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

2025-09-23

AI Summary

Robotic cutting of deformable objects faces challenges including complex topological evolution, difficult state perception, and lack of standardized evaluation metrics. Method: This paper proposes a high-fidelity, simulation-driven, topology-aware policy learning framework. It establishes a physics-based simulation environment using a particle-based elastoplastic solver coupled with the von Mises constitutive model; designs a damage-driven topology discovery mechanism and a pose-invariant spectral reward model for robust, quantitative assessment of cutting outcomes; and introduces Particle-based Discrete Diffusion Policy (PDDP), integrating Laplace–Beltrami spectral analysis and dynamics-aware modules to enhance control generalization. Contribution/Results: Experiments demonstrate that the framework enables high-quality trajectory generation across diverse geometries, scales, and object poses. It significantly outperforms existing methods in evaluation accuracy, policy generalization, and task scalability.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Intelligent Robots: Manipulation
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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) We introduce 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 that enables accurate tracking of multiple cutting pieces. (2) We develop a comprehensive reward design that integrates the topology discovery with a pose-invariant spectral reward model based on Laplace-Beltrami eigenanalysis, facilitating consistent and robust assessment of cutting quality. (3) We propose 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 supports trajectory generation, scalable learning, precise evaluation, and strong generalization across diverse object geometries, scales, poses, and cutting goals.

Problem

• Addressing robotic cutting challenges for deformable objects with complex topological behaviors
• Developing efficient evaluation methods for cutting outcomes in multi-step tasks
• Overcoming difficulties in perceiving dense object states during cutting operations

Innovation

• Particle-based elastoplastic solver with topology discovery
• Spectral reward model using Laplace-Beltrami eigenanalysis
• Particle-based discrete diffusion policy with topology embeddings