Differentiable Fluid Physics Parameter Identification BY Stirring AND FOR STIRRIng

Abstract

Fluid interactions are crucial in daily tasks, with properties like density and viscosity being key parameters. The property states can be used as control signals for robot operation. While density estimation is simple, assessing viscosity, especially for different fluid types, is complex. This study introduces a novel differentiable fitting framework, DiffStir, tailored to identify key physics parameters through stirring. Then, given the estimated physics parameters, we can generate commands to guide the robotic stirring. Comprehensive experiments were conducted to validate the efficacy of DiffStir, showcasing its precision in parameter estimation when benchmarked against reported values in the literature.

Supplementary Material

supplementary_material.pdf 

Pipeline of DiffStir

1) It takes the recorded real-world trajectories and the forces of a robot grasping a rod and stirring in a container. With the measured force, it can estimate the fluid density. 

2) The estimated density along with the trajectories can help to replicate the robotic stirring scene in a differentiable simulator. 

3) By comparing the force calculated from the simulator and the real-world measurements, it can adaptively find the most proper parameters and models. 

4) It adopts a neural network to refine the estimated parameters. 

5) Finally, in the application of mixture ratio inference, by comparing the recognized refined viscosity with the target viscosity, the agent makes decisions and outputs operational commands to adjust the ratio, helping to obtain liquid mixtures that meet the target viscosity in robotics operations.

CONSTITUTIVE MODEL

DiffStir's innovative constitutive model combines the Kelvin-Voigt viscoelastic framework with the Neo-Hookean model for volumetric responses, capturing the behaviors of both Newtonian and non-Newtonian fluids, including those characterized by Carreau, Cross, and Herschel-Bulkley models. This integration ensures adherence to Navier-Stokes principles, enabling DiffStir to offer a unified and precise simulation of fluid dynamics across a diverse spectrum of material types and conditions. Specifically tailored for automated processes, this integrated and universal perspective is highly suited for industrial and research applications.

SIMULATION ENGINE

DiffStir employs a differentiable MLS-MPM approach, offering natural collision handling, fluid-solid coupling, and momentum conservation. Under specific conditions, DiffStir's model can be mathematically reduced to the Corotated model. FluidLab has successfully demonstrated the Corotated model's ability to represent various physical phenomena within MLS-MPM simulations, such as Kármán Vortex Street, Dam Break, Magnus Effect, Rayleigh–Taylor Instability, incompressibility, volume stability, and buoyancy. This highlights that DiffStir's observations and understanding of liquids encompass these phenomena in simulation.

Experiment A: Density Estimation

Experiment B: Apparent Viscosity Estimation

DiffStir's constitutive model offers a more accurate representation of the mechanical phenomena during stirring processes than the general Corotated model, and the viscosity values it identifies closely approximate those observed in empirical physical experiments.

Note: 

DiffStir system establishes a novel robotics fluid understanding framework, advancing beyond the current benchmark set by FluidLab for complex fluid manipulation. Unlike FluidLab which uses the simpler Corotated model and lacks an automated real-to-sim pipeline, DiffStir employs a more sophisticated model,  enabling a more accurate and comprehensive understanding of fluid behaviors and ensuring better alignment between physical parameters and real-world values.

Experiment C: Fluid Dynamics Behavior Classification

DiffStir enables the analysis and classification of fluid types by examining the viscosity response to varying stirring rates. 

Experiment D: FLUID MIxing AnALYSIS

DiffStir excels in bridging real-world mixtures to simulations, accurately capturing the dynamic interplay of components within liquid mixtures. 

Experiment E: MIxture RATIO INFERENCE

During robotic operations, DiffStir can provide guidance on adjusting ratios based on the viscosity state of liquid mixtures. It successfully infers the proportions of various syrup and water mixtures in experiments and can stop stirring at the appropriate state to replicate samples of unknown mixture ratios. 

This demonstrates the potential of the DiffStir system for applications in kitchen tasks and food engineering.