Core Concepts
Seamlessly integrating MPM with rigid bodies through frictional contact using a novel convex formulation.
Abstract
The paper introduces a novel convex formulation that integrates the Material Point Method (MPM) with articulated rigid body dynamics in frictional contact scenarios. The approach extends the linear corotational hyperelastic model into elastoplasticity, ensuring global convergence and stability. The method is validated through rigorous testing, demonstrating superior capabilities in managing complex simulations relevant to robotics. The content covers mathematical formulations, contact point computation, corotational model with plasticity, and results from various simulation scenarios.
I. Introduction
- Importance of simulation in robotics.
- Rise in popularity of MPM due to its accuracy.
- Dichotomy between MPM and rigid body dynamics.
II. Previous Work
- Overview of Material Point Method (MPM).
- Applications of MPM in various engineering problems.
- Challenges in integrating MPM into robotics simulation.
III. Outline and Novel Contributions
- Description of the proposed convex formulation.
- Mathematical formulations for coupling MPM with rigid bodies.
- Contact point computation process.
- Elastoplastic model with plasticity for robust simulations.
IV. Mathematical Formulation
- State representation for generalized positions and velocities.
- Two-stage implicit time stepping approach.
- Discretization strategy for deformable bodies with MPM.
V. Contact Point Computation
- Pressure field contact model used for sampling contact points.
- Generation of contact points between rigid geometries and deformable bodies discretized with MPM.
VI. Corotational Model with Plasticity
- Introduction of an elastoplastic material model satisfying convexity requirements.
- Approximation methods for von Mises yield criterion.
- Return mapping procedure for computing plastic deformation gradient.
VII. Results
- Validation through comparison against analytical solutions.
- Simulation scenarios including dough tearing, rolling, liquid transfer, and comparison with ManiSkill2 solver.
VIII. Limitations and Future Work
- Runtime performance considerations for parallel implementation.
- Discrete contact detection challenges addressed by low-speed movements assumption.
- Rotational invariance limitations discussed along with future research directions.
Stats
"Our method follows a similar approach by adopting a variational framework but differs from previous work by formulating a convex optimization problem."
"The convexity of the problem guarantees global convergence and stability even in highly challenging scenarios."
Quotes
"Our method ensures global convergence, enabling the use of large simulation time steps without compromising robustness."
"Compared to previous MPM-based robotic simulators, our method significantly improves the stability of contact resolution—a critical factor in robot manipulation tasks."