TopoCut: Learning Multi-Step Cutting with Spectral Rewards and Discrete Diffusion Policies

Liquan Wang, Jiangjie Bian, Eric Heiden, Animesh Garg
Proceedings of The 9th Conference on Robot Learning, PMLR 305:1282-1310, 2025.

Abstract

Robotic manipulation tasks involving cutting deformable objects remain challenging due to complex topological behaviors, difficulties in perceiving dense object states, and the lack of efficient evaluation methods for cutting outcomes. In this paper, we introduce TopoCut, a comprehensive benchmark for multi-step robotic cutting tasks that integrates a cutting environment and generalized policy learning. TopoCut is built upon three core components: (1) a high-fidelity simulation environment based on a particle-based elastoplastic solver with compliant von Mises constitutive models, augmented by a novel damage-driven topology discovery mechanism for accurate tracking of multiple cutting pieces; (2) a comprehensive reward design that combines this topology discovery with a pose-invariant spectral reward model based on Laplace–Beltrami eigenanalysis, enabling consistent and robust assessment of cutting quality; and (3) an integrated policy learning pipeline, where a dynamics-informed perception module predicts topological evolution and produces particle-wise, topology-aware embeddings to support PDDP—Particle-based Score-Entropy Discrete Diffusion Policy—for goal-conditioned policy learning. Extensive experiments demonstrate that TopoCut enables trajectory generation, scalable learning, precise evaluation, and strong generalization across diverse object geometries, scales, poses, and cutting goals.

Cite this Paper

BibTeX
@InProceedings{pmlr-v305-wang25c, title = {TopoCut: Learning Multi-Step Cutting with Spectral Rewards and Discrete Diffusion Policies}, author = {Wang, Liquan and Bian, Jiangjie and Heiden, Eric and Garg, Animesh}, booktitle = {Proceedings of The 9th Conference on Robot Learning}, pages = {1282--1310}, year = {2025}, editor = {Lim, Joseph and Song, Shuran and Park, Hae-Won}, volume = {305}, series = {Proceedings of Machine Learning Research}, month = {27--30 Sep}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v305/main/assets/wang25c/wang25c.pdf}, url = {https://proceedings.mlr.press/v305/wang25c.html}, abstract = {Robotic manipulation tasks involving cutting deformable objects remain challenging due to complex topological behaviors, difficulties in perceiving dense object states, and the lack of efficient evaluation methods for cutting outcomes. In this paper, we introduce TopoCut, a comprehensive benchmark for multi-step robotic cutting tasks that integrates a cutting environment and generalized policy learning. TopoCut is built upon three core components: (1) a high-fidelity simulation environment based on a particle-based elastoplastic solver with compliant von Mises constitutive models, augmented by a novel damage-driven topology discovery mechanism for accurate tracking of multiple cutting pieces; (2) a comprehensive reward design that combines this topology discovery with a pose-invariant spectral reward model based on Laplace–Beltrami eigenanalysis, enabling consistent and robust assessment of cutting quality; and (3) an integrated policy learning pipeline, where a dynamics-informed perception module predicts topological evolution and produces particle-wise, topology-aware embeddings to support PDDP—Particle-based Score-Entropy Discrete Diffusion Policy—for goal-conditioned policy learning. Extensive experiments demonstrate that TopoCut enables trajectory generation, scalable learning, precise evaluation, and strong generalization across diverse object geometries, scales, poses, and cutting goals.} }
Endnote
%0 Conference Paper %T TopoCut: Learning Multi-Step Cutting with Spectral Rewards and Discrete Diffusion Policies %A Liquan Wang %A Jiangjie Bian %A Eric Heiden %A Animesh Garg %B Proceedings of The 9th Conference on Robot Learning %C Proceedings of Machine Learning Research %D 2025 %E Joseph Lim %E Shuran Song %E Hae-Won Park %F pmlr-v305-wang25c %I PMLR %P 1282--1310 %U https://proceedings.mlr.press/v305/wang25c.html %V 305 %X Robotic manipulation tasks involving cutting deformable objects remain challenging due to complex topological behaviors, difficulties in perceiving dense object states, and the lack of efficient evaluation methods for cutting outcomes. In this paper, we introduce TopoCut, a comprehensive benchmark for multi-step robotic cutting tasks that integrates a cutting environment and generalized policy learning. TopoCut is built upon three core components: (1) a high-fidelity simulation environment based on a particle-based elastoplastic solver with compliant von Mises constitutive models, augmented by a novel damage-driven topology discovery mechanism for accurate tracking of multiple cutting pieces; (2) a comprehensive reward design that combines this topology discovery with a pose-invariant spectral reward model based on Laplace–Beltrami eigenanalysis, enabling consistent and robust assessment of cutting quality; and (3) an integrated policy learning pipeline, where a dynamics-informed perception module predicts topological evolution and produces particle-wise, topology-aware embeddings to support PDDP—Particle-based Score-Entropy Discrete Diffusion Policy—for goal-conditioned policy learning. Extensive experiments demonstrate that TopoCut enables trajectory generation, scalable learning, precise evaluation, and strong generalization across diverse object geometries, scales, poses, and cutting goals.
APA
Wang, L., Bian, J., Heiden, E. & Garg, A.. (2025). TopoCut: Learning Multi-Step Cutting with Spectral Rewards and Discrete Diffusion Policies. Proceedings of The 9th Conference on Robot Learning, in Proceedings of Machine Learning Research 305:1282-1310 Available from https://proceedings.mlr.press/v305/wang25c.html.

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