussian bridge. No load-bearing self-citation appears: the only co-authored reference ([32], a related-work item by two of the present authors) is not used to justify the central results. The Franka experiment concern (SE(2) generalization claimed from 2D canonicalization in a 7-DoF joint-space setting) is a potentially serious validity/generalization gap and should be assessed as a correctness risk, but it is not a circular step of the derivation: no equation in the paper reduces to its own input, and no fitted quantity is renamed as a prediction. Accordingly the circularity score is 0.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claims rest on (i) an elementary but correct transport-cost identity whose 'strictly positive' margin requires the self-flagged dataset symmetry E[delta]=0 and the user-chosen bound sigma-bar^2<1; (ii) equivariance-by-canonicalization, whose 2D algebra is exact under s≠g; and (iii) an empirical evaluation that is single-run, code-free, and built on a questionable joint-space SE(2) premise for the arm experiment. The named free knobs — sigma_prior, omega, p_drop — are all undisclosed. No new physical entities are postulated; the graviton-problem ledger is empty.

free parameters (3)
  • sigma_prior (Brownian bridge noise scale) = not disclosed
    Scales the bridge prior variance; the Remark in Sec III-B2 calls it 'a critical hyperparameter balancing transport efficiency and generative diversity'; it directly enters Theorem 1's margin via sigma-bar^2.
  • omega (CFG guidance weight) = not disclosed
    Extrapolation strength v_CFG = v_empty + omega*(v_M - v_empty); described as a 'crucial control lever' (Sec III-D); value and tuning protocol never reported.
  • p_drop (environment-conditioning dropout) = not disclosed
    Dropout probability for maskable environment conditioning in CFG training (Sec III-D); never reported, though it shapes the unconditional field used at inference.
assumptions (6)
  • domain assumption Dataset-wide deformation symmetry: E[delta] = 0
    Theorem 1's 'strictly positive' margin relies on 'the expected deformation neutralizes (delta-bar -> 0)' for symmetrically distributed obstacles (Sec III-B2 Proof). The paper flags this as a dataset property, not a proof.
  • ad hoc to paper Prior noise bound sigma-bar^2 < 1
    Authors 'strictly bound the base noise' so the (1 - sigma-bar^2)D term stays positive (Sec III-B2). This is a user choice ensuring the theorem's conclusion, not an identity.
  • domain assumption Start != goal for canonical frame
    theta = atan2(g_y - s_y, g_x - s_x) is undefined when s = g (Sec III-E2); the degenerate edge case is never addressed.
  • domain assumption Franka tabletop transfers are SE(2)-equivariant in the planning space
    Sec IV-A1 asserts test tasks B->C / D->B are 'pure SE(2) rigid body transformations' of A->B/C/D although planning is described in 7-DoF joint space, where a fixed-base arm is not SE(2)-equivariant. This premise supports the Franka RQ3 numbers.
  • domain assumption RRT-Connect + B-spline experts define the target distribution
    All training and evaluation use this expert generator (Sec IV-A1); completeness and reachability of the expert distribution are assumed, not analyzed.
  • domain assumption Kinematic time-reversibility for data augmentation
    Start-goal swapping doubles the dataset 'without incurring additional simulation overhead' (Sec IV-A1); valid for drift-free reversible kinematics but unchecked for the Franka case.

how reviews work

0 comments
Cite this review

Pith. "Pith review of BridgeFlow: Fast and Robust SE(2)-Equivariant Motion Planning with Flow Matching." pith.science (2026). https://pith.science/paper/Z5XCQ6Y6

@misc{pith2026260714725,
  author       = {Pith},
  title        = {Pith review of: BridgeFlow: Fast and Robust SE(2)-Equivariant Motion Planning with Flow Matching},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Z5XCQ6Y6}},
  note         = {Machine review of arXiv:2607.14725}
}
read the original abstract

In robotic motion planning, equivariance to rigid body transformations is crucial for robust spatial generalization. However, current learning-based planners face a critical dilemma: they either lack inherent equivariance, treating transformed tasks as novel scenarios, or enforce it via computationally expensive specialized architectures that bottleneck real-time inference. To break this trade-off, we propose BridgeFlow, a fast and strictly SE(2)-equivariant generative motion planning framework. Rather than relying on heavy equivariant networks, BridgeFlow achieves exact spatial equivariance via a lightweight task-centric canonicalization module, enabling generalization using standard architectures. To further accelerate inference, we pair a Brownian bridge informative prior with context-aware mini-batch optimal transport. This constructs a straightened vector field that minimizes transport costs and stabilizes training. Furthermore, environmental awareness is explicitly embedded via Classifier-Free Guidance. Evaluations in dense 2D environments and on a 7-DoF Franka manipulator demonstrate that BridgeFlow achieves up to a 15x inference speedup and a 2x higher valid trajectory rate over state-of-the-art diffusion baselines, alongside robust generalization to entirely unseen environments and arbitrary spatial transformations.

Figures

Figures reproduced from arXiv: 2607.14725 by the authors.

Figure 1
Figure 1. Comparison of initial priors. The Brownian bridge [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Task-Centric Canonicalization Framework. The system achieves strict [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Experimental setups for evaluating generative mo [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Visualization of the 3-step Flow Matching generative process in the PointMass2D Dense environment. The top [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

36 extracted references · 2 linked inside Pith

  1. [1]

    Rapidly-exploring random trees: A new tool for path planning

    LaValle, Steven. “Rapidly-exploring random trees: A new tool for path planning.” Research Report 9811, 1998

    1998

  2. [2]

    RRT-connect: An efficient approach to single-query path planning

    Kuffner, James J., and Steven M. LaValle. “RRT-connect: An efficient approach to single-query path planning.” IEEE International Confer- ence on Robotics and Automation (ICRA), 2000

    2000

  3. [3]

    CHOMP: Gradient optimization techniques for efficient motion planning

    Ratliff, Nathan, et al. “CHOMP: Gradient optimization techniques for efficient motion planning.” IEEE International Conference on Robotics and Automation (ICRA), 2009

    2009

  4. [4]

    STOMP: Stochastic trajectory optimiza- tion for motion planning

    Kalakrishnan, Mrinal, et al. “STOMP: Stochastic trajectory optimiza- tion for motion planning.” IEEE International Conference on Robotics and Automation (ICRA), 2011

    2011

  5. [5]

    Finding locally optimal, collision-free tra- jectories with sequential convex optimization

    Schulman, John, et al. “Finding locally optimal, collision-free tra- jectories with sequential convex optimization.” Robotics: science and systems (RSS), 2013

    2013

  6. [6]

    Continuous-time Gaussian process motion planning via probabilistic inference

    Mukadam, Mustafa, et al. “Continuous-time Gaussian process motion planning via probabilistic inference.” The International Journal of Robotics Research (IJRR), 2018

    2018

  7. [7]

    Denoising diffusion probabilistic models

    Ho, Jonathan, Ajay Jain, and Pieter Abbeel. “Denoising diffusion probabilistic models.” Advances in neural information processing systems (NeurIPS), 2020

    2020

  8. [8]

    Denoising diffu- sion implicit models

    Song, Jiaming, Chenlin Meng, and Stefano Ermon. “Denoising diffu- sion implicit models.” Proceedings of the International Conference on Learning Representations (ICLR), 2021

    2021

Show all 36 references
  1. [9]

    Motion planning diffusion: Learning and plan- ning of robot motions with diffusion models

    Carvalho, Joao, et al. “Motion planning diffusion: Learning and plan- ning of robot motions with diffusion models.” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2023

    2023

  2. [10]

    Motion planning diffusion: Learning and adapt- ing robot motion planning with diffusion models

    Carvalho, Joao, et al. “Motion planning diffusion: Learning and adapt- ing robot motion planning with diffusion models.” IEEE Transactions on Robotics, 2025

    2025

  3. [11]

    Edmp: Ensemble-of-costs-guided diffusion for motion planning

    Saha, Kallol, et al. “Edmp: Ensemble-of-costs-guided diffusion for motion planning.” IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2024

    2024

  4. [12]

    Hierarchical diffu- sion motion planning with task-conditioned uncertainty-aware priors

    Kim, Amelie Minji, Anqi Wu, and Ye Zhao. “Hierarchical diffu- sion motion planning with task-conditioned uncertainty-aware priors.” arXiv preprint arXiv:2509.25685, 2025

    2025

  5. [13]

    Presto: Fast motion planning using diffusion models based on key-configuration environment representation

    Seo, Mingyo, et al. “Presto: Fast motion planning using diffusion models based on key-configuration environment representation.” IEEE International Conference on Robotics and Automation (ICRA), 2025

    2025

  6. [14]

    Diffusion policy: Visuomotor policy learning via action diffusion

    Chi, Cheng, et al. “Diffusion policy: Visuomotor policy learning via action diffusion.” The International Journal of Robotics Research (IJRR), 2025

    2025

  7. [15]

    Equivariant diffusion policy

    Dian Wang, Stephen Hart, et al. “Equivariant diffusion policy.” Pro- ceedings of The 8th Conference on Robot Learning (PMLR), 2025

    2025

  8. [16]

    EquiBot: SIM (3)-Equivariant Diffusion Policy for Generalizable and Data Efficient Learning

    Yang, Jingyun, et al. “EquiBot: SIM (3)-Equivariant Diffusion Policy for Generalizable and Data Efficient Learning.” Proceedings of The 8th Conference on Robot Learning (PMLR), 2025

    2025

  9. [17]

    ”Et-seed: Efficient trajectory-level se (3) equivari- ant diffusion policy.” Proceedings of the International Conference on Learning Representations (ICLR), 2024

    Tie, Chenrui, et al. ”Et-seed: Efficient trajectory-level se (3) equivari- ant diffusion policy.” Proceedings of the International Conference on Learning Representations (ICLR), 2024

    2024

  10. [18]

    Diffusion-based generation, optimization, and planning in 3d scenes

    Huang, Siyuan, et al. “Diffusion-based generation, optimization, and planning in 3d scenes.” Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2023

    2023

  11. [19]

    Flow matching for generative modeling

    Lipman, Yaron, et al. “Flow matching for generative modeling.” Pro- ceedings of the International Conference on Learning Representations (ICLR), 2023

    2023

  12. [20]

    Improving and generalizing flow-based gen- erative models with minibatch optimal transport

    Tong, Alexander, et al. “Improving and generalizing flow-based gen- erative models with minibatch optimal transport.” Transactions on Machine Learning Research (TMLR), 2024

    2024

  13. [21]

    The curse of conditions: Analyzing and improving optimal transport for conditional flow-based generation

    Cheng, Ho Kei, and Alexander Schwing. “The curse of conditions: Analyzing and improving optimal transport for conditional flow-based generation.” Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2025

    2025

  14. [22]

    Flowmp: Learning motion fields for robot planning with conditional flow matching

    Nguyen, Khang, et al. “Flowmp: Learning motion fields for robot planning with conditional flow matching.” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2025

    2025

  15. [23]

    Actionflow: Equivariant, accurate, and efficient policies with spatially symmetric flow matching

    Funk, Niklas, et al. “Actionflow: Equivariant, accurate, and efficient policies with spatially symmetric flow matching.” arXiv preprint arXiv:2409.04576, 2024

    2024 arXiv

  16. [24]

    Riemannian flow matching policy for robot motion learning

    Braun, Max, et al. “Riemannian flow matching policy for robot motion learning.” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2024

    2024

  17. [25]

    Stochastic interpolants with data- dependent couplings

    Albergo, Michael S., et al. “Stochastic interpolants with data- dependent couplings.” Proceedings of the 41st International Confer- ence on Machine Learning (ICML), 2024

    2024

  18. [26]

    Classifier-free diffusion guidance

    Ho, Jonathan, and Tim Salimans. “Classifier-free diffusion guidance.” NeurIPS Workshop on Deep Generative Models and Downstream Applications, 2021

    2021

  19. [27]

    Cfg-zero*: Improved classifier-free guidance for flow matching models

    Fan, Weichen, et al. “Cfg-zero*: Improved classifier-free guidance for flow matching models.” arXiv preprint arXiv:2503.18886, 2025

    2025 arXiv

  20. [28]

    Accelerated multi-modal motion plan- ning using context-conditioned diffusion models

    Sandra, Edward, et al. “Accelerated multi-modal motion plan- ning using context-conditioned diffusion models.” arXiv preprint arXiv:2510.14615, 2025

    2025

  21. [29]

    Motion planning networks

    Qureshi, Ahmed H., et al. “Motion planning networks.” International Conference on Robotics and Automation (ICRA), 2019

    2019

  22. [30]

    Motion planning networks: Bridging the gap between learning-based and classical motion planners

    Qureshi, Ahmed Hussain, et al. “Motion planning networks: Bridging the gap between learning-based and classical motion planners.” IEEE Transactions on Robotics, 2020

    2020

  23. [31]

    Constrained motion planning net- works x

    Qureshi, Ahmed Hussain, et al. “Constrained motion planning net- works x.” IEEE Transactions on Robotics, 2021

    2021

  24. [32]

    Learning-based motion planning with mixture density networks

    Wang, Yinghan, Xiaoming Duan, and Jianping He. “Learning-based motion planning with mixture density networks.” IEEE International Conference on Robotics and Automation (ICRA), 2024

    2024

  25. [33]

    Equivalence, invariants and symmetry

    Olver, Peter J. Equivalence, invariants and symmetry. Cambridge University Press, 1995

    1995

  26. [34]

    Group equivariant convolutional networks

    Cohen, Taco, and Max Welling. “Group equivariant convolutional networks.” International conference on machine learning (ICML), 2016

    2016

  27. [35]

    Se (3)-transformers: 3d roto-translation equiv- ariant attention networks

    Fuchs, Fabian, et al. “Se (3)-transformers: 3d roto-translation equiv- ariant attention networks.” Advances in neural information processing systems (NeurIPS), 2020

    2020

  28. [36]

    SE (3)-Equivariant robot learning and control: a tutorial survey

    Seo, Joohwan, et al. “SE (3)-Equivariant robot learning and control: a tutorial survey.” International Journal of Control, Automation and Systems, 2025

    2025

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.