Optimal Control of Granular Material

TL;DR

This paper presents an optimal control approach for granular materials using a GNN-based learned model and DDP, enabling efficient shape formation with validation on physics-based simulations.

Contribution

It introduces a novel combination of GNN, PCA, and DDP for controlling granular materials, improving speed and accuracy over traditional methods.

Findings

The GNN model accurately predicts granular dynamics.

Optimal control commands successfully shape particles into target forms.

Validation confirms the approach's effectiveness on physics-based simulations.

Abstract

The control of granular materials, showing up in many industrial applications, is a challenging open research problem. Granular material systems are complex-behavior (as they could have solid-, fluid-, and gas-like behaviors) and high-dimensional (as they could have many grains/particles with at least 3 DOF in 3D) systems. Recently, a machine learning-based Graph Neural Network (GNN) simulator has been proposed to learn the underlying dynamics. In this paper, we perform an optimal control of a rigid body-driven granular material system whose dynamics is learned by a GNN model trained by reduced data generated via a physics-based simulator and Principal Component Analysis (PCA). We use Differential Dynamic Programming (DDP) to obtain the optimal control commands that can form granular particles into a target shape. The model and results are shown to be relatively fast and accurate. The control commands are also applied to the ground-truth model,(i.e., physics-based simulator) to further validate the approach.