Related papers: Convergence proof for first-order position-based d…
The position-based dynamics (PBD) algorithm is a popular and versatile technique for real-time simulation of deformable bodies, but is only applicable to forces that can be expressed as linearly compliant constraints. In this work, we…
Simulation modeling of robots, objects, and environments is the backbone for all model-based control and learning. It is leveraged broadly across dynamic programming and model-predictive control, as well as data generation for imitation,…
Interactive real-time rigid body simulation is a crucial tool in any modern game engine or 3D authoring tool. The quest for fast, robust and accurate simulations is ever evolving. PBRBD (Position Based Rigid Body Dynamics), a recent…
Position based dynamics is a powerful technique for simulating a variety of materials. Its primary strength is its robustness when run with limited computational budget. We develop a novel approach to address problems with PBD for…
Exploiting the efficiency and stability of Position-Based Dynamics (PBD), we introduce a novel crowd simulation method that runs at interactive rates for hundreds of thousands of agents. Our method enables the detailed modeling of per-agent…
Robotics demands simulation that can reason about the diversity of real-world physical interactions, from rigid to deformable objects and fluids. Current simulators address this by stitching together multiple subsolvers for different…
Projected Gradient Descent (PGD) under the $L_\infty$ ball has become one of the defacto methods used in adversarial robustness evaluation for computer vision (CV) due to its reliability and efficacy, making a strong and easy-to-implement…
We present DiffXPBD, a novel and efficient analytical formulation for the differentiable position-based simulation of compliant constrained dynamics (XPBD). Our proposed method allows computation of gradients of numerous parameters with…
Many tasks in robot-assisted surgery require planning and controlling manipulators' motions that interact with highly deformable objects. This study proposes a realistic, time-bounded simulator based on Position-based Dynamics (PBD)…
In this work, a numerical simulation of 1D Burgers' equation is developed using finite difference method and a reduced order model (ROM) of the simulation is developed using proper orthogonal decomposition (POD). The objective of this work…
We develop new perturbation techniques for conducting convergence analysis of various first-order algorithms for a class of nonsmooth optimization problems. We consider the iteration scheme of an algorithm to construct a perturbed…
The Position Based Fluids (PBF) method is a state-of-the-art approach for fluid simulations in the context of real-time applications like games. It uses an iterative solver concept that tries to maintain a constant fluid density…
Simulating stiff materials in applications where deformations are either not significant or can safely be ignored is a pivotal task across fields. Rigid body modeling has thus long remained a fundamental tool and is, by far, the most…
Ill-posed linear inverse problems appear in many scientific setups, and are typically addressed by solving optimization problems, which are composed of data fidelity and prior terms. Recently, several works have considered a back-projection…
This paper studies equality-constrained composite minimization problems. This class of problems, capturing regularization terms and inequality constraints, naturally arises in a wide range of engineering and machine learning applications.…
Effective models for slender structures derived from well-known plate (or shell) theories are justified within the limit of a small thickness, and may therefore prove limited for intermediate slenderness. On the other hand, direct 3D…
In this paper, we restructure the Neural Interconnection and Damping Assignment - Passivity Based Control (Neural IDA-PBC) design methodology, and we formally analyze its closed-loop properties. Neural IDA-PBC redefines the IDA-PBC design…
Autonomy in robotic surgery is very challenging in unstructured environments, especially when interacting with deformable soft tissues. The main difficulty is to generate model-based control methods that account for deformation dynamics…
This note discusses proofs for convergence of first-order methods based on simple potential-function arguments. We cover methods like gradient descent (for both smooth and non-smooth settings), mirror descent, and some accelerated variants.
First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…