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  1. We propose a height-field-based real-time simulation method for sand and water mixtures. Inspired by the shallow-water assumption, our approach extends the governing equations to handle two-phase flows of sand and water using height fields. Our depth-integrated governing equations can model the elastoplastic behavior of sand, as well as sand-water-mixing phenomena such as friction, diffusion, saturation, and momentum exchange. We further propose an operator-splitting time integrator that is both GPU-friendly and stable under moderate time step sizes. We have evaluated our method on a set of benchmark scenarios involving large bodies of heterogeneous materials, where our GPU-based algorithm runs at real-time frame rates. Our method achieves a desirable trade-off between fidelity and performance, bringing an unprecedentedly immersive experience for real-time applications. 
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    Free, publicly-accessible full text available December 10, 2024
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  4. Tensegrity robots, composed of rigid rods and flexible cables, exhibit high strength-to-weight ratios and significant deformations, which enable them to navigate unstructured terrains and survive harsh impacts. They are hard to control, however, due to high dimensionality, complex dynamics, and a coupled architecture. Physics-based simulation is a promising avenue for developing locomotion policies that can be transferred to real robots. Nevertheless, modeling tensegrity robots is a complex task due to a substantial sim2real gap. To address this issue, this paper describes a Real2Sim2Real (R2S2R) strategy for tensegrity robots. This strategy is based on a differentiable physics engine that can be trained given limited data from a real robot. These data include offline measurements of physical properties, such as mass and geometry for various robot components, and the observation of a trajectory using a random control policy. With the data from the real robot, the engine can be iteratively refined and used to discover locomotion policies that are directly transferable to the real robot. Beyond the R2S2R pipeline, key contributions of this work include computing non-zero gradients at contact points, a loss function for matching tensegrity locomotion gaits, and a trajectory segmentation technique that avoids conflicts in gradient evaluation during training. Multiple iterations of the R2S2R process are demonstrated and evaluated on a real 3-bar tensegrity robot. 
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    Free, publicly-accessible full text available October 1, 2024
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  8. We present a generalized constitutive model for versatile physics simulation of inviscid fluids, Newtonian viscosity, hyperelasticity, viscoplasticity, elastoplasticity, and other physical effects that arise due to a mixture of these behaviors. The key ideas behind our formulation are the design of a generalized Kirchhoff stress tensor that can describe hyperelasticity, Newtonian viscosity and inviscid fluids, and the use of pre-projection and post-correction rules for simulating material behaviors that involve plasticity, including elastoplasticity and viscoplasticity. We show how our generalized Kirchhoff stress tensor can be coupled together into a generalized constitutive model that allows the simulation of diverse material behaviors by only changing parameter values. We present several side-by-side comparisons with physics simulations for specific constitutive models to show that our generalized model produces visually similar results. More notably, our formulation allows for inverse learning of unknown material properties directly from data using differentiable physics simulations. We present several 3D simulations to highlight the robustness of our method, even with multiple different materials. To the best of our knowledge, our approach is the first to recover the knowledge of unknown material properties without making explicit assumptions about the data.

     
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    Free, publicly-accessible full text available August 16, 2024
  9. For rearranging objects on tabletops with overhand grasps, temporarily relocating objects to some buffer space may be necessary. This raises the natural question of how many simultaneous storage spaces, or “running buffers,” are required so that certain classes of tabletop rearrangement problems are feasible. In this work, we examine the problem for both labeled and unlabeled settings. On the structural side, we observe that finding the minimum number of running buffers (MRB) can be carried out on a dependency graph abstracted from a problem instance and show that computing MRB is NP-hard. We then prove that under both labeled and unlabeled settings, even for uniform cylindrical objects, the number of required running buffers may grow unbounded as the number of objects to be rearranged increases. We further show that the bound for the unlabeled case is tight. On the algorithmic side, we develop effective exact algorithms for finding MRB for both labeled and unlabeled tabletop rearrangement problems, scalable to over a hundred objects under very high object density. More importantly, our algorithms also compute a sequence witnessing the computed MRB that can be used for solving object rearrangement tasks. Employing these algorithms, empirical evaluations reveal that random labeled and unlabeled instances, which more closely mimic real-world setups generally have fairly small MRBs. Using real robot experiments, we demonstrate that the running buffer abstraction leads to state-of-the-art solutions for the in-place rearrangement of many objects in a tight, bounded workspace.

     
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