Related papers: Time Integrating Articulated Body Dynamics Using P…
Dynamic systems have a fundamental relevance in the description of physical phenomena. The search for more accurate and faster numerical integration methods for the resolution of such systems is, therefore, an important topic of research.…
We propose an algorithm to compute the dynamics of articulated rigid-bodies with different sensor distributions. Prior to the on-line computations, the proposed algorithm performs an off-line optimisation step to simplify the computational…
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…
Simulation of contact and friction dynamics is an important basis for control- and learning-based algorithms. However, the numerical difficulties of contact interactions pose a challenge for robust and efficient simulators. A…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
Most dynamic simulation tools parameterize the configuration of multi-body robotic systems using minimal coordinates, also called generalized or joint coordinates. However, maximal-coordinate approaches have several advantages over…
We have proposed new algorithms for the numerical integration of the equations of motion for classical spin systems. In close analogy to symplectic integrators for Hamiltonian equations of motion used in Molecular Dynamics these algorithms…
We present non-convex maximal dissipation principle (NMDP), a time integration scheme for articulated bodies with simultaneous contacts. Our scheme resolves contact forces via the maximal dissipation principle (MDP). Prior MDP solvers…
Humanoid robots have the potential capability to perform a diverse range of manipulation tasks, but this is based on a robust and precise standing controller. Existing methods are either ill-suited to precisely control high-dimensional…
This paper describes a fourth-order integration algorithm for the gravitational N-body problem based on discrete Lagrangian mechanics. When used with shared timesteps, the algorithm is momentum conserving and symplectic. We generalize the…
In this note we approach the classical, Newtonian, gravitational $N$-body problem by mean of a new, original numerical integration method. After a short summary of the fundamental characteristics of the problem, including a sketch of some…
We present an efficient variational integrator for multibody systems. Variational integrators reformulate the equations of motion for multibody systems as discrete Euler-Lagrange (DEL) equations, transforming forward integration into a…
This technical report provides an in-depth evaluation of both established and state-of-the-art methods for simulating constrained rigid multi-body systems with hard-contact dynamics, using formulations of Nonlinear Complementarity Problems…
We propose a high order adaptive-rank implicit integrators for stiff time-dependent PDEs, leveraging extended Krylov subspaces to efficiently and adaptively populate low-rank solution bases. This allows for the accurate representation of…
We present a novel method for efficient direct integration of gravitational N-body systems with a large variation in characteristic time scales. The method is based on a recursive and adaptive partitioning of the system based on the…
This paper presents a novel framework for Jacobian computation in motion optimization problems involving multi-link systems, where physical quantities are represented using higher-order time derivatives. In motion optimization of robots and…
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…
We present a new symplectic integrator designed for collisional gravitational $N$-body problems which makes use of Kepler solvers. The integrator is also reversible and conserves 9 integrals of motion of the $N$-body problem to machine…
We present a general, high-order, fully explicit relaxation scheme which can be applied to any system of nonlinear hyperbolic conservation laws in multiple dimensions. The scheme consists of two steps. In a first (relaxation) step, the…
Using Suzuki-Trotter decompositions of exponential operators we describe new algorithms for the numerical integration of the equations of motion for classical spin systems. These techniques conserve spin length exactly and, in special…