The control of granular materials, which are found 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 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 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.

Granular flows interacting with rigid bodies are key to machine-terrain interactions in robotics and related fields, and still pose several open problems. Continuum methods and deep learning, separately and in combination, show promise. This research advances machine learning methods for modeling rigid body-driven granular flows, for terrestrial industrial machine and planetary rover (where gravity is an important factor) applications. The original contribution of this research is the application of a subspace machine learning simulation approach for these engineering problems. To generate training datasets, a high-fidelity continuum method, the material point method (MPM) is utilized. Principal component analysis (PCA) is used to reduce the dimensionality of data. It is shown that the first few (8 in our datasets) principal components of our high-dimensional data keep almost the entire variance in data. A graph network simulator (GNS) is trained to learn the underlying subspace dynamics. The learned GNS is then able to predict particle positions and interaction forces with good accuracy, averaging 6 × 1 0 − 5 and 3 × 1 0 − 6 mean squared position error and 7% and 17% mean percentage force error, for excavation and wheel data, respectively. More importantly, PCA significantly enhances the time and memory efficiency of GNS in both training and rollout. This enables GNS to be trained using a single desktop graphics processing unit (GPU) with moderate video random-access memory (VRAM). This also makes the GNS real-time on large-scale 3D physics configurations (700x faster than our continuum method), which is the first demonstration of such significantly accelerated high-fidelity granular flow engineering simulations.