714 research outputs found
Multi-contact Walking Pattern Generation based on Model Preview Control of 3D COM Accelerations
We present a multi-contact walking pattern generator based on preview-control
of the 3D acceleration of the center of mass (COM). A key point in the design
of our algorithm is the calculation of contact-stability constraints. Thanks to
a mathematical observation on the algebraic nature of the frictional wrench
cone, we show that the 3D volume of feasible COM accelerations is a always a
downward-pointing cone. We reduce its computation to a convex hull of (dual) 2D
points, for which optimal O(n log n) algorithms are readily available. This
reformulation brings a significant speedup compared to previous methods, which
allows us to compute time-varying contact-stability criteria fast enough for
the control loop. Next, we propose a conservative trajectory-wide
contact-stability criterion, which can be derived from COM-acceleration volumes
at marginal cost and directly applied in a model-predictive controller. We
finally implement this pipeline and exemplify it with the HRP-4 humanoid model
in multi-contact dynamically walking scenarios
A Riemannian low-rank method for optimization over semidefinite matrices with block-diagonal constraints
We propose a new algorithm to solve optimization problems of the form for a smooth function under the constraints that is positive
semidefinite and the diagonal blocks of are small identity matrices. Such
problems often arise as the result of relaxing a rank constraint (lifting). In
particular, many estimation tasks involving phases, rotations, orthonormal
bases or permutations fit in this framework, and so do certain relaxations of
combinatorial problems such as Max-Cut. The proposed algorithm exploits the
facts that (1) such formulations admit low-rank solutions, and (2) their
rank-restricted versions are smooth optimization problems on a Riemannian
manifold. Combining insights from both the Riemannian and the convex geometries
of the problem, we characterize when second-order critical points of the smooth
problem reveal KKT points of the semidefinite problem. We compare against state
of the art, mature software and find that, on certain interesting problem
instances, what we call the staircase method is orders of magnitude faster, is
more accurate and scales better. Code is available.Comment: 37 pages, 3 figure
Approaching Capacity at High-Rates with Iterative Hard-Decision Decoding
A variety of low-density parity-check (LDPC) ensembles have now been observed
to approach capacity with message-passing decoding. However, all of them use
soft (i.e., non-binary) messages and a posteriori probability (APP) decoding of
their component codes. In this paper, we show that one can approach capacity at
high rates using iterative hard-decision decoding (HDD) of generalized product
codes. Specifically, a class of spatially-coupled GLDPC codes with BCH
component codes is considered, and it is observed that, in the high-rate
regime, they can approach capacity under the proposed iterative HDD. These
codes can be seen as generalized product codes and are closely related to
braided block codes. An iterative HDD algorithm is proposed that enables one to
analyze the performance of these codes via density evolution (DE).Comment: 22 pages, this version accepted to the IEEE Transactions on
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