6,750 research outputs found
Projection Methods: Swiss Army Knives for Solving Feasibility and Best Approximation Problems with Halfspaces
We model a problem motivated by road design as a feasibility problem.
Projections onto the constraint sets are obtained, and projection methods for
solving the feasibility problem are studied. We present results of numerical
experiments which demonstrate the efficacy of projection methods even for
challenging nonconvex problems
Keep Rollin' - Whole-Body Motion Control and Planning for Wheeled Quadrupedal Robots
We show dynamic locomotion strategies for wheeled quadrupedal robots, which
combine the advantages of both walking and driving. The developed optimization
framework tightly integrates the additional degrees of freedom introduced by
the wheels. Our approach relies on a zero-moment point based motion
optimization which continuously updates reference trajectories. The reference
motions are tracked by a hierarchical whole-body controller which computes
optimal generalized accelerations and contact forces by solving a sequence of
prioritized tasks including the nonholonomic rolling constraints. Our approach
has been tested on ANYmal, a quadrupedal robot that is fully torque-controlled
including the non-steerable wheels attached to its legs. We conducted
experiments on flat and inclined terrains as well as over steps, whereby we
show that integrating the wheels into the motion control and planning framework
results in intuitive motion trajectories, which enable more robust and dynamic
locomotion compared to other wheeled-legged robots. Moreover, with a speed of 4
m/s and a reduction of the cost of transport by 83 % we prove the superiority
of wheeled-legged robots compared to their legged counterparts.Comment: IEEE Robotics and Automation Letter
Solving the Monge-Amp\`ere Equations for the Inverse Reflector Problem
The inverse reflector problem arises in geometrical nonimaging optics: Given
a light source and a target, the question is how to design a reflecting
free-form surface such that a desired light density distribution is generated
on the target, e.g., a projected image on a screen. This optical problem can
mathematically be understood as a problem of optimal transport and equivalently
be expressed by a secondary boundary value problem of the Monge-Amp\`ere
equation, which consists of a highly nonlinear partial differential equation of
second order and constraints. In our approach the Monge-Amp\`ere equation is
numerically solved using a collocation method based on tensor-product
B-splines, in which nested iteration techniques are applied to ensure the
convergence of the nonlinear solver and to speed up the calculation. In the
numerical method special care has to be taken for the constraint: It enters the
discrete problem formulation via a Picard-type iteration. Numerical results are
presented as well for benchmark problems for the standard Monge-Amp\`ere
equation as for the inverse reflector problem for various images. The designed
reflector surfaces are validated by a forward simulation using ray tracing.Comment: 28 pages, 8 figures, 2 tables; Keywords: Inverse reflector problem,
elliptic Monge-Amp\`ere equation, B-spline collocation method, Picard-type
iteration; Minor revision: reference [59] to a recent preprint has been added
and a few typos have been correcte
Parallel ADMM for robust quadratic optimal resource allocation problems
An alternating direction method of multipliers (ADMM) solver is described for
optimal resource allocation problems with separable convex quadratic costs and
constraints and linear coupling constraints. We describe a parallel
implementation of the solver on a graphics processing unit (GPU) using a
bespoke quartic function minimizer. An application to robust optimal energy
management in hybrid electric vehicles is described, and the results of
numerical simulations comparing the computation times of the parallel GPU
implementation with those of an equivalent serial implementation are presented
- …