16,557 research outputs found
New Acceleration of Nearly Optimal Univariate Polynomial Root-findERS
Univariate polynomial root-finding has been studied for four millennia and is
still the subject of intensive research. Hundreds of efficient algorithms for
this task have been proposed. Two of them are nearly optimal. The first one,
proposed in 1995, relies on recursive factorization of a polynomial, is quite
involved, and has never been implemented. The second one, proposed in 2016,
relies on subdivision iterations, was implemented in 2018, and promises to be
practically competitive, although user's current choice for univariate
polynomial root-finding is the package MPSolve, proposed in 2000, revised in
2014, and based on Ehrlich's functional iterations. By proposing and
incorporating some novel techniques we significantly accelerate both
subdivision and Ehrlich's iterations. Moreover our acceleration of the known
subdivision root-finders is dramatic in the case of sparse input polynomials.
Our techniques can be of some independent interest for the design and analysis
of polynomial root-finders.Comment: 89 pages, 5 figures, 2 table
ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics
Physical simulators have been widely used in robot planning and control.
Among them, differentiable simulators are particularly favored, as they can be
incorporated into gradient-based optimization algorithms that are efficient in
solving inverse problems such as optimal control and motion planning.
Simulating deformable objects is, however, more challenging compared to rigid
body dynamics. The underlying physical laws of deformable objects are more
complex, and the resulting systems have orders of magnitude more degrees of
freedom and therefore they are significantly more computationally expensive to
simulate. Computing gradients with respect to physical design or controller
parameters is typically even more computationally challenging. In this paper,
we propose a real-time, differentiable hybrid Lagrangian-Eulerian physical
simulator for deformable objects, ChainQueen, based on the Moving Least Squares
Material Point Method (MLS-MPM). MLS-MPM can simulate deformable objects
including contact and can be seamlessly incorporated into inference, control
and co-design systems. We demonstrate that our simulator achieves high
precision in both forward simulation and backward gradient computation. We have
successfully employed it in a diverse set of control tasks for soft robots,
including problems with nearly 3,000 decision variables.Comment: In submission to ICRA 2019. Supplemental Video:
https://www.youtube.com/watch?v=4IWD4iGIsB4 Project Page:
https://github.com/yuanming-hu/ChainQuee
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