281 research outputs found
Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems
The present article presents a summarizing view at differential-algebraic
equations (DAEs) and analyzes how new application fields and corresponding
mathematical models lead to innovations both in theory and in numerical
analysis for this problem class. Recent numerical methods for nonsmooth
dynamical systems subject to unilateral contact and friction illustrate the
topicality of this development.Comment: Preprint of Book Chapte
Time-stepping numerical simulation of switched circuits with the nonsmooth dynamical systems approach
International audienceThe numerical integration of switching circuits is known to be a tough issue when the number of switches is large, or when sliding modes exist. Then, classical analog simulators may behave poorly, or even fail. In this paper, it is shown on two examples that the nonsmooth dynamical systems (NSDS) approach, which is made of: 1) a specific modeling of the piecewise-linear electronic devices (ideal diodes, Zener diodes, transistors); 2) the Moreau's time-stepping scheme; and 3) specific iterative one-step solvers, supersedes simulators of the simulation program with integrated circuit emphasis (SPICE) family and hybrid simulators. An academic example constructed in [Maffezzoni, , IEEE Trans. CADICS, vol 25, no. 11, Nov. 2006], so that the Newton-Raphson scheme does not converge, and the buck converter are used to make extensive comparisons between the NSDS method and other methods of the SPICE family and a hybrid-like method. The NSDS method, implemented in the siconos platform developed at INRIA, proves to be on these two examples much faster and more robust with respect to the model parameter variations
The nonsmooth dynamical systems approach for the analog simulation of switched circuits within the Siconos framework
The numerical integration of switching circuits is known to be a tough issue when the number of switches is high, or when sliding modes exist. Then classical analog simulators may behave poorly, or even fail. In this paper it is shown on two examples that the nonsmooth dynamical systems (NSDS) approach, which is made of 1) a specific modelling of the piecewise- linear electronic devices (ideal diodes, Zener diodes, transistors), 2) the Moreau's time-stepping scheme, and 3) specific iterative one-step solvers, supersedes simulators of the SPICE family and hybrid simulators. An academic example constructed in [Maffezzoni et al, IEEE Trans. on CADICS, Vol 25, No 11, November 2006], so that the Newton-Raphson scheme does not converge, and the buck converter, are used to make extensive comparisons between the NSDS method and other methods of the SPICE family and a hybrid-like method. The NSDS method, implemented in the Siconos platform developed at INRIA, proves to be on these two examples much faster and more robust with respect to the models parameters variations
ADD: Analytically Differentiable Dynamics for Multi-Body Systems with Frictional Contact
We present a differentiable dynamics solver that is able to handle frictional
contact for rigid and deformable objects within a unified framework. Through a
principled mollification of normal and tangential contact forces, our method
circumvents the main difficulties inherent to the non-smooth nature of
frictional contact. We combine this new contact model with fully-implicit time
integration to obtain a robust and efficient dynamics solver that is
analytically differentiable. In conjunction with adjoint sensitivity analysis,
our formulation enables gradient-based optimization with adaptive trade-offs
between simulation accuracy and smoothness of objective function landscapes. We
thoroughly analyse our approach on a set of simulation examples involving rigid
bodies, visco-elastic materials, and coupled multi-body systems. We furthermore
showcase applications of our differentiable simulator to parameter estimation
for deformable objects, motion planning for robotic manipulation, trajectory
optimization for compliant walking robots, as well as efficient self-supervised
learning of control policies.Comment: Moritz Geilinger and David Hahn contributed equally to this wor
Multi-contact Stochastic Predictive Control for Legged Robots with Contact Locations Uncertainty
Trajectory optimization under uncertainties is a challenging problem for
robots in contact with the environment. Such uncertainties are inevitable due
to estimation errors, control imperfections, and model mismatches between
planning models used for control and the real robot dynamics. This induces
control policies that could violate the contact location constraints by making
contact at unintended locations, and as a consequence leading to unsafe motion
plans. This work addresses the problem of robust kino-dynamic whole-body
trajectory optimization using stochastic nonlinear model predictive control
(SNMPC) by considering additive uncertainties on the model dynamics subject to
contact location chance-constraints as a function of robot's full kinematics.
We demonstrate the benefit of using SNMPC over classic nonlinear MPC (NMPC) for
whole-body trajectory optimization in terms of contact location constraint
satisfaction (safety). We run extensive Monte-Carlo simulations for a quadruped
robot performing agile trotting and bounding motions over small stepping
stones, where contact location satisfaction becomes critical. Our results show
that SNMPC is able to perform all motions safely with 100% success rate, while
NMPC failed 48.3% of all motions
- …