38,578 research outputs found
Balancing experiments on a torque-controlled humanoid with hierarchical inverse dynamics
Recently several hierarchical inverse dynamics controllers based on cascades
of quadratic programs have been proposed for application on torque controlled
robots. They have important theoretical benefits but have never been
implemented on a torque controlled robot where model inaccuracies and real-time
computation requirements can be problematic. In this contribution we present an
experimental evaluation of these algorithms in the context of balance control
for a humanoid robot. The presented experiments demonstrate the applicability
of the approach under real robot conditions (i.e. model uncertainty, estimation
errors, etc). We propose a simplification of the optimization problem that
allows us to decrease computation time enough to implement it in a fast torque
control loop. We implement a momentum-based balance controller which shows
robust performance in face of unknown disturbances, even when the robot is
standing on only one foot. In a second experiment, a tracking task is evaluated
to demonstrate the performance of the controller with more complicated
hierarchies. Our results show that hierarchical inverse dynamics controllers
can be used for feedback control of humanoid robots and that momentum-based
balance control can be efficiently implemented on a real robot.Comment: appears in IEEE/RSJ International Conference on Intelligent Robots
and Systems (IROS), 201
Optimization of mesh hierarchies in Multilevel Monte Carlo samplers
We perform a general optimization of the parameters in the Multilevel Monte
Carlo (MLMC) discretization hierarchy based on uniform discretization methods
with general approximation orders and computational costs. We optimize
hierarchies with geometric and non-geometric sequences of mesh sizes and show
that geometric hierarchies, when optimized, are nearly optimal and have the
same asymptotic computational complexity as non-geometric optimal hierarchies.
We discuss how enforcing constraints on parameters of MLMC hierarchies affects
the optimality of these hierarchies. These constraints include an upper and a
lower bound on the mesh size or enforcing that the number of samples and the
number of discretization elements are integers. We also discuss the optimal
tolerance splitting between the bias and the statistical error contributions
and its asymptotic behavior. To provide numerical grounds for our theoretical
results, we apply these optimized hierarchies together with the Continuation
MLMC Algorithm. The first example considers a three-dimensional elliptic
partial differential equation with random inputs. Its space discretization is
based on continuous piecewise trilinear finite elements and the corresponding
linear system is solved by either a direct or an iterative solver. The second
example considers a one-dimensional It\^o stochastic differential equation
discretized by a Milstein scheme
Relative Entropy Relaxations for Signomial Optimization
Signomial programs (SPs) are optimization problems specified in terms of
signomials, which are weighted sums of exponentials composed with linear
functionals of a decision variable. SPs are non-convex optimization problems in
general, and families of NP-hard problems can be reduced to SPs. In this paper
we describe a hierarchy of convex relaxations to obtain successively tighter
lower bounds of the optimal value of SPs. This sequence of lower bounds is
computed by solving increasingly larger-sized relative entropy optimization
problems, which are convex programs specified in terms of linear and relative
entropy functions. Our approach relies crucially on the observation that the
relative entropy function -- by virtue of its joint convexity with respect to
both arguments -- provides a convex parametrization of certain sets of globally
nonnegative signomials with efficiently computable nonnegativity certificates
via the arithmetic-geometric-mean inequality. By appealing to representation
theorems from real algebraic geometry, we show that our sequences of lower
bounds converge to the global optima for broad classes of SPs. Finally, we also
demonstrate the effectiveness of our methods via numerical experiments
Divergence-Free Adaptive Mesh Refinement for Magnetohydrodynamics
In this paper we present a full-fledged scheme for the second order accurate,
divergence-free evolution of vector fields on an adaptive mesh refinement (AMR)
hierarchy. We focus here on adaptive mesh MHD. The scheme is based on making a
significant advance in the divergence-free reconstruction of vector fields. In
that sense, it complements the earlier work of Balsara and Spicer (1999) where
we discussed the divergence-free time-update of vector fields which satisfy
Stoke's law type evolution equations. Our advance in divergence-free
reconstruction of vector fields is such that it reduces to the total variation
diminishing (TVD) property for one-dimensional evolution and yet goes beyond it
in multiple dimensions. Divergence-free restriction is also discussed. An
electric field correction strategy is presented for use on AMR meshes. The
electric field correction strategy helps preserve the divergence-free evolution
of the magnetic field even when the time steps are sub-cycled on refined
meshes. The above-mentioned innovations have been implemented in Balsara's
RIEMANN framework for parallel, self-adaptive computational astrophysics which
supports both non-relativistic and relativistic MHD. Several rigorous, three
dimensional AMR-MHD test problems with strong discontinuities have been run
with the RIEMANN framework showing that the strategy works very well.Comment: J.C.P., figures of reduced qualit
A robust fuzzy possibilistic AHP approach for partner selection in international strategic alliance
The international strategic alliance is an inevitable solution for making competitive advantage and reducing the risk in today’s business environment. Partner selection is an important part in success of partnerships, and meanwhile it is a complicated decision because of various dimensions of the problem and inherent conflicts of stockholders. The purpose of this paper is to provide a practical approach to the problem of partner selection in international strategic alliances, which fulfills the gap between theories of inter-organizational relationships and quantitative models. Thus, a novel Robust Fuzzy Possibilistic AHP approach is proposed for combining the benefits of two complementary theories of inter-organizational relationships named, (1) Resource-based view, and (2) Transaction-cost theory and considering Fit theory as the perquisite of alliance success. The Robust Fuzzy Possibilistic AHP approach is a noveldevelopment of Interval-AHP technique employing robust formulation; aimed at handling the ambiguity of the problem and let the use of intervals as pairwise judgments. The proposed approach was compared with existing approaches, and the results show that it provides the best quality solutions in terms of minimum error degree. Moreover, the framework implemented in a case study and its applicability were discussed
Grassmannians Gr(N-1,N+1), closed differential N-1 forms and N-dimensional integrable systems
Integrable flows on the Grassmannians Gr(N-1,N+1) are defined by the
requirement of closedness of the differential N-1 forms of rank
N-1 naturally associated with Gr(N-1,N+1). Gauge-invariant parts of these
flows, given by the systems of the N-1 quasi-linear differential equations,
describe coisotropic deformations of (N-1)-dimensional linear subspaces. For
the class of solutions which are Laurent polynomials in one variable these
systems coincide with N-dimensional integrable systems such as Liouville
equation (N=2), dispersionless Kadomtsev-Petviashvili equation (N=3),
dispersionless Toda equation (N=3), Plebanski second heavenly equation (N=4)
and others. Gauge invariant part of the forms provides us with
the compact form of the corresponding hierarchies. Dual quasi-linear systems
associated with the projectively dual Grassmannians Gr(2,N+1) are defined via
the requirement of the closedness of the dual forms . It
is shown that at N=3 the self-dual quasi-linear system, which is associated
with the harmonic (closed and co-closed) form , coincides with the
Maxwell equations for orthogonal electric and magnetic fields.Comment: 26 pages, references adde
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