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

Liquan Wang, Jiangjie Bian, Eric Heiden, Animesh Garg

Keywords: Deformable object manipulation, multi-step cutting, topology tracking, spectral reward, perception, discrete diffusion policy

TL;DR: We present TopoCut, a unified framework for learning goal-conditioned multi-step cutting of deformable objects, combining spectral rewards for precise evaluation with a discrete diffusion policy for stable and generalizable control.

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.

Submission Number: 831