Material Point Method

Cutting is a recurring operation in robotic au tomation, from food preparation to surgical tissue resection. For highly compliant targets, blade motion may deform or displace the material rather than advance the intended cut, while progressive failure changes load transfer and subsequent tool tissue interaction. A computational description must therefore connect cut formation to the evolving mechanical response, rather than specifying the incision independently of material failure. We present STC-MPM (Soft Tissue Cutting with the Material Point Method), a framework that couples finite-strain deformation, history-driven continuum damage, and configurable post-failure treatment. Damage initiates only when a tensile strain history exceeds a material threshold within the blade process zone. Progressive degradation changes stress transmission before the post-failure policy is applied, while the remaining tissue continues to deform, move, and interact with the tool. Numerical scalpel studies using delayed particle deactivation follow this response through insertion and withdrawal. Under identical blade motion, reducing the damage-rate limit leaves the first recorded damage time unchanged but delays and increases peak reaction force, delays particle deactivation, and increases the fixed-cohort displacement statistic at maximum insertion. The matched comparison illustrates how post-initiation failure evolution alters subsequent tool loading and recorded material motion. STC-MPM thus supports joint analysis of cut formation and accompanying tissue response without a pre-inserted cutting interface.

Differentiable physics is increasingly used in robotic material manipulation for system identification, trajectory or skill optimization, demonstration generation, and robot or end-effector design. These applications depend on gradients propagated through long, contact-rich simulation rollouts. We study the numerical reliability of those gradients using two Material Point Method (MPM) system-identification benchmarks derived from elastoplastic and granular manipulation. The benchmarks provide controlled cases for three effects that also arise in broader differentiable physics-based optimization. GPU many-to-one sums whose order depends on thread scheduling changed long-horizon gradients and reversed the sign of one parameter gradient relative to a deterministic reference. Finite-difference checks became less reliable for longer rollouts because repeated-run loss variation grew much faster than the loss change produced by the tested parameter perturbations. Observation and loss definitions changed optimization behaviour and the solution preferred by an independent metric. These results motivate reproducible accumulation, finite-difference validation that compares perturbation-induced loss changes with repeated-run variation, and explicit reporting of objective construction when differentiable simulation is used for robotic optimization.

Cutting changes both the shape and topology of deformable objects, making accurate simulation challenging for robotic manipulation. A simulator must track the cutting tool as a cut develops, preserve the resulting discontinuities after tool withdrawal, and enable newly exposed surfaces to interact with the tool and with each other. Existing formulations often prescribe cut surfaces in advance or couple material separation to auxiliary geometric fields. We introduce BladeMaster, a GPU-accelerated cutting framework based on the total Lagrangian material point method (TLMPM). Our key idea is to encode the cutting history directly on material points through persistent side labels generated online from the blade geometry. These labels govern particle-grid coupling, preserving connectivity within intact material while preventing spurious coupling across cut faces after tool withdrawal. Our formulation supports progressive and intersecting cuts without predefined cut surfaces or particle duplication. Material-material contact enables cut surfaces to recontact and slide against each other without reconnecting, while two-way tool-material coupling allows material reaction forces to influence tool motion. Experiments demonstrate tool-driven cutting followed by manipulation, with faster-than-real-time performance on representative tasks. Project page: https://jango6324.github.io/blademaster/.

Efficient, fully automatic, and physically plausible 4D Gaussian synthesis is an important goal for dynamic scene generation. Recent physics-based methods couple 3D Gaussians with the Material Point Method (MPM) to generate physically driven motion, but extending this paradigm to heterogeneous multi-part objects and interacting multi-object scenes remains challenging. Object-level physical assignment collapses distinct parts into a single material state, while one-shot predictions from large language models, vision-language models, or agents neither reliably bind different materials to identified parts nor verify that the resulting MPM configuration is executable. Score Distillation Sampling (SDS)-based parameter optimization, meanwhile, requires repeated per-scene score evaluations and gradient backpropagation, incurring lengthy optimization and potentially yielding suboptimal or unstable solutions. We therefore present PhysMAS, a physics-grounded multi-agent framework. From a motion prompt and four scene views, an Object-Part Scene Agent establishes persistent identities and calls a Material Reasoning Agent for part-wise profiles. It invokes solver-aware skills to bind these identities and profiles to per-particle MPM fields and execute all objects in a shared domain; the framework then screens candidate forward-simulation results. This supports heterogeneous multi-part and interacting multi-object scenes without per-scene diffusion-score backpropagation. Extensive experiments demonstrate that, compared with recent physics-based 4D Gaussian baselines that rely on SDS, PhysMAS achieves better semantic alignment and perceived physical plausibility while requiring less runtime.

Recent advances in robotics research have created a strong demand for high-performance simulators. Surgical robotics simulation faces unique challenges due to the need to model diverse objects, such as rigid instruments, soft tissue, and fluids. While many studies simulate sutures or soft tissue independently, only a few have considered the complete soft-tissue suturing scenario, including the contact between sutures and deformable tissue during suture insertion. Building on previous work, this paper presents a novel suturing simulation environment using sutures modelled by position-based dynamics (PBD) and soft bodies modelled by the material point method (MPM) while considering two-way contact with frictional and drag forces. We introduce a contact coupling method between the PBD suture and the MPM soft tissue, enabling visually plausible suture-tissue interactions. The simulator is optimized for GPU execution with parallel scenes using multiple CUDA streams, and we present a Reinforcement Learning (RL) environment for autonomous suturing sub-tasks, including needle insertion, driving, and extraction. Using ML-Agents, RL agents trained in the simulator show stable learning and achieve 80% and 68% success rates in needle insertion and extraction, respectively, under the strictest distance threshold.

3D human avatars have shown impressive visual fidelity driven by pose-conditioned models, yet they still lack the physical ability required for interactions with each other and environments. Although recent studies have made various attempts to incorporate physical characteristics into 3D avatars, they only exhibit limited physical deformations, often leading to constrained interaction behaviors. To resolve this issue, we present PIAvatar, a framework to simultaneously enable physically aware interactions between avatar-avatar and avatar-environment, and a non-rigid deformable human body simulation. In this work, our key insight is to decouple kinematic velocity from deformation gradient. When external forces act on avatars, the kinematic velocity induces stress which hinders the avatar's ability to achieve a desired pose. In addition, we integrate a skeletal framework within the avatar. It allows estimating its poses and real-time tracking in a closed form, even during non-rigid physical interactions. Our approach is implemented within a conventional Material Point Method framework to ensure physically consistent dynamics. We lastly evaluate the method on both human-object and human-human interaction scenarios to assess its behavior under diverse interaction settings.

To study the ability to infer physical dynamics from videos and extrapolate them forward in time, we assemble a dataset of 2D Material Point Method (MPM) physical simulations covering rich physical phenomena such as deformable objects, fluids, kinetic objects, and emitters. We study code generation and video diffusion approaches on this dataset, identifying their strengths and weaknesses by varying the amount of physically relevant side information. The code generation model, beyond giving a working demonstration of automatic synthesis of MPM simulations, reveals that such an approach struggles with inferring physical parameters from visual input, but relative to video diffusion, produces physically and temporally stable extrapolations forward in time, while the video diffusion model more strongly identifies geometric properties from visual input but produces physically implausible extrapolations.

Tactile perception is key to dexterous manipulation, yet simulating high-resolution elastomer deformation remains computationally prohibitive. Finite element methods (FEM) deliver high fidelity but demand costly remeshing, while Material Point Methods (MPM) suffer from heavy particle-memory tradeoffs. We propose a {reduced-order neural simulation framework} that couples coarse-grained MPM dynamics with an implicit neural decoder to reconstruct sub-particle tactile details from compact latent states. The framework learns a continuous deformation manifold from paired high- and low-resolution simulations, enabling physically consistent, differentiable inference. Compared to the TacIPC, our method achieves over 65% faster simulation and {40% lower memory usage}, while maintaining better geometric fidelity. In tactile rendering and 3D surface reconstruction, our methods further improve accuracy by 25% and produce realistic depth images and surface mesh within a faster inference speed. These results demonstrate that the proposed reduced-order neural model enables high-detail, physically grounded tactile simulation with substantial efficiency gains for robotic interaction and optimization.

Simulating optical tactile sensors presents significant challenges due to their high deformability and intricate optical properties. To address these issues and enable a physically accurate simulation, we propose DOT-Sim: Differentiable Optical Tactile Simulation. Unlike prior simulators that rely on simplified models of deformable sensors, DOT-Sim accurately captures the physical behavior of soft sensors by modeling them as elastic materials using the Material Point Method (MPM). DOT-Sim enables rapid calibration of optical tactile sensor simulation using a small number of demonstrations within minutes, which is substantially faster than existing methods. Compared to current baselines, our approach supports much larger and non-linear deformations. To handle the optical aspect, we propose a novel approach to simulating optical responses by learning a residual image relative to the real-world idle state. We validate the physical and visual realism of our method through a series of zero-shot sim-to-real tasks. Our experiments show that DOT-Sim (1) accurately replicates the physical dynamics of a DenseTact optical tactile sensor in reality, (2) generates realistic optical outputs in contact-rich scenarios, (3) enables direct deployment of simulation-trained classifiers in the real world, achieving 85% classification accuracy on challenging objects and 90% accuracy in embedded tumor-type detection, and (4) allows precise trajectory following with a policy trained from demonstrations in simulation, with an average error of less than 0.9 mm.