Abstract

An important challenge in robotics is understanding the interactions between robots and deformable terrains that consist of granular material. Granular flows and their interactions with rigid bodies still pose several open questions. A promising direction for accurate, yet efficient, modeling is using continuum methods. Also, a new direction for real-time physics modeling is the use of geometric machine learning. This research advances continuum and machine learning methods for modeling rigid body-driven granular flows, for application to space robotics (where the effect of gravity is an important factor) as well as terrestrial industrial machines.

For accurate and efficient design applications, this research develops a continuum method comprising a modern constitutive model, nonlocal granular fluidity (NGF), and a state-of-the-art numerical solver, material point method (MPM). We design a numerical approach, within a hyperelasticity framework, to implement the dynamical form of the viscoplastic NGF constitutive model in three-dimensional MPM. This approach is thermodynamically consistent, and the dynamical form includes the nonlocal effect of flow cessation. This is verified by both quantitative measurements and qualitative visualization of our excavation and wheel experiments. Furthermore, this research explores the gravity sensitivity of continuum numerical solvers. It explains why MPM is an appropriate continuum solver to model granular flows under different gravity.

For real-time control applications, this research considers the development of a subspace machine learning simulation approach. To generate training datasets, we utilize our high-fidelity MPM-NGF method. Principal component analysis (PCA) is used to reduce the dimensionality of data. This research shows that the first few 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. 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-RAM. This also makes the GNS real-time on large-scale 3D physics configurations (and 700x faster than our MPM-NGF).