Material-agnostic Shaping of Granular Materials with Optimal Transport

From construction materials, such as sand or asphalt, to kitchen ingredients, like rice, sugar, or salt; the world is full of granular materials. Despite impressive progress in robotic manipulation of single objects, granular materials remain a challenge due to difficulties in modelling these highly deformable and inhomogeneous materials, which are governed by dynamics that are hard to capture analytically. We argue that despite the high degrees of freedom and the complex underlying dynamics of granular materials, many practical problems that require manipulating them can be solved by leveraging simple models, informative motion priors, and a fast feedback loop. In this work, we show that computational Optimal Transport (OT) can be leveraged to derive informative, robot-agnostic motion priors for transforming a pile of granular materials from a source into a target distribution and generate robot motion plans with a next-best sweep planner that uses a simple material-agnostic sweep model. We plan sweeps directly on a height map representation of the material distribution and hence avoid a costly particle-level treatment of the problem. We validate our approach with a large set of simulation and hardware experiments that demonstrate several complex shaping tasks, including gathering, separating, and writing letters with different types of granular materials.