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Matrix Riccati differential equations arise in many different areas and are particular important within the field of control theory. In this paper we consider numerical integration for large-scale systems of stiff matrix Riccati…
Accurate physical simulation is crucial for the development and validation of control algorithms in robotic systems. Recent works in Reinforcement Learning (RL) take notably advantage of extensive simulations to produce efficient robot…
A fundamental task in particle-in-cell (PIC) simulations of plasma physics is solving for charged particle motion in electromagnetic fields. This problem is especially challenging when the plasma is strongly magnetized due to numerical…
Differentiable simulation establishes the mathematical foundation for solving challenging inverse problems in computer graphics and robotics, such as physical system identification and inverse dynamics control. However, rigor in frictional…
The efficient numerical solution of many kinetic models in plasma physics is impeded by the stiffness of these systems. Exponential integrators are attractive in this context as they remove the CFL condition induced by the linear part of…
We present a quasi-static finite element simulator for human face animation. We model the face as an actuated soft body, which can be efficiently simulated using Projective Dynamics (PD). We adopt Incremental Potential Contact (IPC) to…
Physical interactive robotics, ranging from wearable devices to collaborative humanoid robots, require close coordination between mechanical design and control. However, evaluating interactive dynamics is challenging due to complex human…
Differentiable physics simulation provides an avenue to tackle previously intractable challenges through gradient-based optimization, thereby greatly improving the efficiency of solving robotics-related problems. To apply differentiable…
Simulating physical problems involving multi-time scale coupling is challenging due to the need of solving these multi-time scale processes simultaneously. In response to this challenge, this paper proposed an explicit multi-time step…
We present an elastic simulator for domains defined as evolving implicit functions, which is efficient, robust, and differentiable with respect to both shape and material. This simulator is motivated by applications in 3D reconstruction: it…
This paper presents a novel simulation platform, ZeMa, designed for robotic manipulation tasks concerning soft objects. Such simulation ideally requires three properties: two-way soft-rigid coupling, intersection-free guarantees, and…
We present a novel convex formulation that models rigid and deformable bodies coupled through frictional contact. The formulation incorporates a new corotational material model with positive semi-definite Hessian, which allows us to extend…
Simulations of the dynamic deformations of metal samples require elastic-plastic constitutive updates of the material behavior to be performed over a small time step between updates, as dictated by the Courant condition. Depending on the…
Dexterous manipulation requires careful reasoning over extrinsic contacts. The prevalence of deforming tools in human environments, the use of deformable sensors, and the increasing number of soft robots yields a need for approaches that…
Stiff ordinary differential equations (ODEs) are common in many science and engineering fields, but standard neural ODE approaches struggle to accurately learn these stiff systems, posing a significant barrier to widespread adoption of…
We present a method for efficient differentiable simulation of articulated bodies. This enables integration of articulated body dynamics into deep learning frameworks, and gradient-based optimization of neural networks that operate on…
We propose two new classes of time integrators for stiff DEs: the implicit-explicit exponential (IMEXP) and the hybrid exponential methods. In contrast to the existing exponential schemes, the new methods offer significant computational…
The direct-forcing immersed boundary method (DF-IBM) algorithm previously developed by the authors is extended by coupling the Navier-Stokes equations with the Newton-Euler equations for rigid body dynamics within the DF-IBM framework. This…
Differentiable simulators promise to improve sample efficiency in robot learning by providing analytic gradients of the system dynamics. Yet, their application to contact-rich tasks like locomotion is complicated by the inherently…
This paper presents a novel implicit scheme for the constraint resolution in real-time finite element simulations in the presence of contact and friction. Instead of using the standard motion correction scheme, we propose an iterative…