Related papers: Position-Based Nonlinear Gauss-Seidel for Quasista…
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…
NVIDIA researchers have pioneered an explicit method, position-based dynamics (PBD), for simulating systems with contact forces, gaining widespread use in computer graphics and animation. While the method yields visually compelling…
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…
PBD and its extension, XPBD, have been predominantly applied to compliant constrained elastodynamics, with their potential in finite strain (visco-) elastoplasticity remaining underexplored. XPBD is often perceived to stand in contrast to…
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…
Understanding the quasi-static fracture formation and evolution is essential for assessing the mechanical properties and structural load-bearing capacity of materials. Peridynamics (PD) provides an effective computational method to depict…
High-index saddle dynamics (HiSD) is an effective approach for computing saddle points of a prescribed Morse index and constructing solution landscapes for complex nonlinear systems. However, for problems with ill-conditioned Hessians…
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,…
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…
The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…
The vast majority of mesh-based modelling applications iteratively transform the mesh vertices under prescribed geometric conditions. This occurs in particular in methods cycling through the constraint set such as Position-Based Dynamics…
We introduce a novel Unsmoothed Aggregation (UA) Algebraic Multigrid (AMG) method combined with Preconditioned Conjugate Gradient (PCG) to overcome the limitations of Extended Position-Based Dynamics (XPBD) in high-resolution and…
Primal-dual gradient dynamics that find saddle points of a Lagrangian have been widely employed for handling constrained optimization problems. Building on existing methods, we extend the augmented primal-dual gradient dynamics (Aug-PDGD)…
Recent advances in symbolic dynamic programming (SDP) combined with the extended algebraic decision diagram (XADD) data structure have provided exact solutions for mixed discrete and continuous (hybrid) MDPs with piecewise linear dynamics…
This work presents a numerical analysis of computing transition states of semilinear elliptic partial differential equations (PDEs) via the index-1 saddle dynamics, or equivalently, the gentlest ascent dynamics. To establish clear…
This paper presents an improved non-ordinary state-based peridynamics (NOSB PD) framework for modelling the elastoplastic behaviour and damage of geomaterials, such as soil, rock, and concrete, under quasi static conditions. Conventional…
Despite decades of work in fast reactive planning and control, challenges remain in developing reactive motion policies on non-Euclidean manifolds and enforcing constraints while avoiding undesirable potential function local minima. This…
This paper presents a rigorous numerical framework for computing multiple solutions of semilinear elliptic problems by spatiotemporal high-index saddle dynamics (HiSD), which extends the traditional HiSD to the continuous-in-space setting,…
Peridynamics is a nonlocal continuum-mechanical theory based on minimal regularity on the deformations. Its key trait is that of replacing local constitutive relations featuring spacial differential operators with integrals over differences…
Peridynamic (PD) theories have gained widespread diffusion among various research areas, due to the ability of modeling discontinuities formation and evolution in materials. Bond-Based Peridynamics (BB-PD), notwithstanding some modeling…